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STUDENT PERCEPTION AND CONCEPTUAL DEVELOPMENT
AS REPRESENTED BY STUDENT MENTAL MODELS OF
ATOMIC STRUCTURE
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Eun Jung Park, M.S.
The Ohio State University
2006
Dissertation Committee:
Approved by
Professor Arthur L. White, Adviser
Professor Donna F. Berlin
Professor Anita Roychoudhury
__________________________
Adviser
Graduate Program in Education
© Copyright
by
Eun Jung Park,
2006
ABSTRACT
The nature of matter based upon atomic theory is a principal concept in science;
hence, how to teach and how to learn about atoms is an important subject for science
education. To this end, this study explored student perceptions of atomic structure and
how students learn about this concept by analyzing student mental models of atomic
structure. Changes in student mental models serve as a valuable resource for
comprehending student conceptual development. Data was collected from students who
were taking the introductory chemistry course. Responses to course examinations, preand post-questionnaires, and pre- and post-interviews were used to analyze student
mental models of atomic structure.
First, this study reveals that conceptual development can be achieved, either by
elevating mental models toward higher levels of understanding or by developing a single
mental model. This study reinforces the importance of higher-order thinking skills to
enable students to relate concepts in order to construct a target model of atomic structure.
Second, Bohr’s orbital structure seems to have had a strong influence on student
perceptions of atomic structure. With regard to this finding, this study suggests that it is
instructionally important to teach the concept of “orbitals” related to “quantum theory.”
Third, there were relatively few students who had developed understanding at the level of
ii
the target model, which required student understanding of the basic ideas of quantum
theory. This study suggests that the understanding of atomic structure based on the idea
of quantum theory is both important and difficult. Fourth, this study included different
student assessments comprised of course examinations, questionnaires, and interviews.
Each assessment can be used to gather information to map out student mental models.
Fifth, in the comparison of the pre- and post-interview responses, this study showed that
high achieving students moved toward more improved models or to advanced levels of
understanding.
The analysis of mental models in this study has provided information describing
student understanding of the nature and structure of an atom. In addition to an assessment
of student cognition, information produced from this study can serve as an important
resource for curriculum development, teacher education, and instruction.
iii
DEDICATION
To the memory of my father, Jong Hwa Park who had showed his love to his little
daughter till his last day, 2006, 2, 11.
This thesis is dedicated to my parents and my husband who have given me endless love,
care, support, and encouragement.
iv
ACKNOWLEDGMENTS
First of all, I would like to express my sincere gratitude to my advisor, Dr. Arthur
White, for his support, patience, and encouragement throughout my graduate studies and
all steps for this dissertation writing. He has been an adviser who always finds time to
listen to my concerns with my course work, research, and writing. Dr. White has taught
me many lessons specific to my research and learning in general. Dr. White spent a great
amount of time in reviewing my dissertation and gave me valuable suggestions and
feedback for the progress document. His editorial advice was essential to the completion
of this dissertation. Without his advice and guidance, I would not have come this far.
I want to extend a special thanks to Dr. Berlin, who has made a major
contribution to the development and refining of my research and to this document. Dr.
Berlin has always provided prompt and thoughtful feedback which enabled me to focus
my thoughts and sequence the sections of the dissertation so as to result in a logical and
professional scholarly document. Dr. Berlin spent a great amount of time, far beyond
what can be expected of a faculty dissertation committee member, to help me to revise
and rethink the reporting of my research up to and including the last moments of the
writing process. I have benefited greatly from her pointed comments and her professional
dedication to me as a student.
v
My thanks also go to Dr. Anita Roychoudhury who served on my dissertation
committee and provided valuable comments that improved the content of this dissertation.
Dr. Roychoudhury’s classes were always a challenge and led me to extend my interests
in education and the research ideas for this study.
The teaching and advice from Drs. Douglas Owens and Christopher Andersen are
much appreciated and have led to many interesting and good-spirited discussions related
to my studies. Dr. Owens and Dr. Andersen always encouraged me with their faith in me
and respect for my work and studies. Specifically, advice from Dr. Owens inspired me to
be positive and to find confidence. Discussions with Dr. Andersen always led me to find
new areas and to grow in my thinking. Dr. Andersen always encouraged me and
responded with timely feedback. He treated all graduate students not only as students, but
also as colleagues.
I am also grateful to Dr. Patrick Woodward who helped me to make this research
possible. Dr. Woodward was an excellent teacher in chemistry and a scientist who
always showed an interest and enthusiasm for teaching. The advice from my discussions
with him became an important base from which I built the details about chemistry for
this study. My thanks also go to Dr. John Olesik who allowed me an opportunity to pilot
his class and helped me to develop my research interests. Special thanks go to Dr. Susan
Olesik for serving on my general exam committee.
I would like to thank my friends in the College of Education with whom I often
shared the difficulties and positive aspects of graduate student life. My friends in
vi
Columbus, and my old time friends from my home country, Korea, were always a big
support group for me.
I would also like to thank my husband, YooTai, for his understanding and love
during the past few years. The time we shared as students and family is a precious
chapter of our memories. Because I was with him, the good things I experienced were
doubled and the difficult periods were bearable. His support and encouragement has
made this dissertation possible.
My special thanks also go to my little brother, Jin Yeon, although he is a father of
two lovely daughters and is not little any more. I would like to thank Jin Yeon for his
being to our parents as a responsible son and for his big support and faith in his sister.
Lastly, my parents receive my deepest gratitude and love for their dedication and
years of support. They provide me unending support and encouragement. Without their
support, care, and love, I know I would not have come this far. My sincere and special
thanks go to their devotion and love.
Although I have finished this paper, I still feel that I have missed something and
there may be still a better way to explain my study. As Dr. White told me once, yes, this
dissertation is not the final piece of my studies, but is the first step in my studies. Today,
as I write these acknowledgements, I again want to thank all of you for supporting me
and my safe arrival to the first step.
vii
VITA
March 1, 1971
1994. . . . . . . . . .
Born – Pusan, Korea.
B.S. Chemistry Education, Pusan National University, Pusan, Korea.
1997 . . . . . . . . . . . .. . . . . . .
2002 . . . . . . . . . . . . .
M.S. Chemistry, Pusan National University, Pusan, Korea.
M.S. Chemistry, Texas Tech University, Lubbock, Texas, U.S.A.
PUBLICATIONS
Park, E. J., Lee, H. W., & Kim, Y-I. (1997). Tetrathiafulvalene (TTF) charge transfer
compounds of Fe2Cl2 and Fe2(SO4)3; (TTF)3FeCl3·0.5CH3OH and
(TTF)2.5Fe(SO4)2·CH3OH. Bulletin of Korean Chemical Society, 18(12), 1308-1311.
Kim, Y-I., Park, E. J., Lee, H-W., & Choi, S-N. (2000). Synthesis and properties of
Fe(TCNQ)SO4·2H2O and Fe(TCNQ)2·2.5H2O. Journal of Korean Chemical Society,
44(3), 281-285.
FIELDS OF STUDY
Major Field: Science Education
viii
TABLE OF CONTENTS
Abstract ............................................................................................................................... ii
Dedication .......................................................................................................................... iv
Acknowledgments............................................................................................................... v
Vita................................................................................................................................... viii
List of Tables ................................................................................................................... xiii
List of Figures ................................................................................................................. xvii
Chapters:
1
Introduction............................................................................................................. 1
1. 1. Objectives of the study.................................................................................... 1
1. 2. Research questions.......................................................................................... 4
1. 3. Theoretical framework.................................................................................... 5
1. 3. 1. Mental models .................................................................................... 5
1. 3. 2. Model-based learning (MBL) and model-based teaching (MBT).... 11
1. 3. 3. Atomic theory................................................................................... 13
1. 3. 4. Definition of terms ........................................................................... 17
2
Literature review................................................................................................... 21
2. 1. Defining mental models................................................................................ 21
2. 2. Model-based teaching and learning .............................................................. 24
2. 2. 1. Scientific representations ................................................................. 24
2. 2. 2. Alternative models ........................................................................... 29
2. 2. 3. Modeling in science and mathematics education ............................. 32
2. 2. 4. Teachers and modeling..................................................................... 37
2. 3. Atomic theory and the nature of matter ........................................................ 38
3
Methodology ......................................................................................................... 44
3. 1. Data collection .............................................................................................. 44
3. 1. 1. Course description............................................................................ 44
3. 1. 2. Participants ....................................................................................... 47
ix
3. 1. 3. Assessments and data collection ...................................................... 48
3. 2. Data analysis ................................................................................................. 54
3. 2. 1. Course examinations ........................................................................ 54
3. 2. 1. 1. Descriptive analysis of course examinations.......................... 56
3. 2. 1. 2. Q-type factor analysis of the 20 students by their responses to
items related to atomic structure on the multiple-choice course exams. 56
3. 2. 2. Questionnaires .................................................................................. 57
3. 2. 2. 1. Schemes for analyzing mental models of atomic structure.... 59
3. 2. 2. 2. Analysis of mental models of atomic structure from
questionnaire responses.......................................................................... 63
3. 2. 3. Interviews ......................................................................................... 64
3. 2. 3. 1. Schemes for analyzing mental models of atomic structure.... 64
3. 2. 3. 2. Data analysis: Alternative models as represented by
interviews ............................................................................................... 65
3. 2. 3. 3. Data analysis: Comparing pre- and post- interview
responses ................................................................................................ 65
3. 2. 4. Data analysis: Comparing mental models of atomic structure as
represented in different assessments ............................................................ 67
4
Research findings.................................................................................................. 70
4. 1. Course assessments....................................................................................... 70
4. 1. 1. Academic achievement..................................................................... 70
4. 1. 2. Conceptual understanding of atomic structure in course
examinations................................................................................................. 72
4. 1. 2. 1. Analysis of items related to atomic structure ......................... 72
4. 1. 2. 2. Q-type factor analysis of the 20 interviewed students based
upon their responses to items related to atomic structure ...................... 78
4. 2. Analysis of student responses to questionnaires .......................................... 81
4. 2. 1. Mental models of atomic structure as represented by questionnaire
responses ...................................................................................................... 81
4. 2. 2. Changes of mental models of atomic structure as represented in
questionnaire responses ................................................................................ 87
4. 3. Analysis of student responses in interviews ................................................. 94
4. 3. 1. Mental models of atomic structure................................................... 94
4. 3. 1. 1. Particle model (P) and levels of understanding (1/1 and 1/2) 95
4. 3. 1. 2. Bohr’s model (B) and levels of understanding (3/1, 3/2, and
3/3)........................................................................................................ 100
4. 3. 1. 3. Bohr’s model (B) and level of understanding (3/2) ............. 104
4. 3. 1. 4. Bohr’s model (B) and level of understanding (3/3) ............. 107
4. 3. 1. 5. Quantum model (Q) and levels of understanding
(4/1, 4/2, 4/3, 4/4, and 4/5) ................................................................... 108
x
4. 3. 1. 6. Quantum model (Q) and level of understanding (4/2) ......... 115
4. 3. 1. 7. Quantum model (Q) and level of understanding (4/3) ......... 118
4. 3. 1. 8. Quantum model (Q) and level of understanding (4/4) ......... 121
4. 3. 1. 9. Quantum model (Q) and level of understanding (4/5) ......... 125
4. 3. 1. 10. The summary of the analysis of student mental models of
atomic structure from interviews.......................................................... 132
4. 3. 2. Changes of mental models of atomic structure .............................. 138
4. 3. 3. Analysis of alternative models of atomic structure as represented
in interview responses ................................................................................ 151
4. 3. 3. 1. Particle model and the 1/2 level of understanding ............... 152
4. 3. 3. 2. Bohr’s model and the 3/1 level of understanding................. 153
4. 3. 3. 3. Bohr’s model and the 3/1 level of understanding with marked
quantum numbers ................................................................................. 155
4. 3. 3. 4. Bohr’s model and the 3/2 level of understanding with
different orbital shapes ......................................................................... 158
4. 3. 3. 5. Quantum model with Bohr’s orbital structure at the 4/1 level
of understanding ................................................................................... 159
4. 3. 3. 6. Quantum model with marked quantum numbers at the 4/1
level of understanding .......................................................................... 160
4. 4. Mental models of atomic structure as represented by different
assessments ......................................................................................................... 163
4. 4. 1. Comparative analysis of student responses to questionnaires and
interviews ................................................................................................... 163
4. 4. 2. Cluster analysis of student mental models by q methodology ....... 170
5
Conclusion and discussion.................................................................................. 176
5. 1. Objectives of this study............................................................................... 176
5. 2. Description of research method .................................................................. 178
5. 2. 1. Sampling......................................................................................... 178
5. 2. 2. Assessments.................................................................................... 179
5. 2. 2. 1. Course assessments .............................................................. 179
5. 2. 2. 2. Questionnaires ...................................................................... 180
5. 2. 2. 3. Interviews ............................................................................. 181
5. 3. Research findings by research question...................................................... 181
5. 3. 1. How do student mental models of atomic structure, as represented
by responses to an open-ended interview, compare to the scientific models
of atomic structure? .................................................................................... 182
5. 3. 2. How do student mental models of atomic structure, as represented
by responses to an open-ended interview, compare to the levels of
understanding of atomic structure? ............................................................ 183
xi
5. 3. 3. What alternative models of atomic structure are represented by
responses to the interviews? ....................................................................... 183
5. 3. 4. How do student mental models of atomic structure, as represented
in open-ended interview responses, change after experiencing the
introductory college chemistry course?...................................................... 185
5. 3. 5. How are the student perceptions of atomic structure as represented
by questionnaires and interviews related to each other? ............................ 187
5. 3. 6. What are the defining characteristics of students who are clustered
together as a result of the Q-factor analysis of their responses to the
atomic structure related content knowledge assessment items?................. 188
5. 4. Discussion and educational implications .................................................... 189
5. 4. 1. Understanding and learning atomic structure in college chemistry189
5. 4. 2. A proposed model for learning and teaching atomic structure by
mental model development ........................................................................ 194
5. 5. Limitations of this study ............................................................................. 197
5. 6 Further study ................................................................................................ 198
5. 6. 1 Short-term research proposal relating to this study......................... 198
5. 6. 2. Long-term research proposals related to this study........................ 201
References....................................................................................................................... 204
Appendices
A
B
C
D
E
Course syllabus .................................................................................................... 211
Recruitment letter................................................................................................. 217
Consent form ........................................................................................................ 219
Questionnaires...................................................................................................... 221
Interview protocol ............................................................................................... 225
xii
LIST OF TABLES
Table
Page
1.1
Typology of mental models .....................................................................................9
3.1
Chemistry course information.................................................................................46
3.2
Number of students who participated in assessments.............................................48
3.3
Interview sample participation by assessments ......................................................49
3.4
Schedule and textbook chapters covered by course examinations .........................50
3.5
Schedule for data collection....................................................................................52
3.6
Schedule of instruction and assessments ................................................................53
3.7
Analysis of student perception of atomic structure as represented in course
examinations...........................................................................................................55
3.8
Items related to atomic structure included in the questionnaire .............................58
3.9
Scheme for analyzing mental models of atomic structure by level of
understanding and scientific model ........................................................................62
3.10 Framework for the analysis of student mental models as represented by
questionnaire responses. .........................................................................................64
3.11 Framework for the analysis of student mental models as represented by
interview responses...............................................................................................67
3.12 Framework for comparing student mental models as represented by responses
to different assessments ..........................................................................................68
xiii
3.13 Framework for characterizing student clusters by atomic structure achievement
and by mental models of atomic structure as represented by interview
responses ................................................................................................................69
4.1
Mean academic achievement scores by exam and GPA for the CHEM 121
course by Group......................................................................................................71
4.2
Number and percentage distribution of students by group and course grade .........72
4.3
Content of first nine chapters of the CHEM 121 course textbook..........................73
4.4
Items selected from mid-term 1 as related to atomic structure...............................74
4.5
Items selected from mid-term 2 as related to atomic structure...............................75
4.6
Items selected from the final exam as related to atomic structure..........................76
4.7
Number and percentage of correct responses for the 34 items related to atomic
structure...................................................................................................................77
4.8
Mean percentage comparison of student achievement on items related to atomic
structure by group ...................................................................................................78
4.9
Student loadings on the three-component rotated solution resulting from the
person by item principal components analysis for Group 2 ...................................80
4.10 The analysis of student mental models of atomic structure as represented by the
pre- and post-questionnaire responses ....................................................................83
4.11 Number of student mental models of atomic structure in the pre- and postquestionnaire responses by scientific model...........................................................87
4.12 Number of student mental models of atomic structure from the pre- and postquestionnaire responses by level of understanding.................................................89
4.13 Student mental models of atomic structure in the pre- and post-questionnaire
responses by scientific model and level of understanding......................................92
4.14 Criteria for analyzing mental models of atomic structure by levels of
understanding, 1/1 and 1/2, for the Particle model .................................................95
xiv
4.15 Analysis of student mental models as represented by KC’s pre-interview
responses ...............................................................................................................100
4.16 Criteria for analyzing mental models of atomic structure by the levels of
understanding, 3/1, 3/2 and 3/3, for Bohr’s model ...............................................101
4.17 Analysis of student mental models as represented by KC’s post-interview
responses and RZ’s pre-interview responses ........................................................103
4.18 Analysis of student mental models as represented by MK’s and KT’s postinterview responses...............................................................................................107
4.19 Criteria for analyzing mental models of atomic structure by levels of
understanding, 4/1, 4/2, 4/3, 4/4, and 4/5 for the Quantum model .......................109
4.20 Analysis of student mental models as represented by CE’s, HJ’s, and VB’s
post-interview responses.......................................................................................115
4.21 Analysis of student mental models as represented by TK’s pre-interview
responses ...............................................................................................................118
4.22 Analysis of student mental models as represented by CZ’s post-interview
responses ...............................................................................................................121
4.23 Analysis of student mental models as represented by MK’s and RZ’s postinterview responses...............................................................................................125
4.24 Analysis of student mental models as represented by LJ’s post-interview
responawa ............................................................................................................131
4.25 The analysis of student mental models of atomic structure as represented in the
pre- and post-interview responses.........................................................................133
4.26 Number of student mental models of atomic structure for students with preand post-interview responses by scientific models...............................................138
4.27 Number of student mental models of atomic structure in the pre- and postinterview responses by level of understanding .....................................................141
4.28 Change of student mental models of atomic structure in the pre- and postinterview responses by scientific model and by level of understanding...............143
xv
4.29 Change of student mental models of atomic structure from the pre- and postinterview responses by level of understanding .....................................................145
4.30 The number and percentage of agreement between questionnaire and interview
classification of scientific model and level of understanding for mental models
of atomic structure ................................................................................................164
4.31 The analysis of 13 student mental models of atomic structure as represented in
the interview and questionnaire responses to the course exam items related to
atomic structure and to the course grade...............................................................166
4.32 Student loadings on the three-component rotated solution resulting from the
person by item principal components analysis for Group 2 .................................171
4.33 Component analysis by gender, atomic structure related percentage
achievement, course grade, mental models of atomic structure from interview
responses, and component loadings......................................................................173
5.1
Number of students who participated. ..................................................................179
xvi
LIST OF FIGURES
Figure
Page
1.1
Mental models: Internal mental models and external mental models.......................7
1.2
Visual, symbolic, gesture, concrete, and verbal types of expressed models ............8
1.3
Consensus model ....................................................................................................10
1.4
Theoretical framework for model-based learning (Clement, 2000) .......................12
1.5
Scientists’ atomic models (Brown et al., 2000) ......................................................18
1.6
Scientists’ Quantum model components: Electron density distribution and
orbitals.....................................................................................................................20
4.1
Scree plot of q-type principal components analysis of the 20 interviewed
students’ responses to 34 selected items related to atomic structure ......................79
4.2
Number of student mental models of atomic structure from the pre- and postquestionnaire responses by scientific model...........................................................88
4.3
Number of student mental models of atomic structure from the pre- and postquestionnaire by level of understanding .................................................................90
4.4
MD’s response to the pre-questionnaire .................................................................93
4.5
MD’s response to the post-questionnaire................................................................94
4.6
Example of student (KC) diagrammatic description of atomic structure during
pre-interview of the Particle model at the 1/2 level of understanding....................97
4.7
Examples of student (KC and RZ) diagrammatic descriptions of atomic
structure of Bohr’s model at the 3/1 level of understanding.............................102
xvii
4.8
Examples of student (MK and KT) diagrammatic descriptions of atomic
structure of Bohr’s model at the 3/2 level of understanding................................105
4.9
Example of student (CE) post-interview diagrammatic description of atomic
structure of the Quantum model at the 4/1 level of understanding.......................110
4.10 Example of students (VB and HJ) post-interview diagrammatic descriptions of
atomic structure of the Quantum (Bohr) model at the 4/1 level of
understanding........................................................................................................112
4.11 Example of student (TK) pre-interview diagrammatic descriptions of atomic
structure of the Quantum model at the 4/2 level of understanding.......................117
4.12 Example of student (CZ) post-interview diagrammatic descriptions of atomic
structure of the Quantum model at the 4/3 level of understanding.......................119
4.13 Example of students (TK and RZ) post-interview diagrammatic descriptions
of atomic structure of the Quantum model at the 4/4 level of understanding.......123
4.14 Example of student (LJ) post-interview diagrammatic descriptions of atomic
structure of the Quantum model at the 4/5 level of understanding.......................127
4.15 Example of student (LJ) post-interview diagrammatic descriptions of atomic
structure of the Quantum model at the 4/5 level of understanding.......................130
4.16 Number of student mental models of atomic structure from the pre- and postinterview responses by scientific model ...............................................................140
4.17 Number of student mental models of atomic structure in the pre- and postnterview responses by level of understanding ......................................................142
4.18 Comparison of MK’s mental models of atomic structure in the pre- and postinterview responses...............................................................................................147
4.19 Comparison of RZ’s mental models of atomic structure in the pre- and postinterview responses...............................................................................................149
4.20 Example of student (KC) alternative models of atomic structure during preinterview for the Particle model at the 1/2 level of understanding .......................153
4.21 Example of student (KC) alternative models of atomic structure during postinterview for Bohr’s model at the 3/1 level of understanding ..............................154
xviii
4.22 Example of students (BJ and KF) alternative models of atomic structure during
post-interview for Bohr’s model at the 3/1 level of understanding with
quantum numbers..................................................................................................155
4.23 Example of students (MK and KT) alternative models of atomic structure from
post-interview responses for Bohr’s model at the 3/2 level of understanding......159
4.24 Example of students (VB and HJ) alternative models of atomic structure from
the post-interview responses for the Quantum model with Bohr’s model at the
4/1 level of understanding...................................................................................160
4.25 Example of student (CE) alternative models of atomic structure from the postinterview responses for the Quantum model at the 4/1 level of understanding
with quantum numbers..........................................................................................162
4.26 Number of student mental models of atomic structure in the pre- and postquestionnaire and the pre- and post-interview responses by scientific model......168
4.27 Number of student mental models of atomic structure in the pre- and postquestionnaire and the pre- and post-interview responses by level of
understanding........................................................................................................169
5.1
Theoretical framework for model based learning (Clement, 2000)......................195
5.2
Theoretical framework for model-based learning of atomic structure .................196
xix
CHAPTER 1
INTRODUCTION
1. 1. Objectives of the study
From Democritus’ philosophy of materialism based on the atomic nature of the
physical world (460-370 B.C.) to the electron-cloud model based on quantum theory,
atomic structure has been an important concept in chemistry and in the history of science.
Quantum theory opened a new era in the progress of science and provided revolutionary
changes in atomic theory. In the scientific history of atomic models, quantum theory
influenced scientists to replace the classical particle model of atoms with Bohr’s model
and again later with the Quantum model. The Quantum model represents the probability
density of electrons, and it leaves the position of electrons in the atom at any point in
time uncertain. Atoms are no longer defined as the indivisible particle in science.
However, atomic structure does not have a finite representation and is still in the process
of discovery.
Because of the abstract nature of the microscopic world of atoms and of quantum
theory, scientists have provided various atomic models to represent atomic structure and
to explain scientific knowledge. Various atomic models based upon both theory and
1
evidence have been accepted by the science community throughout the history of science
and have been a part of the school curriculum. Atomic models have been used to help
students understand scientific theories by illustrating the theoretical structure of atoms
using a visual representation. However, difficulties and misconceptions in student
understanding of atomic structure and the related theories have been discussed in many
studies of science education (Gilbert & Watts, 1983; Griffiths & Preston, 1992). While
learning about or understanding the abstract concept of atomic structure, it has been
suggested that students are engaged in cognitive processes requiring internalization of the
concept through the development of mental models. Mental models are representations
reflecting student understanding and difficulties in learning concepts. Therefore, the
analysis of these mental models can provide information for better understanding of
student cognitive processes related to learning about atomic structure.
With a focus on student perceptions of atomic structure, this study analyzes
student mental models of atomic structure with three primary objectives. First, data from
this study provides information for assessing student conceptions of atomic structure and
related scientific models. This study compares student responses to different assessments
and to different representations for the purpose of understanding student mental models
of atomic structure. The comparisons relating multiple representations can further our
understanding of the relationship between cognitive processes and types of
representations.
2
Second, this study explores student alternative models of atomic structure which
are constructed for or from their own experience and understanding. As scientists
develop models to explain their theories and teachers are using teacher models reflecting
their perceptions of scientific models for better instruction, students often construct their
own models by way of remodeling, rephrasing, or analogizing. The analysis of
alternative models provides valuable information for the interpretation of student mental
models and for better teaching and learning in science education.
Third, this study analyzes the development of student models after they have been
exposed to the Quantum model and related atomic theories that are very important in
school science. The analysis of changes in student mental models can be a useful
resource for making inferences about student learning processes, misconceptions,
conceptual development, and the interaction of scientific models with student mental
models. Furthermore, the analysis can be an educational reference for future teaching and
curriculum development for learning about atomic structure, property, bonding, and
orbitals.
Data for this study were collected from students enrolled in a general chemistry
course at a mid-western university. This course was an introductory college chemistry
course that covered the first nine chapters of the introductory course curriculum. The
chapters included the definition of an atom, properties of atoms, electronic structure of
atoms, introduction to quantum theory, and bonding theories. Student responses to three
course examinations were collected.
3
Questionnaires were given to all students and open-ended interviews for 20
volunteers were conducted at the beginning and at the end of the course. Six hundred
thirty-three students who were enrolled in this course participated in data collection for
this study. Out of the 633 students, 439 students responded to both the pre-and postquestionnaires, which were included as a part of their recitation activities. Twenty
students volunteered for the pre- and post-interviews. The questionnaires and interviews
were designed to determine what the students knew about atomic structure prior to and
after instruction. Students responded by representing their understanding through verbal
and non-verbal responses. Pre- and post-responses to questionnaires and interviews,
verbal and non-verbal responses to questionnaires, and responses on the course
examinations were compared quantitatively and qualitatively.
The nature of matter based on the atomic theory is a principal concept in science;
hence, how to teach and how to learn about the structure of an atom is an important issue
in science education. To this end, this study provides information about student
perceptions of atomic structure and how they learn.
1. 2. Research questions
1) How do student mental models of atomic structure, as represented by responses
to a questionnaire and an open-ended interview, compare to the scientific models
of atomic structure?
4
2) How do student mental models of atomic structure, as represented by responses
to a questionnaire and an open-ended interview, compare to the levels of
understanding of atomic structure?
3) What alternative models of atomic structure are represented by responses to the
interviews?
4) How do student mental models of atomic structure, as represented in
questionnaire and open-ended interview responses, change after experiencing the
introductory college chemistry course?
5) How are the student perceptions of atomic structure as represented by
questionnaires and interviews related to each other?
6) What are the defining characteristics of students who are clustered together as a
result of the Q-factor analysis of their responses to the atomic structure related
content knowledge assessment items?
1. 3. Theoretical framework
1. 3. 1. Mental models
The term Mental Model originated in the early 1940s from Kenneth Craik’s
(1943) description of the mind’s activity as “the internal construction of small-scale
models of reality (p. 39).” According to Craik, mental models are constructed to predict
and make inferences about the external world. Based on empirical research about
cognitive thinking and deduction, Johnson-Laird (1983) provided several pieces of
5
evidence of mental models that were explained as structural analogues of the world in the
process of perception or conceptualization. Since then, mental models have been studied
in various areas of cognitive psychology, neuroscience, philosophy of science, humancomputer interaction (HCI) research, and science education. Almost at the same time as
Johnson-Laird’s work, Gentner and Stevens (1983) applied the concept of mental models
to the study of cognitive understanding of physical phenomena. In the book, Mental
Models, Gentner and Stevens explained a mental model as basic domain knowledge used
to make inferences within the domain.
To clarify the meaning of a mental model, O’Malley and Draper (1992) defined a
mental model as an internal representation that is separated from external knowledge
representation while Gilbert and Boulter (1998) included both internal and external
representation within the category of mental models. Although Gilbert and Boulter
agreed that the mental model is a representation of a target such as an object, event,
process, or system, their justification and use of the mental model is closer to the
meaning of O’Malley and Draper’s internal representation. In order to use the analysis of
mental models and model-based learning methods in science education, Boulter and
Buckley (2000) adopted the categorization of internal and external representation. Figure
1.1 illustrates the use and the relationship of the internal and external representations in
this study.
6
Figure 1.1: Mental models: Internal mental models and external mental models
Regarding the two representations, this study defines an internal mental model as
a cognitive representation of the world, which was previously addressed by Gilbert and
Boulter (1998). Because an internal mental model is a component of underlying personal
domains and it is a form of representation constructed in one’s mind, it is also considered
as an individual mental model. Development of a mental model can be explained as the
process of the 1st representation of the world projected inside the mind. An expressed
mental model is a further representation of the internal model, which requires the process
of the 2nd representation. An expressed model can be represented as a concept map,
equation, formula, number, picture, speech, symbol, word, and/or gesture through the
processes of abstraction, inference, description, or explanation. Boulter and Buckley
(2000) categorized five types of expressed models: a visual model, symbolic (textual and
mathematical) model, gestural model, concrete object model, and verbal model. Figure
7
1.2 shows the use and relationship of five expressed models and the internal mental
model in this study.
Figure 1.2: Visual, symbolic, gesture, concrete, and verbal types of expressed models
Concerning the personal nature of an internal mental model, educational research,
especially in science education, has widely used the external representations termed as
expressed models (Gilbert, Boulter, and Rutherford, 2000) and consensus models
(Norman, 1983) to make internal models tangible in ways such as visual, symbolic,
gesture, concrete, and verbal models. In addition to Boulter and Buckley’s (2000)
categorization via representations, several typologies have been applied to analyze
8
expressed models as an indirect way to characterize and describe mental models of the
mind. Table 1.1 introduces some criteria of types of mental models and their examples.
Criteria
Types of mental models
By steps of representation
(Boulter & Buckley, 2000)
1. Internal model,
2. Expressed (external) model
concrete, symbolic (textual & mathematical)
visual, gestural, verbal model
By creators
(Norman, 1983)
1. Scientist’s (scientific) model
2. Teacher’s model
3. Student’s model
By aspects
(Young, 1983)
1. Performance model
2. Learning model
3. Reasoning model
4. Design model
By social consensus
(Norman, 1983)
1. Individual model
2. Consensus (social) model
3. Historical model
Table 1.1: Typology of mental models.
Norman (1983) differentiated expressed models in terms of who represented the
models such as student, teacher, or scientist. Moreover, social acceptance was also
considered in Norman’s classification. Depending on whether an expressed model
represented the mind of an individual or commonly accepted consensus for the specific
domain use, an expressed model is categorized as an individual model or a consensus
9
model. Consensus models are constructed within social contexts and Figure 1.3 shows
examples for this category such as a scientific model, teacher model, or a historical
model.
Figure 1.3: Consensus model
Although an expressed mental model may not provide the holistic description of
the mind as Norman (1983) suggested, it represents certain degrees of understanding and
progress in the human mind. Therefore, the analysis of mental models is an important
tool to approach and to understand the human mind. Particularly, it can provide useful
information in the field of education for understanding of student perception and learning.
10
1. 3. 2. Model-based learning (MBL) and model-based teaching (MBT)
Model-based learning is a process of building mental models of phenomena as a
learning curriculum (Gobert & Buckley, 2000). In model-based learning, a target model,
knowledge required in a school curriculum, is achieved through the iterative and
continuous processes of model construction. The process of model construction includes
not only formation of mental models but also use, evaluation, revision, and elaboration of
mental models. Clement (2000) proposed a theoretical framework of model-based
learning. Figure 1.4 illustrates Clement’s framework describing the learning process
through model construction. Clement explains the learning process as the continual
construction and revision of a student’s mental model. Through the several steps in the
construction of intermediate models (called modeling), students can develop a pathway
toward the target model and the desired knowledge to be achieved by instruction. In
order to develop a target model, students are able to make steps of reflection or
evaluative analysis of mental models including modification, integration, combination, or
addition to their intermediate models.
11
Preconceptions
1. Alternative
conceptions and
models
2. Useful
conceptions and
models
Intermediate
Model (M1)
Intermediate
Model (M2)
Target
Model
(Mn)
Expert
Consensus
Model
Learning processes
Natural
reasoning skills
Figure 1.4: Theoretical framework for model-based learning (Clement, 2000)
Model-based teaching correlates to model-based learning. Gobert and Buckley
(2000) explain, “Model-based teaching is any implementation that brings together
information resources, learning activities, and instructional strategies intended to
facilitate mental model-building both in individuals and among groups of learners” (p.
892). As explained by Gobert and Buckley, modeling in Clement’s framework can also
be applied to instruction. In the use of models or modeling, expressed models such as
scientific, historical, or consensus models can be directly implemented into a school
curriculum for science. Because they are commonly accepted within a social context, the
models are meaningful resources and guidance for teaching or learning science. In
addition, teachers can develop their own model for classroom use. Such models are
designed to help learners understand concepts through the guidance of the teacher.
Considering student learning ability, previous knowledge, attitude, and the teacher’s
12
teaching experiences, the teacher can design appropriate models for teaching. Modelbased learning and teaching is a way to make learning meaningful, which is a valuable
commodity in the field of science and science education. Model-based learning and
teaching can be a valuable way to integrate resource models, learning activities,
instructional strategies, and evaluation (Gobert & Buckley).
For studies in science education, various measures analyzing mental models can
be used as assessment tools. Expressed models representing student perceptions can be
obtained as written essays, journals, verbal descriptions, drawings, tables, concept maps,
equations, responses to questionnaires, gestures, and/or concrete models. Particularly,
various instructional methods within formal or informal environments of science
education require empirical assessments that are able to evaluate the effectiveness of
these methods. To this end, studies based on mental models can provide qualitative data
compensating for some lack of quantitative data in science education. Information from
studies analyzing mental models can also be valuable references for designing
curriculum and instruction.
1. 3. 3. Atomic theory
Human beings have always wondered about the nature of the world. Various
views of understanding the world have become essential issues in philosophy. Around 6
B.C., people in Greece made changes in their world view from religion centered to a
focus on nature or being itself. The transition was led by two groups of philosophers,
13
monists and pluralists. In monism, the world originates from an ultimate essence such as
water as claimed by Thales (624-546 B.C.) of the Miletus school or number as claimed
by Pythagoras (569-475 B.C.). On the other hand, pluralism asserts that the world is
composed of various essences such as the four elements as identified by Empedocles
(495-435 B.C.; water, fire, air, and earth) or atoms as proposed by Democritus (460-320
B.C.). The nature of the world was also perceived by physical or mental reality, which
developed as materialism and idealism, respectively.
Atomic theory had been developed early in Greek philosophy based upon
materialism according to Leucippus (490-? B.C.) and Democritus (460-320 B.C.). In
contrast to the Eleatics purporting that being and nothing are the ultimate reality,
atomists presumed the ultimate being of the world as an unbreakable matter. Leucippus
and Democritus believed in the existence of fundamental and unbreakable fragments
which were named Atomos. Particularly, Democritus, who was a disciple of Leucippus,
divided the physical world into atoms as being and the void as nothing (Asimov, 1991;
Bang, n.d.; Oh, n.d.).
However, the philosophies of Socrates (469-399 B.C.), Plato (427-347 B.C.), and
Aristotle (384-322 B.C.) flourished in Greece after the era of Democritus. Their idealism,
seeking mental reality of being, had survived for a long time. In addition to idealism,
theology and seeking spiritual reality became the mainstream in understanding the world.
Because of human beings’ curiosity about the world in mental or spiritual reality,
atomism was accepted by some until the sixteenth century when people re-directed their
14
inquiry back to human beings and nature throughout the Renaissance. With the growing
development in geometry and astronomy, atomism was kept alive with Epicurus (341270 B.C.) and the Roman Epicurean Titus Carus (96-55 B.C.). Later, Democritus’s
description of the world, a matter composed of atoms and spaces, was revived in modern
science as a crucial theoretical foundation to comprehend the nature of the world. Around
the sixteenth century, Pierre Gassendi (1592-1655) addressed the atomic view about the
world in his writing. Robert Boyle (1627-1691) adopted Democritus’s atomism, atom
and void, not only as a conceptual assertion such as in ancient philosophy but as
theoretical support of scientific experimentation. He explained his empirical observation
of the inverse relationship between volume and pressure known as Boyle’s Law. Later,
atomism was used as a fundamental idea to interpret the law of definite proportions by
Joseph L. Proust (1754-1826) and the law of multiple proportions by John Dalton (17661822).
Dalton named the fundamental unit of matter as an atom and established atomic
theory based on scientific measurement. The theory explains: (a) all matter is composed
of atoms that are extremely small and indivisible particles, (b) atoms of an element are
identical in mass and properties, (c) compounds consist of two or more different atoms,
and (d) chemical reaction is the rearrangement of the composition of atoms and there is
no change in the number of atoms during the reaction (Asimov, 1991; Herbert, 1985).
Although atomic theory has been modified by progress in science, atomic theory
15
exploring the nature of the physical world or phenomena opened a new chapter in the
history of science.
The first challenge to Dalton’s particle atom was Thomson’s cathode ray
experiment in a partially evacuated tube. In the early 1900s, Thomson discovered that an
atom is composed of positively and negatively charged particles. His observation proved
the existence of sub-atomic particles and was represented as the plum pudding model.
Atoms were not Dalton’s indivisible particle any more and the atomic model was revised.
The positively charged parts of an atom are much larger than the negatively charged ones,
which are embedded in the uniform positive sphere like raisins in pudding. Later in 1911,
by analyzing scattered alpha (α) particles passing through a thin gold foil, Rutherford
found empty space between the two different charged particles. He designed a Nuclear
model with a centered nucleus and orbiting electrons in the almost empty space. A
positively charged nucleus representing most of the mass of an atom was located in the
center of the atom with negatively charged electrons revolving around the nucleus so as
to keep the distance between the two charges. However, Rutherford’s model also needed
revision because of its limited utility in explaining line spectra of chemical elements and
because the revolving electron would lose energy due to a changing magnetic field and
eventually it would collapse into the nucleus. Bohr revised the Nuclear model by
incorporating the concept of energy quantization in 1913. The Bohr model of quantized
energy levels, called shells or orbits, explains absorption and emission of energy.
Although Bohr’s atomic structure has also been modified to explain quantum reality, he
16
established a foundation for further progress in science (Brown, LeMay, & Bursten,
2000; Morris, 1987).
Quantum theory made revolutionary scientific progress and opened a new era in
science. Interest and changes concerning atoms brought the need of a new theory or
model to explain the nature of the quantum world. An atom in the Quantum model
includes quantized energy levels as mathematically represented orbitals from
Schrödinger’s equation of the wave function. In addition, the motion and location of
electrons are explained by the concept of probability based on Heisenberg’s uncertainty
principle. Atomic structure, which was an indivisible particle according to Dalton (17661842), was modified by the Quantum model and the discovery of the sub-atomic
structure is still in progress through further study in the field of science. The occurrence
of quantum theory and the changes in atomic structure have also supplied important
evidence requiring modification of philosophical rationales to understand science, to
infer scientific progress, and to understand the nature of the world (Kuhn, 1970; Lakatos,
1981; Lauden, 1977; Popper, 1987a, 1987b).
1. 3. 4. Definition of terms
Mental model
A mental model is an internalized representation of the physical world or
phenomena and includes procedural knowledge which enables one to make inferences
and predictions.
17
Atomic structure
An atom is the infinitesimally small building block of matter. Atomic structure is
the way that an atom is set up with its components and is an expressed representation of
an atom based on experimental observation and theoretical understanding. Figure 1.5
shows diagrammatic descriptions that have developed chronologically throughout the
history of science (Brown et al., 2000).
Scientists’
model
Particle
Model
Nuclear Model
Thomson’s
Model
Rutherford’s
Model
Bohr Model
Quantum
Model
Description
of Atoms
Figure 1.5: Scientists’ atomic models (Brown et al., 2000)
Particle model
According to Democritus’ assertion and Dalton’s definition, an atom is an
extremely small indivisible particle. The particle model represents particle shapes as
atomic structure.
18
Nuclear model
The Nuclear model includes both Thomson’s and Rutherford’s discovery of subatomic particles. This model represents the atomic structure as the combination of a
centered nucleus and electrons revolving around the nucleus. The nucleus is composed of
neutrons and positively charged protons.
Bohr model
The Bohr model describes an atom as composed of the centered nucleus and
orbiting electrons in quantized energy levels.
Quantum model
The Quantum model involves orbitals that represent a mathematical embodiment
resulting in a particular configuration of electron density distribution and energy. An
atom is composed of the centered nucleus and electrons in orbitals that are quantized
energy levels and occupy a mathematically calculated space around the nucleus. The
probability of finding electrons is often described as the electron cloud model of orbitals.
Figure 1.6 illustrates scientists’ Quantum model that has been calculated mathematically
and theorized scientifically (Brown et al., 2000).
19
Atomic structure of the Quantum model (Brown et al., 2000)
Figure 1.6: Scientists’ Quantum model components: Electron density distribution and
orbitals
By referencing the developmental history of atomic structure in Figure 1.5, this
study explored student mental models of atomic structure as represented by student
responses to course assessments, questionnaires, and interviews. Data was used to
explain student perceptions and learning of atomic structure.
20
CHAPTER 2
LITERATURE REVIEW
2. 1. Defining mental models
Proposed by Craik (1943), mental models as an internal construction have been
applied in many areas to describe cognition and cognitive processes. Through
experiments in psychology and brain research, Johnson-Laird (1983, 1993) has moved
the direction of theories of thinking on mental representations from a philosophical
discussion to the need for scientific study. Scientific studies have provided empirical data
supporting the existence of mental models and defined mental models as “the natural
way in which the human mind constructs reality, conceives alternatives to it, and
searches out the consequences of assumptions” (Johnson-Laird, 1995, p. 999).
In comparing human and machine thinking, Johnson-Laird (1993) defined the
cognitive process of the human mind as involving three sorts of thinking: deduction,
induction, and creation. Johnson-Laird introduced his explanation about the three sorts of
thinking in terms of mental models. First, in regard to mental models representing
entities, properties, and relations, the model theory offers a better understanding of
deductive reasoning. Particularly, propositional reasoning, relational reasoning, and
21
quantified reasoning in deductive thinking were appropriately explained by mental
models based on a semantic approach. His explanation for deduction by mental models
was supported by empirical data from neurological studies (Johnson-Laird, 1995). In
relation to the brain studies, he explained deductive reasoning of inference by comparing
a syntactic approach based on formal rules and a semantic approach of mental models.
Studies of individuals with damage of the right hemisphere of the brain showed evidence
of better application of mental models. Second, he defined induction as “any process of
thought yielding a conclusion that increases the semantic information in its initial
observations or premises” (Johnson-Laird, 1993, p. 60). Compilation, composition, or
combination of mental models explained the mechanism of inductive reasoning. Third,
regarding the manipulation of models, he explained that thinking in relation to scientific
discoveries has been achieved by constructing mental models of phenomena.
Development of new concepts by building models is inferred as the thinking process of
creativity.
Recognizing the difficulty and ambiguity of psycho (mental)-logic and evidence
from scientific reasoning, Halford (1993) extended Johnson-Laird’s definition of mental
models into representations including active processes for inference and mental
operations. In addition, he discussed interpreting analogy in terms of mental models by
quoting Johnson-Laird’s description of mental models as structural analogues. Knauff,
Rauh, and Schlieder (1995) analyzed spatial reasoning in deduction by mental models
constructed during the reasoning process. The semantic reasoning process by mental
22
models was previously explained as three phases by Johnson-Laird and Byrne (1991):
the comprehension phase of building internal models, description phase of constructing
models including putative conclusion, and validation phase of finding alternative models.
Johnson-Laird and Byrne showed the potential use of mental model theory to infer
spatial relations as relational reasoning. The analysis of mental models (Knauff et al.) in
spatial reasoning showed statistically significant differences in error rates. These
differences reflected preference in constructing mental models.
According to Paivio (1971), coding is a way to internalize captured information
from the external world. The theory explains that activities of coding are specialized by
two distinct systems of verbal and imagery representations. Paivio’s coding systems are
based on three types of processing connections: “representational, referential, and
associative.” Representational processing connects sensory detection of external stimulus
and internal activation of representational units. Cognitive activities within and between
systems are explained by associative and referential connection, respectively. In Paivio’s
dual coding theory, the mental model refers to all representational units and related
connections. Mental models were defined as an inclusive term that includes mental
language, mental images, and a combination of both (Paivio & Sadoski, 2001).
Differences in response time were analyzed to understand the effect of abstractness of
representations (imagery or verbal). Their study reports that information which is stored
either as verbal or imagery codes have advantages (e.g., rapid retrieval) when retrieval
stimuli matches the stored coding forms.
23
2. 2. Model-based teaching and learning
Because of the informative nature of models, the analysis of mental models can
be of value for assessment. Particularly, a learner’s models are very important resources
to determine a learner’s cognitive processes, development, and perceptions. In addition, a
model is a representation of the mind that describes, explains, infers, and predicts the
phenomena or the world, a model expressed by writings, drawings, speech, concrete
objects, and actions that can represent a great deal of qualitative information for
curriculum development, instructional method design, and science education research.
Model-based teaching and learning is based on the representative and informative nature
of models.
Clement (2000) proposed a theoretical framework of model-based learning. In his
theoretical framework of model-based learning, Clement explains the learning process as
the continuous construction and revision of a student’s mental model. Through the
several steps in the construction of intermediate models, students can develop a pathway
toward the target model or desired knowledge. As explained by Tiberghien (1994) and
Clement, modeling itself is a learning process. Students can learn through the
construction, evaluation, and revision (modification and elaboration) of models.
2. 2. 1. Scientific representations
Science explains the world and phenomena. Some of scientific knowledge
describes invisible phenomena such as energy, universe movement, microorganism
activities, and the subatomic world. Because of the abstract nature of science, it requires
24
analogous explanation and scientific models to visualize the phenomena. Most of all,
scientific models are very important for the purposes of science education. A multitude
of textbooks and media include scientific models which have been developed by
scientists, educators, and scientific communities. A phenomenon can be explained by
several scientific models such as in the study of Coll and Treagust (2003a). However, all
scientific models for a phenomenon are not necessarily related to each other. Some of
those models explain only a part of the phenomenon and they may not be transferable.
Because of this, appropriate selection and application of scientific models in science
textbooks is very important in science teaching, learning, and curriculum development.
Many scientific models are created by scientists and are often composed of specific
science terms. Therefore, in order to use the scientific models for classroom teaching, it
often requires translating or rephrasing the specific scientific terms into terms that relate
to experiences and understandings of students, teachers, and science educators. In this
translation of scientific models into classroom models, model-based research can provide
much information related to questions about scientific models such as effectiveness,
appropriateness, possibility of making alternative models, integrity, transferability, and
instructional use.
There are several studies (Good, 1993; Ralof, 2001) that reported the limitation of
textbooks as teaching and learning tools. In order to investigate the inadequacy of
scientific representations in high school biology textbooks, Pozzer and Roth (2003)
analyzed photographs and associated texts which were major aspects in high school
25
biology textbooks. Because the inclusion of photographs may increase the pedagogical
function of the photographical images, the relationships between photographs, texts, and
the subject matter were considered together in this textbook analysis. Many studies in
science have addressed the importance of the role of representation. When the
representations are categorized into a continuum from world phenomena with more detail
and less abstraction to equation with less detail and more abstraction, photographs are
considered as a representation that includes more information about the world than an
abstract generalization. This could be done with a focus on the word, photographs,
naturalistic drawings, maps or diagrams, graphs or tables, and equations (Pozzer & Roth).
High school science material seems to include more photographs and drawings when
compared to professional science literature.
For another example, scientific representations from four Brazilian high school
biology textbooks were selected, sorted into categories, and counted. The inscriptions
from ecology-related chapters were compared to the previous North American study
(Roth, Bowen, & McGinn, 1999). A total of 148 photographs were classified as (a)
decorative with no caption or reference in the text; (b) illustrative with a caption, but no
additional information; (c) explanatory with a caption and further explanation or
classification; and (d) complementary with a caption, explanation, classification, and new
information that was not available in the main text. Although Brazilian biology textbooks
include more inscriptions, but fewer photographs than North American resources, this
study showed a relatively high frequency of photographs and natural drawings in
26
Brazilian biology textbooks. However, both studies explain that inscriptions are
considered to be important in the curriculum context of biology textbooks. As to the
function of photographs, Brazilian biology textbooks were analyzed and determined to
contain 5.4% decorative, 35.1% illustrative, 28.4% explanatory, and 31.1%
complementary photographs. As the previous research (Roth et al., 1999) described,
photographs and captions are often inappropriately referred to in the main text.
Directly related to the topic of the current study, Shiland (1997) explored
chemistry textbooks by comparing atomic models. Shiland reports that most chemistry
textbooks explain atoms with two different models: the elementary Bohr’s model and the
sophisticated electron cloud (quantum mechanical) model. Based on the history of
science, the sophisticated quantum model is the currently accepted theory to explain
atoms. As scientists experienced the change from Bohr’s model to the quantum
mechanical model, chemistry textbooks reflected the changes and they have been
modified by following the scientific discoveries. Related previous research reveals that
there is more advanced, theoretical, mathematical, and abstract content in modern
chemistry textbooks; however, the current textbooks overemphasize content knowledge
over conceptual development. Shiland explained the transition process in chemistry
textbooks from Bohr’s model to the quantum mechanical model by applying conceptual
change theories. Based on the term “conceptual changes,” Shiland analyzed the quantum
mechanical models as presented in eight different high school textbooks. In order to
analyze the conceptual changes called for by the eight chemistry textbooks, this research
27
used four factors in the conceptual change model of Posner’s research: dissatisfaction,
intelligibility, plausibility, and fruitfulness. The study analyzed chemistry textbooks of
eight secondary schools and looked further into the elements required for the rational
replacement of an existing belief, the Bohr model of the atom, with a new theory, the
quantum mechanical model.
Six modern secondary chemistry textbooks from eight high schools were
compared to the two textbooks that were published prior to the era of curriculum reform
of the 1960s. The content of texts relating Bohr and the quantum mechanical models
were analyzed and categorized into the four factors of the conceptual change model. First,
all six textbooks briefly stated dissatisfaction with Bohr’s model; however, there were no
pictures of spectra or observable data explaining this dissatisfaction. Because of the weak
support for this claim, this study concluded that the textbooks didn’t create adequate
dissatisfaction with Bohr’s model. Second, intelligibility was analyzed by counting the
number of pages explaining the quantum mechanical model in the textbooks. Though
these textbooks included from 7 to 18 pages for describing the theory, this study
concluded that few examples and applications were included to build meaningful
intelligibility. Third, plausibility requires addressing the inadequacy of Bohr’s model and
the adequacy of the quantum mechanical model. This study concluded that there was no
evidence for this explanation from the textbooks. Fourth, fruitfulness was counted by the
lists of problems and questions to explain or predict observable phenomena by quantum
theory. The study revealed that the selected chemistry textbooks didn’t provide any
28
application supporting explanation or prediction which only required the quantum
mechanical model. In addition, this study analyzed the two old textbooks selected from
the previous curriculum and showed the same problems as the modern chemistry
textbooks in the context of the conceptual change model. There were changes in the
scientific theory and curriculum explaining atoms. Though the secondary chemistry
textbooks adopted the changes in content, appropriate conceptual changes weren’t
provided in the selected textbooks. Further studies on teaching and learning related to
textbooks are required to understand the conceptual changes that will be necessary to
move toward the quantum mechanical model.
Students construct their own models as a result of conceptualization of
information in textbooks or from instruction. Among various representative types of
models, imagery representations have a strong influence on student models. In order to
analyze student models of atomic structure in this study, the exploration of scientific
representations in textbooks is important to better understand student models or
alternative models, especially, as represented by diagrammatic representations. Because
of the abstract nature of the atom, scientific representations related to atomic structure are
a very important source in the process of mental model development.
2. 2. 2. Alternative models
Children’s alternative models in learning science are well introduced in the book
“Children’s Ideas in Science” by Driver, Guesne, and Tiberghien (1985). This book
discusses the analysis of learners’ models based on international literature searches and
29
the educational use of the results in science education. Driver et al. point out that
children’s models are strongly bonded in their mind. Often, when a child has an
alternative model, it recurs to his/her mind and it is difficult to modify through
instruction. The studies of Coll and Treagust (2003a, 2003b) also report the same
observation. Although graduate students received instruction of advanced knowledge
about chemical bonding, they preferred to use simple models for explanation and
reasoning related to chemical bonding. This persistence of alternative models raises
many questions that science education researchers should discuss and address. The
questions can be about types of alternative models; their formation and duration;
instructional methods of how to teach and how to help student understanding; curricular
preparation; environmental effects; and cognitive mechanisms. Further research in
science education is required to understand better the interconnections of these aspects
and learning.
Mental (or external) models are expressed representations of parts of the mind.
Hence, it can be a useful tool to indicate how a student develops not only desirable
understanding similar to the target models but also alternative models about science.
Learners’ alternative models are also interesting and valuable resources for study in
cognitive psychology and science education. The analysis of alternative models provides
information about the cognitive processes of student learning. To this end, Gobert (2000)
studied various alternative models in geo-science. He examined representations of the
structure of the Earth which were developed in learners’ minds of 47 fifth-grade students
30
who participated in the research. After having the students read text descriptions of plate
tectonics prepared by the research group, Gobert asked students to describe the Earth and
their understanding of tectonics. Questionnaires and interviews were used to elicit
student responses about special, causal, and dynamic processes inside of the Earth.
Drawings and interview transcripts were used for constructing and analyzing students’
mental models about the inner structure of the Earth and the dynamics of plate tectonics.
Two students of different achievement levels were selected for case study. The two
students for these case studies received individual tutoring which was designed to correct
alternative concepts (or models) and to guide students toward target models. Students
could revise their alternative models gradually through the tutoring. This research
showed the development of mental models and conceptual development through several
revising processes in learning plate tectonics. Based on the analysis of class observations,
interview transcripts, and drawings, Gobert identified the nature of the students’ models
and discussed the effectiveness of model-based learning as a method for assessment and
meaningful learning as well as implementing model-based teaching and learning for
construction and revision of student models.
These findings support the need to explore student alternative models of atomic
structure. In addition, the analysis of student mental models may be an important way to
evaluate student alternative models for atomic structure.
31
2. 2. 3. Modeling in science and mathematics education
Research on student mental models in learning chemistry by Chiu, Chou, and Liu
(2002) examined student mental models and conceptual development in understanding
chemical equilibrium. This research compared different instructional methods in 2 tenthgrade classrooms. The 20 students in the treatment group were instructed by cognitive
apprenticeship (CA) which provided educational support such as coaching, modeling,
scaffolding, articulation, reflection, and exploration. In contrast, 10 students in a control
group were instructed by an instructor without CA support. The analysis of students’
models indicated that the treatment group, supported by the CA program, showed better
performance in achievement. Students in the control group without CA support showed
difficulties in constructing correct mental models. This research showed the effectiveness
of the support program and the dynamic nature of students’ mental models.
Similar to the approaches in science education research, Mohan (1998) applied
model-based learning to mathematics education. The research was designed to
investigate the relationship between ability to understand fundamental concepts and
solving problems in geometry. Students’ mental models represented geometric schema
and described their process knowledge for solving problems. Thirty high school students
were selected from 10 mathematics classes of a suburban high school. Individual
interviews were conducted during problem solving in geometry. Interview responses
were analyzed and sorted into 17 categories (models) of geometry content. Two groups,
divided by levels of student achievement were compared across the 17 categories. As a
32
result of this study, Mohan asserts that as a result of model-based learning, students of
high-achieving ability developed clearer mental models that enabled them to analyze a
problem methodically and that facilitated novel approaches to solving problems.
Ray and Martin (1999) introduced a teaching strategy implementing modeling in
learning about computers. This study explained three important implications of
modeling as a teaching method. Because students construct mental models while they are
learning, building mental models facilitates students’ performance in problem-solving
activities. Modeling also helps students to build structural knowledge which is
systematically organized knowledge. This teaching strategy can help students to bring
about meaningful learning. Two different sets of computer instructions were given to a
control and a treatment group. For the treatment group, the instruction led students to
construct the structural knowledge through the process of modeling. This study showed
better performance of students in the modeling group.
Buckley’s (2000) research is a good example of the appropriate use of modeling
(student model development) in learning science and the proper use of scientific models
in teaching science. To this end, a multimedia project, “Science for Living Project”
(SFL), was created for tenth-grade biology classes. SFL is an interactive multimedia
program developed at Stanford University including video images, additional
information, and manipulation tools for computer presentation of the circulatory system.
Buckley used the interactive multimedia resource, Science for Living (SFL): The
Circulatory System as an instructive model in a science class in a Midwestern high
33
school. Twenty-eight grade 10 students participated in this research. Twenty-seven of the
students were involved in group activities to create a project to demonstrate
understanding of the circulatory system. In addition, this study reported a case study of
one student, Joanne, by analyzing her mental models. Joanne conducted the project
activity individually and she made a final project and presentation based on her
understanding and searches of SFL resources. The individual data were collected in
forms of written tests (pre- and post-tests), exams, notes, video observation, a final
project, class presentation, and interviews. Data was used for analyzing Joanne’s mental
models and conceptual or model changes during the period of learning about the
circulatory system. The case study showed the dynamics of continuous change and
revision of mental models. During the program, Joanne developed various
representations of the circulatory system. She raised many questions about the circulatory
system and tried to get answers by accessing the SFL media and textbooks interactively.
Through the active interaction of her mental models and the scientific models from the
media, Joanne could develop and elaborate the structure and dynamics of her circulatory
models. Since Joanne could develop integrated and useful knowledge at the end of the
class, it was inferred that this interactive environment for modeling was important for
promoting meaningful learning of science. Therefore, modeling can be used
appropriately as a part of inquiry or classroom activities in science class.
A mental model as structural knowledge includes not only concepts but also
relations between the concepts and causal mechanism between the concepts and relations
34
(Koffijberg, 1996; Schwartz & Black, 1996; Tsuei, Hachey, & Black, 2003). The causal
mechanism explains the representative and predictive function of mental models. In this
respect, design activities can facilitate the development of the causal mechanism of
mental models. Hachey, Tsuei, and Black (2001) reported a case study of developing
mental models through design activity to advance first students’ reasoning and then,
problem-solving abilities. They administered two individual paper-and-pencil tasks to 23
seventh-grade students who participated in a general science class. For the first task,
students were asked to design a colony for a hundred people on Mars with scientific
background information provided by class discussions. On the second day, students were
asked to explore and troubleshoot a hypothetical scenario. Student responses were coded
by three categories of thinking: entity, relationship, and mechanism. The design and
troubleshooting activity was analyzed by the three types of thinking and gender. Data
explained that only a few students showed the development of relationship and
mechanism in their design and troubleshooting thinking. In the design activity, male
students performed better and they showed a significant difference in reasoning
relationships between concepts compared to females. However, there was no statistical
gender effect in thinking for troubleshooting. Tsuei et al. concluded that students in the
seventh grade are not developmentally ready for dynamic relational thinking.
Model-based teaching under a teacher’s guidance may decrease the construction
of alternative models and the number of intermediate models. As can be seen from
Gobert’s (2000) research, though students were given the same texts by teachers, they
35
showed varied models and modeling processes including many alternative ideas. As
Norman (1983) explained, mental models are not stable and complete. If a student’s
knowledge and learning was not developed in a meaningful way, it is very vulnerable
and flexible. To this end, model-based teaching was developed to create clear
understanding and meaningful representations in the learner’s mind. Buckley’s (2000)
case example showed that a student revised and modified her models through searching
scientific models. The student may acquire a target model through the guidance of
model-based teaching provided by the teacher of the class. Model-based teaching is a
way to develop meaningful learning, which is a valuable goal of science education.
With regard to growing interests in visualization or mental imagery, analysis of
mental models, particularly, diagrammatic representation has gathered attention in many
areas such as cognitive science, science education, and computer science. Yulin and
Herbert (1995) introduced an experiment to assess the use of mental modeling as process
representation in problem solving. After taking a pretest designed to reveal student
understanding of special relativity, students were asked to read a part of Einstein’s paper
on special relativity and then, they again explained their understanding by verbal and
non-verbal description. On a posttest measure, some students were allowed to use
diagrams for problem solving and others were not. This study compared the number of
various representations and switches between reasoning methods. In addition, time and
reasoning methods required to solve problems were measured. Data showed a positive
influence of using diagrams and reading texts on student mental models. Relationships
36
between constructing mental images and performance in problem solving were also
discussed.
2. 2. 4. Teachers and modeling
Although there have been many studies about content-specific models (Coll &
Treagust, 2003b; Gobert, 2000; Taber, 2003) or students’ knowledge about
models/modeling (Grosslight, Unger, Jay, & Smith, 1991), there are few studies
exploring teachers’ knowledge of models. In a Dutch curriculum innovation project that
implemented an integrated approach to teach science along with teaching the traditional
separate disciplines, the nature and role of models or modeling became more important in
science education. Van Driel and Verloop (1999) emphasized the influence of teachers’
knowledge on the project and explored experienced teachers’ knowledge of models and
modeling. This study categorized scientific models by appearance (physical or
mathematical models) or functions (descriptive, explanatory, or predictive models). Van
Driel and Verloop defined scientific models by seven common characteristics.
1. A model is related to a target model, which is represented by the model.
2. A model is a research tool which is used to obtain information about a target
which cannot be observed or measured directly.
3. A model cannot interact directly with the target it represents.
4. A model bears certain analogies to the target.
5. A model always differs in certain respects from the target.
37
6. In designing a model, a compromise must be found between the analogies and
the differences with the target, allowing the researcher to make specific
choices.
7. A model is developed through an iterative process. (p. 1142)
In order to assess teachers’ knowledge of models and modeling, Van Driel and
Verloop (1999) administered two questionnaires including open-ended questions and
Likert-type scale questions, respectively. Fifteen teachers responded to the first
questionnaire of open-ended items and their responses were categorized. Seventy-one
inservice teachers participated in taking the second questionnaire including 32 Likerttype question items. Though there are similar descriptions of a model or modeling in
science as “a simplified representation of reality,” this study showed limits and
inconsistencies in teachers’ knowledge of models. Van Driel and Verloop suggest the
need for specific activities in designing professional development programs, including
(a) emphasize the predictive function of models, (b) focus on the role of creativity and
the aspects of the social context of models, and (c) anticipate teachers’ epistemological
orientation.
2. 3. Atomic theory and the nature of matter
Because of the microscopic nature of concepts in chemistry such as atoms,
bonding, and reactions, chemistry has used various scientific models to help develop
student understand of abstract concepts. Because of the prevalence of abstract concepts,
38
chemistry is widely perceived as a difficult subject (Markow & Lonning, 1998). Some
studies (Nakhleh, Lowery, & Mitchell, 1996; Pestel, 1993) reported that students have
difficulty in understanding chemistry coherently and holistically. Lijnse, Licht, de Vos,
and Waarlo (1990) pointed out that the theoretical and mathematical reality of matter is
related to difficulties in understanding atoms and subatomic particles. Difficulties or
misconceptions in students’ learning about matter have been discussed in many studies
(De Posada, 1997; Gilbert & Watts, 1983; Griffiths & Preston, 1992; Novick &
Nussbaum, 1978). In terms of the application of microscopic understanding to
macroscopic phenomena, Jensen (1995) and Johnstone (2000) compared differences
between experts and students. Although the concept of orbitals for atomic structure have
been taught in the high school and university levels, Taber (1998) discussed student
limitations in the application of learning to describe atomic structure.
As a way to explore the abstract nature and difficulty in chemistry, Coll and
Taylor (2002) and Coll and Treagust (2003a) applied mental model theory to analyze
student perception of chemical bonding. Information about student perceptions gained by
analyzing their mental models can be an important resource for developing curriculum
and instructional methods. Coll and Treagust (2001, 2003a, 2003b) conducted research
on students of different grade levels: high school, undergraduates, and graduates. They
obtained data about how students of different grade levels understand the nature of
chemical bonding. Data were collected from interviews, tests, exams, and class
discussion. The data were compared to target models from curriculum materials and
39
analyzed to determine student mental models reflecting their perceptions of chemical
bonding including ionic bonding, covalent bonding, and metallic bonding. This study
showed what models the students mainly employed to understand atomic structure and
chemical bonding. All students, regardless of their academic grade levels, showed a
similar preference for simple models to explain chemical bonding. Although there were
clear differences in the levels of understanding by groups, students at higher grade levels
responded with and more clearly remembered simple bonding models rather than
advanced models. Concerning this observation, Coll and Treagust (2003a, 2003b) raised
an issue for further discussion about designing differentiated instructional methods and
curriculum materials based upon student abilities or the complexity of concepts. In
addition, Coll and Treagust (2001, 2003a, 2003b) mentioned the need for further studies
on the development of effective and appropriate scientific models for advanced-level
concepts.
In the same year as the work by Coll and Treagust (2003a, 2003b), Taber (2003)
reported another model-based study related to metal bonding or metallic structure.
College students participated in the research. Taber discussed the importance of previous
knowledge on learning. In the analysis of students expressed models, Taber focused on
the relationship of student learning to previous knowledge and alternative concepts.
Fifteen college students in an advanced chemistry class responded to interviews,
repertory tests, conceptual tests, concept maps, and diagrams. A grounded theory
approach was used for this research. This research provides evidence for the relationship
40
between previous knowledge and the development of new ideas by analyzing students’
models. Taber reports that previous knowledge works either as a bridge to developing
new ideas or as a barrier resulting in alternative understandings. This result provides a
direction for further research and addresses the importance of previous knowledge for
meaningful learning.
Eilam (2004) explored the process of problem solving in relation to student
mental models. In the context of problem solving, students first retrieve elements of
models in long-term memory, combine new element for models and then, construct the
problem space depending on individual ability. Eilam analyzed student writing that
explained their observations and interpretation of a given problem about cohesive force.
Data was analyzed by content and mental models. Content analysis was based on the
stepwise procedure of revealing concepts, identifying relations between concepts, and
then, constructing mental models. Student mental models were further classified by level
of specification, correlations with scientific claims, macro/micro level of explanation,
and cited evidences. In addition, the knowledge representations of matter were identified
as four types: (a) Type A - macro view of matter, (b) Type B - static particulate view of
matter, (c) Type C - possibly dynamic particulate view of matter, and (d) Type D explicitly supported dynamic particulate view of matter. Eleven students out of a total of
25 participants showed Type A level of understanding of matter in the context of the
problem-solving experiment. As it has been observed in many studies (Harrison &
Treagust, 1998; Novick & Nussbaum, 1978), this study reaffirmed the difficulty in
41
shifting from Type A to Type D level of understanding which is considered as a shift
towards a higher level of understanding.
Several studies (Coll & Treagust, 2003a, 2003b; Griffiths & Preston, 1992; Krnel,
Glazer, & Watson, 2003; Taber, 2003) used a longitudinal analysis of student
understanding of matter by comparing students at different grade levels. Through the
review of previous studies about matter concepts, Anderson (1990) found four aspects of
concepts of matter: chemical reactions, change of state, conservation, and
atoms/molecules/systems of particles. By analyzing responses to the questions about
concepts of matter from elementary to high school students, Liu and Lesniak (2005) tried
to relate conceptual progression and developmental levels. These authors analyzed the
Third International Mathematics and Science Study (TIMSS) datasets including multiplechoice, short-answer, and extended-answer questions. The study first identified four
aspects of matter concepts assessed by items related to: conservation, physical properties
and change, chemical properties and change, and structure and composition. Second, the
Rasch modeling method was applied to assess difficulties reflected by the responses
related to the four aspects of matter and to compare student competence by grade levels.
Though the difficulty levels among items were not statistically different for the four
aspects, the data represented an increasing order of difficulties by the concepts.
Particularly, student responses indicated maximum difficulty with questions dealing with
structure and composition of matter. On the other hand, there were significant differences
among student groups by grade levels. By using Fisher’s dynamic skill theory, these
42
studies related conceptual progression of matter concepts and student age by grade levels.
Five developmental levels were suggested to explain students’ concepts of matter from
elementary to university and this study suggested modeling as the mechanism for the
stage transition.
43
CHAPTER 3
METHODOLOGY
3. 1. Data collection
3. 1. 1. Course description
Data for this study was collected from an introductory chemistry course (CHEM
121) at a Midwestern university during Autumn quarter, 2004. This 10-week course
consisted of lectures, recitations, and laboratory activities. Students were taught basic
level chemistry twice a week by an instructor who has taught this course for more than 3
years and has over 10 years of research experience. Recitation sessions and laboratory
experiences were supervised by 27 different graduate teaching assistants. Recitations
consisted of problem-solving activities in which students solved problems selected from
each chapter of the course textbook. (See Appendix A for the Course Syllabus.)
General Chemistry 121 (CHEM 121) is a course in fundamental chemical
principles covering the first 9 chapters of the introductory college level chemistry
textbook. The main textbook used for the course was Chemistry: The Central Science by
Brown et al. (2000). Among the nine chapters of the book used for this course, seven
chapters were related to the main topic of this study, “atomic structure.” Chapters 1 and 2
44
of the textbook introduce the nature of matter and atoms. Chapters 5 and 6 of the
textbook explain electronic structure of atoms based upon the concept and developmental
history of quantum theory. Chapter 7 first describes atomic structure and then discusses
properties of atoms in the periodic table. Chapters 8 and 9 cover molecular geometry and
bonding theories. Table 3.1 displays the course information including lecture description,
recitation schedule, and lab schedule.
45
Course information
Tuesday and Thursday
(8:30-9:48 AM)
Lecture time
Š
Š
Š
Š
Lecture
content by
chapters
Š
Š
Š
Š
Š
Š
Š
Tuesday and Thursday
(1:00-2:18 PM)
1 week of 9/22 : The science of matter, units of measurement,
significant figures, atomic structure (Chapter 1)
2 week of 9/27 : Molecules and ions, chemical equations and reactions
(Chapter 2)
3 week of 10/04 : Molecular and formula weights, the mole, reaction
stoichiometry (Chapter 3)
4 week of 10/11 : Solution concentrations, electrolytes and nonelectrolytes, ionic equations, metathesis reactions, oxidation numbers
(Chapter 3 & 4)
5 week of 10/18 : Redox equation balancing, energy, enthalpy
(Chapter 4)
6 week of 10/25 : Thermochemical equations, calorimetry, Hess’s law,
quantum mechanics, the Bohr atom (Chapter 5)
7 week of 11/01 : Orbitals, many-electron atoms, electron
configurations (Chapter 6)
8 week of 11/08 : Periodic trends, the periodic table, group 1A and 2A,
selected metals and non-metals, Lewis symbols (Chapter 7)
9 week of 11/15 : Ionic and covalent bonding, Lewis structures, bond
energy (Chapter 8)
10 week of 11/22 : The VSEPR model and molecular geometry,
polarity, hybrid orbitals (Chapter 8 & 9)
11 week of 11/29 : Multiple bonds, molecular orbital theory (Chapter 9)
Recitation
schedule
Tuesday and Thursday
(8:30-9:48 AM)
Wednesday and Friday
(8:30-11:18 AM)
Laboratory
schedule
Tuesday and Thursday
(1:00-2:18 PM)
Monday, Wednesday and Friday
(11:20 AM -2:18 PM)
Table 3.1: Chemistry course information.
46
3. 1. 2. Participants
There were 668 students enrolled in this course (Total Group). Thirty-five
students dropped the class by the end of the quarter. The recruitment of students for
interviews was made by announcement in each of the CHEM 121 classes and by e-mail
sent to a random selection of 20% of the students enrolled in the course. (See Appendix
B for the Recruitment Letter and Appendix C for the Consent Form.)
Questionnaires for the pre-test were administered on the first day of recitation and
the post-questionnaires were provided at the last laboratory session. Five hundred ninetyfive students responded to the pre-questionnaire and 486 students responded to the postquestionnaire. Four hundred thirty-nine students responded to both the pre- and postquestionnaires. Twenty students from the classes (3.2% of the total class) volunteered for
the pre-interview while only 15 students from the pre-interview completed the postinterview (2.4% of the total class). Pre-interviews with 20 volunteers (Group 2) were
conducted during week 2 and 3 before the first mid-term examination and 15 of the
students were interviewed again at the end of the course.
CHEM 121 was comprised of 350 male students (55.3%) and 283 female students
(44.7%). The students were pursuing 26 different majors for which the chemistry course
would meet their specific needs. For 92.2% of the 633 students, the student’s reason for
taking this course, CHEM 121, was that it was a requirement. There were 69.1% first
year and 23.0% second year college students enrolled in this course. The students
represented differences in learning experiences related to chemistry and ranged from
47
freshman through senior year in college. Ninety-seven point two percent of the students
had completed at least one high school chemistry course and 10.7% of the students
reported having previously taken a college chemistry course. Table 3.2 shows the number
of students who participated in each assessment.
Class Assessment
Assessment
Questionnaire
Interview
Midterm 1
Midterm 2
Final
exam
Pre
Post
Pre
Post
633
633
617
595
486
20
15
Number of
Participants
Table 3.2: Number of students who participated in assessments.
3. 1. 3. Assessments and data collection
In order to assess student mental models of atomic structure, this study used the
responses of 20 students from three multiple choice examinations (two mid- term exams
and a final exam), paper-and-pencil questionnaires (pre and post), and open-ended
interviews (pre and post). Table 3.3 shows the participation in each assessment (course
examinations, questionnaires, and interviews) by the 20 students who volunteered for the
interview sessions.
48
Subject
Midterm 1
Midterm 2
Final
PreQuestionnaire
PostQuestionnaire
PreInterview
PostInterview
KF
9
9
9
9
9
9
9
EJ
9
9
9
9
9
9
MK
9
9
9
9
9
9
9
CE
9
9
9
9
9
9
9
WT
9
9
9
9
9
9
9
SJ
9
9
9
9
9
9
KT
9
9
9
9
9
9
9
LJ
9
9
9
9
9
9
RZ
9
9
9
9
9
9
9
MD
9
9
9
9
9
9
CZ
9
9
9
9
BM
9
9
9
9
LT
9
9
9
TK
9
9
HJ
9
TH
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
BJ
9
9
9
9
9
9
HD
9
9
9
9
9
9
VB
9
9
9
9
9
9
9
KC
9
9
9
9
9
9
9
Total
20
20
20
20
18
20
15
Table 3.3: Interview sample participation by assessments.
49
9
Student performance in the course was evaluated on the basis of total points
earned from three exams (two mid-term exams and one final exam). The course, CHEM
121, evaluation covered material contained in nine chapters of the textbook. The first
mid-term examination was scheduled at the fifth week and it included content knowledge
items related to chapters 1 through 5, before introducing atomic structure related to
Bohr’s model. The second mid-term examination was scheduled during the eighth week
of the quarter covering chapters 6 including electronic atomic structure, to the beginning
section of chapter 8. Each mid-term examination included 25 multiple-choice items. A
final examination was taken on the last day of the quarter and the cumulative final
examination included 40 items covering content from all nine chapters. Table 3.4 shows
the information about course examinations.
Course Examination
Schedule
Chapter
Mid-term
exam 1
10/26, Tuesday
6:30-7:48 PM
Chap 1-5
Mid-term
exam 2
11/16, Tuesday
6:30-7:48 PM
Chap 6-8
Final exam
12/07, Tuesday
1:30-3:18 PM
Chap 1-9
Table 3.4: Schedule and textbook chapters covered by course examinations.
50
The questionnaires were designed to gather information related to student
background and understanding of atomic structure. Information related to student
background included the section number assigned by teaching assistants, class time for
lecture, major, previous learning experience in chemistry, and motivation (reason for
taking the class). Students were then given three questions which asked them to represent
their understanding of atomic structure in written and diagrammatic/graphical forms. In
these questions, students were asked to define the atom, describe atomic structure, and
explain what is meant by orbitals in relation to atomic structure. For the qualitative
analysis related to the questionnaire, the responses from 20 students who volunteered for
the interviews were further studied.
The interviews were recorded by a voice recorder and video camera to capture
verbal descriptions and gestures made while explaining atomic structure. Questions for
the open-ended format interviews were prepared so as to map out student perceptions of
atomic structure. The researcher had discussions with experts in the field of science and
science education about the content and order of the questions: the definition of an atom,
description of atomic structure, description of orbitals, and explanation of the concept of
“quantum.” Interviews were processed for those students who gave their consent to
participate in this study. Data were coded and a random set of pseudonyms for student
names were selected for reference to these individuals.
The data collection schedule for questionnaires and interviews is summarized in
Table 3.5. Questionnaire responses were collected as a part of the recitation or laboratory
51
sessions and the interview responses were collected at individually scheduled times.
Thirty minutes were assigned for the questionnaires and the time for the open-ended
interviews varied from 20 minutes to 2 hours. Table 3.6 illustrates the schedule for the
assessments used in this study by week and by instruction.
Instrument Type
Interview
Questionnaire
Data collection schedule
Pre-interview
9/28 - to 10/09
Post-interview
11/29 - to 12/08
Prequestionnaire
at the first day of recitation
9/22 (Wednesday), 9/24 (Friday), and 9/27 (Monday)
Postquestionnaire
at the end of the quarter
11/29 (Monday), 12/01 (Wednesday), and 12/03
(Friday)
Table 3.5: Schedule for data collection.
52
Assessment
Instruction
Week1
Week2
Week3
Week4
Week5
Week6
Week7
Week8
Week9
Week10
Week11
Chap1
Chap2
Chap3
Chap
3/4
Chap4
Chap5
Chap6
Chap7
Chap8
Chap
8/9
Chap9
9
Mid-term1
9
Mid-term 2
9
Final exam
PreQuestionnaire
PostQuestionnaire
53
Pre-Interview
Week12
9
9
9
9
Post-Interview
Note: Chap= chapter of the textbook of CHEM 121 course.
Table 3.6: Schedule of instruction and assessments.
9
9
3. 2. Data analysis
3. 2. 1. Course examinations
Achievement, as measured by the course examinations, provided general
information about student understanding of introductory college chemistry. Course
grades were analyzed descriptively and used to describe the group of students who
volunteered for interviews. CHEM 121 included important content such as the nature of
matter, thermodynamics, structure and property of atoms, bonding theory, the periodic
table, and chemical reaction. Some concepts were directly related to the understanding of
atomic structure, while other concepts were more indirectly related. In order to evaluate
student perceptions and learning of atomic structure in course examinations, items from
the mid-terms and final examinations which were related to atomic structure were
selected for analysis by the researcher.
The selection was determined through discussions among three experts in
science: one expert with a Ph.D. in chemistry (instructor), one expert with a M.S. in
chemistry, and one expert with a M.S. in Physics. Each expert selected items related to
atomic structure from the three course examinations and the items were selected by all
three of these experts after discussion. A total of 34 items were chosen as questions
related to atomic structure. Four questions from the first mid-term, 13 questions from the
second mid-term, and 17 questions from the final examination were grouped as questions
related to atomic structure.
54
First, the percentage of correct responses for the 34 questions related to atomic
structure was calculated to assess student achievement on items related to atomic
structure in the course examinations. Second, students’ responses related to atomic
structure were further studied by q-type factor analysis. Q methodology was used to
identify persons who cluster together based upon their responses to the set of atomic
structure related items. The clusters of students and the characteristic of these students
were further examined by relating their expressed mental models as identified from the
analysis of the pre- and post-interview transcripts. Table 3.7 summarizes the methods to
analyze student mental models of atomic structure as represented by course examinations.
Goal
Analysis method
Identification of items related to atomic
structure in course examinations
Content analysis
Achievement based upon the items
related to atomic structure
Percentage of correct responses to
questions related to atomic structure
Identification of student clusters
Q-type factor analysis
Table 3.7: Analysis of student perception of atomic structure as represented in course
examinations.
55
3. 2. 1. 1. Descriptive analysis of course examinations
The descriptive information related to the course assessments represents the
distribution of student achievement and general patterns of student performance in the
introductory chemistry course (CHEM121). The mean scores for achievement based
upon the atomic structure items for the 20 interviewed students was compared to the
Total Group mean score.
3. 2. 1. 2. Q-type factor analysis of the 20 students by their responses to items
related to atomic structure on the multiple-choice course exams
Factor analysis is a statistical method to reduce observable variables into a small
number of principal components explaining latent characteristics of data. Principal
components are produced by mathematical operations involving the correlations among
variables. Stephenson (1953) invented the q-factor analysis of inverted variables to show
subjectivity of clustered groups. The q methodology is also a factor analysis method
requiring mathematical operations involving correlations and assemblage (Stephenson;
Van Exel & Graaf, 2005). Rather than using a person by variable array, q methodology
uses a transposed data matrix or variable by person array as the input for the factor
analysis (McKeown & Thomas, 1988). Generally, in a q methodological study, people
are presented as clusters of individuals who have responded in some similar way to the
set of items. As an attempt to explore the nature of each group or cluster, this method is
often described as a bridge combining qualitative and quantitative research.
56
In this study, 90 items from three multiple-choice chemistry examinations were
first examined by content, “atomic structure,” as described by the curriculum guides.
Through content analysis, 34 items were selected as questions related to atomic structure.
Then, q methodology was applied to explore relationships between the student responses
to the atomic structure related multiple-choice course examinations and the student
mental models of atomic structure as derived from the interviews. While factor analysis
is generally used to identify clusters of items and reduce the items into clusters or
subscale groups, the q methodology of this study was used to identify the clusters of the
20 students into subgroups as related to mental models of atomic structure. In order to
characterize the clusters, the background data and the mental models of atomic structure
were examined for commonalities within the groups.
3. 2. 2. Questionnaires
Questionnaires asked students to explain or describe atomic structure by written
and diagrammatic/graphic forms. Responses to both pre- and post-questionnaires were
obtained from 439 students. Responses from the 20 interviewed students (Group 2) were
explored in detail for this study. The same coding schemes and procedures were applied
to assess student mental models of atomic structure as represented by responses to the
questionnaires and the interviews. Students’ written and diagrammatic/graphic
representations were analyzed by categories made up of four different scientific models
and then, compared using the 13 levels of understanding of atomic structure. Table 3.8
57
shows the three main topics for questions included in the questionnaire: (a) definition of
an atom, (b) atomic structure (written and diagrammatic), and (c) orbitals. The pre- and
post-questionnaires can be found in Appendix D.
Questionnaire items asking about atomic structure
5. Define an atom.
6. Atomic Structure
a. Describe or explain atomic structure.
b. Draw a picture of an atom. (you may use any atom as an example)
c. Identify or describe the parts in your drawing.
d. Does your drawing (representation) help you to understand the atom and its
structure?
If so, explain why and if not, explain why not.
7. Orbital
a. Explain what is meant by the term ‘orbital’.
b. Draw an orbital or orbitals based on your understanding.
c. Can orbitals have different shapes? If yes, explain.
d. How many electrons can an orbital hold?
e. What is a node?
Table 3.8: Items related to atomic structure included in the questionnaire.
58
3. 2. 2. 1. Schemes for analyzing mental models of atomic structure
Questionnaire and interview responses were analyzed by two schemes to evaluate
student perceptions of atomic structure: (a) scientific models and (b) levels of
understanding. Table 3.9 introduces the schemes for analyzing mental models of atomic
structure as represented in questionnaires and interviews.
First, because of the abstract nature of an atom, various atomic models have been
used to explain and support scientific observations and the understanding of the nature of
an atom. Following the initial development of atomic theories, atomic models have been
changed throughout science history. Although quantum atomic models are currently
accepted in the scientific community, some models from the past are still in use in the
school curriculum. Student diagrammatic/graphic representations were coded by
categories which represent these scientific models. Four scientific models (SM) were
used to label student mental models of atomic structure: (a) the Particle model (P), (b) the
Nuclear model (N), (c) Bohr’s model (B), and (d) the Quantum model (Q). These four
models were developed chronologically in the history of science. From a developmental
perspective on scientific ideas about atomic structure, these models are considered to
represent hierarchical levels of understanding.
Second, student perceptions of atomic structure were ranked in terms of a
hierarchical order which was used as an analysis scheme. This scheme was developed by
referring to the curriculum guide which explained the concept of atomic structure. The
content and hierarchical order of the items were determined through discussion with
59
experts in the field of science and science education. Thirteen levels of understanding
(LU) were developed to classify student mental models of atomic structure. Students in
levels 1/1 and 1/2 understand an atom as a particle (the Particle Model). Students who are
able to differentiate between atoms and molecules are coded as having a mental model of
atomic structure at a 1/2 level of understanding. Levels 2/1, 2/2, and 2/3 represent details
of the Nuclear model by hierarchical orders of understanding. Levels 3/1, 3/2, and 3/3
represent Bohr’s model description. However, the levels are differentiated by student
ability to comprehend the concept of “energy quantization” for Bohr’s orbital structure.
Level 3/2 is another type of extension of student models at level 3/1. In this level, a
student describes atomic structure with different shapes of orbital structure. However, the
understanding in level 3/2 is limited to the level of Bohr’s orbital structure as represented
by level 3/1. Levels in the Quantum model are listed from 4/1 through 4/5. The levels
were divided by degrees of understanding atomic structure related to quantum theory
such as probability for finding electrons, different orbital shapes, wave functions, and
energy quantization. The descriptions of the mental models of atomic structure of the
student volunteers was derived by their verbal and non-verbal responses to pre- and postquestionnaires and interviews.
In regard to the coding procedure for the 20 students, first, the researcher coded
the student mental models of atomic structure based on the two schemes. A replication of
the coding was done by the researcher and the agreement between results was over 95%
correspondence. Second, five sets of student responses to the questionnaires and
60
interviews were randomly selected and coded by the researcher and the expert with a
Masters of Science degree in physics. These mental models of atomic structure were
coded in terms of the two schemes and the results were compared. For the 10 student
mental models coded for scientific model, the researcher and the expert showed 100%
agreement. For the mental models for the 10 students coded by levels of understanding,
the results were in 80 % agreement. For the two students whose mental models as
assessed by the researcher and the expert differed, the instructor of the course was
consulted and agreement was reached.
61
Level
Criteria for evaluating level
Atomic model
1 (1/1)
A student understands an atom as a particle.
2 (1/2)
A student can differentiate atoms and molecules.
Particle model
(P)
3 (2/1)
A student understands the components of an atomic
structure.
4 (2/2)
A student understands the components of an atom and the
compositional relationship between them.
5 (2/3)
A student understands the Nuclear model and forces that
hold an atom together (electrons in orbits, paths, rings).
6 (3/1)
A student understands the Nuclear model and different
levels of orbitals as a set path of electrons without
understanding energy quantization based on quantum
theory.
7 (3/2)
8 (3/3)
9 (4/1)
10 (4/2)
11 (4/3)
12 (4/4)
13 (4/5)
A student understands the Bohr’s model and different
shapes of orbitals: modified Bohr’s orbital model
considering different shapes of orbitals (without
understanding energy quantization based on quantum
theory).
A student understands the Bohr’s model by understanding
energy quantization in quantum theory.
Nuclear model
(N)
Bohr’s model
(B)
A student arranges electrons not on a set path but within a
certain area (or electrons within orbitals).
A student describes electrons in terms of or consistent with
the meaning of probability.
A student understands about different types and shapes of
orbitals (a mixed model of separate models between
orbitals and atoms).
A student understands the different types and shapes of
orbitals (a single or modified model of orbitals and atoms).
A student understands the basic idea of quantum theory
(probability, wave function, energy quantization, etc.) and
the modern picture of the atom and explains the atom in
terms of particles or waves.
A student explains the concept of probability and orbitals in
terms of quantum theory and integrates both concepts into
atomic structure.
Quantum model
(Q)
Table 3.9: Scheme for analyzing mental models of atomic structure by level of
understanding and scientific model.
62
3. 2. 2. 2. Analysis of mental models of atomic structure from questionnaire
responses
Table 3.10 illustrates the framework for the analysis of student mental models as
represented by the questionnaire responses. The student models for atomic structure were
coded by scientific model and by level of understanding of atomic structure. Responses
to the questions related to atomic structure and orbitals were examined in detail. In
regard to students who had a mixed model including two separate models in their
description of an atom and orbitals, mental models for an atom (Ma) and mental model
for orbitals (Mo) were separately analyzed. A student mental model of atomic structure
was assessed by considering the two models. Table 3.10 displays the format that was
used to describe student mental model of atomic structure and the number of models. In
addition, the achievement score for the atomic structure related items was recorded in the
table. The comparison of responses for individual pre- and post-questionnaire items
provided information as to the student development of mental models of atomic structure
during the chemistry course.
63
Coded
name
Mental model for
atomic structure
SM
LU
Mental model for
orbitals
SM
LU
Ma-pre
(atomic structure)
Mo-pre
(orbital)
Ma-post
(atomic structure)
Mo-post
(orbital)
Mental model of atomic structure
as represented in questionnaires
and number of models
Note: SM=scientific model. LU=level of understanding. Ma=model for atomic structure.
Mo=model for orbitals.
Table 3.10: Framework for the analysis of student mental models as represented by
questionnaire responses.
3. 2. 3. Interviews
3. 2. 3. 1. Schemes for analyzing mental models of atomic structure
Interview recordings were transcribed by matching verbal descriptions and nonverbal descriptions, including gestures and drawings. Two schemes were applied to
evaluate student perceptions of atomic structure: (a) scientific models and (b) levels of
understanding. The description of the mental models of atomic structure of the student
volunteers was derived by their verbal and non-verbal responses to both pre- and postinterviews.
64
3. 2. 3. 2. Data analysis: Alternative models as represented by interviews
Some students develop their own learning models or methods by way of
rephrasing or analogizing to understand atomic structure. Some of these models develop
into misconceptions. Alternative models in this study are defined as student mental
models which are different from scientist or instructor models, i.e., target models of the
course. Because student alternative mental models of atomic structure are constructed for
or from their own understanding, they can serve as a valuable assessment of student
understanding. Changes in student mental models after learning the quantum electron
configuration can provide information related to conceptual development. This study
analyzed student alternative models as represented in their interview responses. In
addition, changes in the alternative models were examined by comparing pre- and postresponses to the interviews. Analysis of the change in student mental models of
alternative conceptions provided useful information to understand student learning
processes, misconceptions, and conceptual development. Alternative conceptions from
student responses were grouped and categorized by applying the schemes of scientific
models and levels of understanding.
3. 2. 3. 3. Data analysis: Comparing pre- and post- interview responses
The comparison of responses for the pre- and post-interviews provided
information as to the student development of mental models of atomic structure. Student
understanding was assessed by using hierarchical grading schemes of (a) 4 scientific
models (SM), and (b) 13 levels of understanding (LU). The student mental models as
65
determined by the analysis of the pre- and post-interviews were compared and identified
by numbers of models, types of models, and levels of models. Table 3.11 shows the
framework for the analysis of student mental models as compared by the pre- and postresponses to interviews. Data analysis included the following: (a) pre- and post-mental
models of atomic structure by levels of understanding (LU), (b) pre- and post-mental
models of atomic structure by scientific models (SM), (c) number of models identified as
student mental models of atomic structure during interviews with students, (d) change of
models through modeling procedure of atomic structure during interviews (Mi, Mb, Mf),
and (e) reasoning for the change in modeling atomic structure. In order to explore the
change or progress of student thinking during interviews, student models by scientific
models were explored by reporting an initial model for atomic structure (Mi), a between
or transitional model for atomic structure with orbitals or with modification during
interviews (Mb), and a final model for atomic structure (Mf). Descriptive analysis of
student responses provided information related to the pattern of learning and for building
knowledge during and after instruction. In addition, the mental model analysis by
scientific models reveals the influence of past and current scientific models on student
mental models of atomic structure.
66
Coded
name
Mental model for
atomic structure
SM
LU
Number of
models for an
atom
Change of models
Pre
Mi
Post
Mi
Mb
Reasoning for the
change
Mf
Mf
Note: SM=scientific model. LU=level of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model of atomic structure. Mf=final mental model of atomic
structure.
Table 3.11: Framework for the analysis of student mental models as represented by
interview responses.
3. 2. 4. Data analysis: Comparing mental models of atomic structure as represented in
different assessments
In this study, conceptual understanding of atomic structure was assessed by
analyzing three different data sets: multiple-choice course examination items related to
atomic structure, pre- and post-questionnaires, and pre- and post-interviews. These
assessments were analyzed to infer student perceptions of atomic structure in an
introductory college chemistry class. Comparison of the mental models represented by
the assessments revealed similarities and differences among these assessments.
Student correct responses to the items related to atomic structure from the course
examinations were calculated by percentage (100* the number of correct responses/34).
Mental models of atomic structure as represented by the questionnaire and interview
67
responses were analyzed using the same criteria of (a) scientific models and (b) levels of
understanding. Student performance in the course was evaluated by the course grades.
While course grades mainly reflect student achievement on the multiple-choice course
examinations, comparative analysis of the three different assessments (course
examinations, questionnaires, and interviews) provided a better understanding about
student perceptions and learning of atomic structure. In addition, the comparison
provides information for teachers and educators to assess student learning and research
methods. Table 3.12 shows the framework prepared to compare student mental models of
atomic structure as represented by responses to the three different assessments.
Coded
name
Analysis
criteria
Atomic structure
(questionnaire)
Pre
Post
Atomic structure
(interview)
Pre
Post
Percentage of
correct
responses
(34 items)
Academic
achievement
Course
grade
Scientific
Model
Level of
Understanding
Table 3.12: Framework for comparing student mental models as represented by
responses to different assessments.
68
For the purpose of identifying groups of students with similar characteristics
related to mental models of atomic structure, the 34 items which were selected as
questions related to atomic structure from the multiple-choice course examinations were
further studied by the q methodology for the 20 students who had volunteered for the
interview sessions. Three principal component clusters of students were identified based
upon these responses. In order to characterize the clusters of students resulting from the q
analysis, student mental models as revealed by interview responses were examined to
search for patterns and/or commonalities describing each of the component clusters of
individuals. Due to the more detailed and in-depth exploration and understanding of the
student mental models of atomic structure obtained from the interview responses, student
mental models from interview responses were used to characterize student clusters. Table
3.13 shows the framework for data analyses used to characterize the three principal
component clusters. This table includes the student model of atomic structure, gender,
and achievement on atomic structure exam questions by component group.
Coded
Name
Gender
Grade
Scientific
Model
(Pre : Post)
Level of
Understanding
(Pre : Post)
Component
1
2
3
Table 3.13: Framework for characterizing student clusters by atomic structure
achievement and by mental models of atomic structure as represented by interview
responses.
69
CHAPTER 4
RESEARCH FINDINGS
4. 1. Course assessments
4. 1. 1. Academic achievement
Student evaluation in the CHEM 121 course was based on student performance
on three multiple-choice exams (mid-term 1, mid-term 2, and the final exam), ten lab
activities, and six take-home quizzes. Six hundred thirty-three students participated in
this course (Total Group), 439 students responded to both pre- and post-questionnaires
(Group 1), and 20 student volunteers participated in the open-ended interviews (Group 2).
To better understand the relationship of Group 2 students who volunteered for interviews
to the Total Group, the achievement mean scores for course examinations (mid-term 1,
mid-term 2, and the final exam) and the GPA of the Total Group and Group 2 are
provided in Table 4.1.
The Total Group had a 2.31 mean GPA and Group 2, those who volunteered for
the interviews, had a 2.73 mean GPA. Table 4.2 displays details of the student
distribution by grade and group. Both groups show similar patterns in student distribution
by course grades. Table 4.2 displays number and percent distribution of students by
70
group and course grade.
Group
Number of
Students
Midterm 1
Midterm 2
Final
exam
GPA
Total
Group
633
124.54
114.51
171.16
2.31
Group 2
20
136.50
124.25
192.75
2.73
Table 4.1: Mean academic achievement scores by exam and GPA for the CHEM 121
course by Group.
The comparison shows that for the Total Group about 16% of the students had
course grades of A/A- and about 19% had course grades of B+/B/B-. For Group 2 about
30% of the students had course grades of A/A- and 10% had course grades of B+/B/B-.
Group 2 showed 40% of the students and the Total Group had 34.92% of the students in
the grade B- or above course grade levels. For the C+/C/C- grade range, there were about
44.39% of the students in the Total Group and about 55% of the Group 2 student sample.
This comparison indicates that the Group 2, which had a bipolar distribution of grades
from between B- or above and C+/C/C-, had 6% more with a grade of B- or above and
10% more with a grade of C+/C/C- than the Total Group.
71
Course
Grade
Total Group
Total Group %
Group 2
Group2 %
A
65
10.27
4
20
A-
36
5.69
2
10
B+
45
7.11
0
0
B
35
5.53
1
5
B-
40
6.32
1
5
C+
123
19.43
7
35
C
101
15.96
4
20
C-
57
9.00
0
0
D+
50
7.90
1
5
D
33
5.21
0
0
E
48
7.58
0
0
Total
633
100
20
100
Table 4.2: Number and percentage distribution of students by group and course grade.
4. 1. 2. Conceptual understanding of atomic structure in course examinations
4. 1. 2. 1. Analysis of items related to atomic structure
Selection of items related to atomic structure
As the first in a series of three courses, CHEM 121 covers the first nine chapters
of an introductory chemistry textbook for college students. Table 4.3 shows the content
of each chapter. Chapters 1, 2, and 6 are directly related to the topic of this study, atomic
structure. Chapter 1 introduces general information and definitions about the science of
matter and measurement. Chapter 2 explains sub-atomic particles, the discovery of
atomic structure, atomic mass, the periodic table, and microscopic classification of
72
substances. Chapters 6 explain the scientific history of quantum theory and the
development of atomic theory. It includes quantum mechanics, electro magnetic
radiation, the Bohr atom, orbitals, many-electron atoms, electron configurations, and a
modern picture of the atom.
Chapter
Content
Chapter 1
Introduction: Matter and measurement
Chapter 2
Atoms, molecules and ions
Chapter 3
Stoichiometry: Calculations with chemical formulas and equations
Chapter 4
Aqueous reactions and solution stoichiometry
Chapter 5
Thermochemistry, Introduction of quantum theory
Chapter 6
Electronic structure of atoms
Chapter 7
Periodic properties of the elements
Chapter 8
Basic concepts of chemical bonding
Chapter 9
Molecular geometry and bonding theories
Table 4.3: Content of first nine chapters of the CHEM 121 course textbook.
Student conceptual understanding for the CHEM 121 course was evaluated by
three multiple-choice course examinations (mid-term1, mid-term 2, and the final exam).
Items for the three examinations were analyzed by content in reference to the curriculum
guide, the textbook, and the instructors notes. Concerning the topic of this study, items
related to atomic structure were selected. The items were categorized into two groups: (1)
73
a group related to atomic structure and (2) a group non-related to atomic structure. The
percentage of items correct for the atomic structure related items was calculated.
Mid-term 1 was composed of 25 multiple-choice questions. Content analysis of
mid-term 1 resulted in four items in the category of “related to atomic structure.” Table
4.4 shows the four items selected and the specific content of the questions.
Question
Number
Content of Mid-term 1
1
Science of matter (symbol and name of elements)
3
Science of matter (Dalton’s atomic theory)
5
Atomic structure (Rutherford’s nuclear atomic model)
6
Atomic structure (fission, nuclear reaction)
Table 4.4: Items selected from mid-term 1 as related to atomic structure.
Mid-term 2 was comprised of 25 multiple-choice questions. Content analysis of
mid-term 2 resulted in 13 items in the category of “related to atomic structure.” Table 4.5
shows the 13 items selected.
74
Question
Number
Content of Mid-term 2
13
Electromagnetic radiation
14
Electromagnetic radiation
15
Electromagnetic radiation, (energy and color of light)
16
Photoelectric effect (calculation wavelength or energy)
17
Electromagnetic radiation, Bohr’s model (emission wavelength)
18
Electromagnetic radiation, Bohr’s model (emission/absorption wavelength)
19
Quantum theory, Heisenberg uncertainty principle
20
Quantum number (shape of an orbital)
21
Electron configuration (Br)
22
Electron configuration (unpaired electron of S)
23
Quantum number
24
Nodes (description, true/false)
25
Quantum number, many-electron atoms
Table 4.5: Items selected from mid-term 2 as related to atomic structure.
The final exam was composed of 40 multiple-choice questions based on the
cumulative content of the course. Content analysis of the final exam resulted in 17 items
in the category of “related to atomic structure.” Table 4.6 shows the 17 items selected.
75
Question
Number
Content of the final exam
10
Bonding, Lewis dot structure (bond order)
11
Bonding, formal charge
14
Molecular geometry, bonding, VSEPR theory
15
Molecular geometry, bonding, VSEPR theory
16
Molecular geometry, bonding, VSEPR theory
17
Molecular geometry, bonding, polarity
18
Molecular geometry, bonding
19
Molecular geometry, bonding,
20
Multiple bonds
21
Hybrid orbital
22
Multiple bonds, hybrid orbital, bonding
23
Multiple bonds, hybrid orbital, bonding (description, true/false)
24
Molecular orbital theory (bond order)
25
Atomic structure (mass number, components)
37
Electron configuration
38
Nodes (description, true/false)
39
Atomic structure, modern picture of an atom (description, true/false)
Table 4.6: Items selected from the final exam as related to atomic structure.
Comparison of student achievement in percentages
The selected items from the three multiple-choice examinations resulted in thirtyfour items related to atomic structure. The internal consistency reliability analysis for the
34 items for the Total Group responses showed 0.83 Cronbach’s alpha value. The
76
reliability for the 34 items with Group 2 responses was 0.80. This suggests that the
internal consistency reliability for the 34 items asking about atomic structure was good.
The number and percentage of correct responses of each individual in Group 2 for these
items was calculated and is presented in Table 4.7.
Coded
Name
KF
Number of correct
responses for the 34 items
23
Percentage of correct
responses for the 34 items
67.65
EJ
19
55.88
MK
24
70.59
CE
24
70.59
WT
22
64.71
SJ
21
61.76
KT
32
94.12
LJ
30
88.24
RZ
30
88.24
MD
25
73.53
CZ
31
91.18
BM
22
64.71
LT
23
67.65
TK
29
85.29
HJ
23
67.65
TH
13
38.24
BJ
13
38.24
HD
25
73.53
VB
19
55.88
KC
18
52.94
Table 4.7: Number and percentage of correct responses for the 34 items related to atomic
structure.
77
Table 4.8 displays the mean percentage of student achievement on items related
to atomic structure by groups. Students in this course (Total Group) got an average of
60.55% and students in Group 2 got an average percentage of 68.53 for the 34 items
related to atomic structure. The average percentage of correct responses to those 34 items
for Group 2 students appeared to be higher than that of the Total Group.
Group
Mean percentage of correct responses to
the 34 atomic structure related items
Total Group
60.55
Group 2
68.53
Table 4.8: Mean percentage comparison of student achievement on items related to
atomic structure by group.
4. 1. 2. 2. Q-type factor analysis of the 20 interviewed students based upon their
responses to items related to atomic structure
Student responses to the selected questions related to atomic structure reflect
student perceptions and understanding of atomic structure. The Q methodology resulted
in clusters of students who responded to the questions related to atomic structure in a
similar fashion or using a similar thought process. Figure 4.1 is the Scree plot of the
principal components by eigenvalue results for the q-type principal components analysis
of the 20 interviewed students by the responses to the 34 items related to atomic structure.
78
Scree Plot
5
Eigenvalue
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Component Number
Figure 4.1: Scree plot of q-type principal components analysis of the 20
interviewed students’ responses to 34 selected items related to atomic structure
From the Scree plot, it was determined that either 2, 3, or 4 components as
indicated by the elbow of the curve, might result in a solution which best fits simple
structure. For solutions using 2, 3, and 4 components with Varimax rotations were
compared. The three-component solution was found to be the best fit to simple structure.
Simple structure is the situation where an individual has a relatively large loading
different from zero on one component and a loading (not significantly different from
zero) on the remaining components. Table 4.9 includes the loadings for each individual
from the highest loading to the lowest. Loadings of 0.40 or less have not been displayed.
79
Coded Name
Component Loading
1
KF
.742
EJ
.718
MK
.590
CE
.530
WT
.520
SJ
.519
KT
.433
2
LJ
.804
RZ
.794
MD
.774
CZ
.557
BM
.495
3
LT
TK
.696
HJ
.657
TH
.638
BJ
.633
HD
.575
VB
.502
KC
.492
Note: Number of persons=20. Number of items=34. Sample=Group 2.
Table 4.9: Student loadings on the three-component rotated solution resulting from the
person by item principal components analysis for Group 2.
The coded name represents the pseudonym initials for the individuals who
responded to the instruments. These three clusters resulted from similarities in the
individual responses to the items related to atomic structure. As can be seen in Table 4.9,
80
LT was the only student who was not included in any of the components. The data
analyzed from the interview responses were further examined in order to characterize the
nature of each cluster. Student mental models of atomic structure were compared and
examined for patterns characterizing each of clusters.
4. 2. Analysis of student responses to questionnaires
4. 2. 1. Mental models of atomic structure as represented by questionnaire responses
Questionnaire responses of the Group 2 students, who were interviewed, were
selected for further analysis of this study. Twenty students participated in the prequestionnaire and 18 students from Group 2 responded to the post-questionnaire. Data
from two students (LJ and CZ) on the post-questionnaire were missing. In order to map
out student mental models of atomic structure as represented in questionnaires, the
responses completed by the 18 students who responded to both the pre- and postquestionnaires were analyzed.
For the comparative analysis of student mental models of atomic structure as
represented by the questionnaire responses, student perceptions of atomic structure were
examined by the two criteria which were used for the analysis of interview responses.
Table 4.26 displays the analysis of student mental models for atomic structure as
represented in the pre-and post-questionnaires by using the two schemes presented in
Table 3.9: a. four scientific models (SM) and b. 13 levels of understanding (LU).
81
Concerning students who have different models of atomic structure by questions
about atomic structure and orbitals, student responses were categorized separately by
models of an atom (Ma) and by models of orbitals (Mo). Then, through detailed analysis
of the two models of Ma and Mo, a student mental model representing atomic structure
was determined. In addition, the number of models was counted. Mental models of
atomic structure from the questionnaire responses were further examined by course
grades to determine the relationships between student mental models represented in
questionnaires and academic achievement. Table 4.10 displays related information.
82
Coded
name
Mental model for
an atom (Ma)
SM
LU
Mental model for
orbitals (Mo)
SM
Mod-pre
Ma-pre
KF
P
1/2
B
Ma-post
B
3/1
B, 3/1
3/1
Mo-post
B
Ma-pre
B
LU
3/1
B
2
B, 3/1
Mo-pre
3/1
Mental model of atomic structure
as represented by questionnaire
responses and number of models
1
B, 3/1
3/1
1
EJ
Ma-post
B
3/1
Mo-post
B
Ma-pre
B
B, 3/1
3/1
Mo-pre
3/1
B
1
B, 3/1
3/1
1
MK
Ma-post
B
3/1
Mo-post
B
Ma-pre
Q
B, 3/1
3/2
Mo-pre
4/1
B
2
Q(B), 4/1
3/1
2
CE
Ma-post
Q
4/1
Mo-post
Q
Q, 4/1
4/1
1
Note: SM=scientific model. LU=levels of understanding. Ma=models of an atom. Mo=models of
orbitals.
Continued
Table 4.10: The analysis of student mental models of atomic structure as represented by
the pre- and post-questionnaire responses.
83
Table 4.10 continued
Ma-pre
WT
Q
Mo-pre
4/2
Q
Ma-post
Q
4/4
B
Q
B
Ma-post
3/1
B
B
Ma-post
3/1
RZ
Q
4/2
Q
4/2
Mo-post
Ma-pre
Mo-pre
3/1
B
Q
Ma-pre
Q
3/1
Q
4/3
Mo-pre
4/2
Q
Ma-post
B
B, 3/1
1
1
B, 3/1
2
1
1
Q, 4/3
1
Q, 4/3
4/3
Mo-post
4/1
1
B, 3/1
Mo-post
4/3
1
Q, 4/2
Ma-post
B
Q
3/2
Mo-pre
Ma-post
MD
3/1
B
Q, 4/4
B, 3/1
Mo-post
Ma-pre
LJ
3/1
Mo-pre
3/1
B
3/1
B
2
B, 3/1
Mo-post
Ma-pre
KT
4/4
Mo-pre
3/1
B
4/3
Mo-post
Ma-pre
SJ
Q, 4/2
3/2
2
Q(B), 4/1
2
Continued
84
Table 4.10 Continued
Ma-pre
CZ
BM
Q
Mo-pre
4/1
Q
Mo-post
Ma-pre
Mo-pre
Q
4/2
Q
Ma-post
4/2
B
B
Ma-post
Ma-pre
4/2
B
4/2
Q
B
Ma-post
4/1
B
3/1
Mo-pre
3/1
B
Ma-post
B
3/1
B
B
1
B, 3/2
1
2
Q, 4/2
1
2
Q(B), 4/1
2
B, 3/1
3/1
Mo-post
3/1
1
Q(B), 4/1
Mo-post
Ma-pre
TH
4/3
Mo-pre
4/1
Q
3/1
Q
Q, 4/2
Q(B), 4/2
Mo-post
Ma-pre
HJ
3/2
Mo-pre
Ma-post
Q
3/1
B
1
B, 3/1
Mo-post
3/2
Q(B)
4/2
Mo-pre
3/1
B
4/2
Q
1
Q, 4/2
Mo-post
Ma-pre
TK
4/1
Ma-post
Q
LT
Q, 4/1
3/2
1
B, 3/1
2
Continued
85
Table 4.10 continued
Ma-pre
BJ
B
Mo-pre
3/1
B
Ma-post
B
3/1
B
B
B
Ma-post
3/2
Q
B
Ma-post
4/1
P
3/1
Mo-pre
1/2
B
Ma-post
Q
3/1
B
B
1
1
B, 3/2
1
2
Q(B), 4/1
2
P(B), 1/2
3/1
Mo-post
4/1
B, 3/1
Q(B), 4/1
Mo-post
Ma-pre
KC
3/2
Mo-pre
4/1
Q
3/1
B
1
B, 3/1
Mo-post
Ma-pre
VB
3/1
Mo-pre
3/1
B
3/1
Mo-post
Ma-pre
HD
B, 3/1,
3/1
86
2
Q(B), 4/1
2
4. 2. 2. Changes of mental models of atomic structure as represented in questionnaire
responses
Student mental models of atomic structure in the pre- and post- questionnaires
were analyzed by scientific models. Table 4.11 shows the number of student mental
models in the pre- and post-questionnaire responses by scientific models [P, P(B), N, B,
Q(B), Q] in the same way that was used to analyze the interview responses. The analysis
of student models of atomic structure from the questionnaires indicates that 10 students
had Bohr’s model for atomic structure from the pre-questionnaire responses and 9 from
the post-questionnaire responses. Four students in the pre- and post-questionnaires
expressed a mixed model with two separate models: the Quantum model for atomic
structure and Bohr’s model for orbitals [coded by Q(B)]. On the pre-questionnaire
response, there was 1 student who had a mixed model of P(B): the Particle model for
atomic structure and Bohr’s orbital structure. Figure 4.2 displays the number of student
mental models of atomic structure as represented by the pre- and post-questionnaire by
scientific model analysis.
Scientific model
P
P(B)
N
B
Q(B)
Q
Total
Number of students from the
pre-questionnaire responses
0
1
0
10
4
3
18
Number of students from the
post-questionnaire responses
0
0
0
9
4
5
18
Table 4.11: Number of student mental models of atomic structure in the pre- and postquestionnaire responses by scientific model.
87
Student Models from Questionnaires
by Scientific Model
Number of Students
12
10
8
6
4
2
0
P
P (B)
N
B
Q (B)
Q
Scientific Model
Pre-Q uestionnaire (by model with 18 students)
Post-Questionnaire (by model with 18 students)
Figure 4.2: Number of student mental models of atomic structure from the pre- and postquestionnaire responses by scientific model
The student mental models of atomic structure from the pre- and postquestionnaire responses were also analyzed by levels of understanding. Table 4.12
provides the distribution of the number of student mental models for atomic structure
from the pre- and post-questionnaire responses by level of understanding. Figure 4.3
represents the number of students by level of understanding and the changes in student
responses to the questionnaires by level of understanding. There were some changes in
the number of models at 3/1, 3/2, 4/1, 4/2, and 4/4 levels of understanding. Although the
88
changes were slight, Figure 4.3 reveals a trend for improvement of the level of
understanding for the models from the questionnaire responses.
Level of
understanding
1/2
3/1
3/2
3/3
4/1
4/2
4/3
4/4
4/5
Total
Number of
students from
the prequestionnaire
1
10
0
0
3
3
1
0
0
18
Number of
students from
the postquestionnaire
0
7
2
0
5
2
1
1
0
18
Table 4.12: Number of student mental models of atomic structure from the pre- and postquestionnaire responses by level of understanding.
89
Number of Students
Student Models from Questionnaires
by Level of Understanding
11
10
9
8
7
6
5
4
3
2
1
0
1/2 3/1 3/2 3/3 4/1 4/2 4/3 4/4 4/5
Level of Understanding
Pre-questionnaire (by level with 18 students)
Post-questionnaire (by level with 18 students)
Figure 4.3: Number of student mental models of atomic structure from the pre- and postquestionnaire by level of understanding
The level of understanding and the scientific model for each student perception of
atomic structure was determined by examining the responses to the question about an
atom (Ma) and the question about an orbital (Mo). Five students from the prequestionnaire responses and 4 students in the post-questionnaire were determined to have
mixed models of two separate models in their description of an atom and orbitals. The
mixed models of two separate models such as P(B) and Q(B) reflect first, a lack of
understanding about orbitals and second, the influence of Bohr’s orbital structure on
student mental models of atomic structure. Concerning the number of the mixed models
90
including Bohr’s orbital structure, data from the questionnaire analysis identified a
relatively large number of Bohr’s models for atomic structure in students’ minds.
In the post-questionnaire, two students showed an increase in the category of the
Quantum model (Q). In the comparison of pre- and post-responses, three students (HJ,
VB, and KC), who had the mixed model of two models for atomic structure in the pre
questionnaire, didn’t show changes in their responses to the post-questionnaire.
Table 4.13 displays the changes in mental models of atomic structure as represented in
the questionnaire responses. LJ and CZ were the two students who participated only in
the pre-questionnaire and did not responded to the post-questionnaire. Including CE and
TK who did not change their level of understanding but changed from the mixed model,
[Q(B)] to one single model (Q), seven students (CE, WT, RZ, LT, TK,HD, KC)
improved their models for atomic structure by the end of the quarter. One student, MD,
decreased in level of understanding atomic structure from 4/3 to 4/1. Figure 4.4 displays
MD’s diagrammatic and written description of an orbital as represented in the prequestionnaire. In the pre-response, MD explained an orbital as “a zone in which an
electron is supposed to be found in.” This reflects his understanding of the probability
concept that electrons can be found in orbitals. In addition, he addressed the different
orbital shapes and showed the p-orbital shape. These data suggest that he has the
Quantum model at the 4/3 level of understanding for atomic structure. Figure 4.4a.
represents MD’s p-orbital representation from his pre-questionnaire responses.
91
Coded
name
1/2
2/1
2/2
2/3
3/1
3/2
3/3
4/1
4/3
4/4
4/5
B
B
B
B
B
B
KF
EJ
MK
Q(B)
Q
CE
WT
Q
Q
B
B
B
B
SJ
KT
LJ
Q
RZ
B
Q
MD
Q(B)
CZ
Q
Q
Q
Q
BM
LT
B
B
Q(B)
Q
TK
Q(B)
Q(B)
HJ
B
B
B
B
TH
BJ
HD
B
B
Q(B)
Q(B)
VB
KC
4/2
P(B)
Q(B)
Table 4.13: Student mental models of atomic structure in the pre- and post-questionnaire
responses by scientific model and level of understanding.
92
a.
b.
Note: a. diagrammatic description of an orbital, b. written description about an orbital
Figure 4.4: MD’s response to the pre-questionnaire
Figure 4.5 displays MD’s responses to the post-questionnaire. MD’s
diagrammatic description of atomic structure in Figure 4.5a. represents the Quantum
model at the 4/1 level of understanding. However, he explained the orbital as “a fixed
path around an object” and responded in terms of the existence of different shapes for
orbitals. MD’s post-questionnaire responses related to atomic structure suggest growth
from the 3/2 level to the 4/3 level of understanding.
93
a.
b.
Note: a. diagrammatic description of an atom, b. written description about an orbital
Figure 4.5: MD’s response to the post-questionnaire
4. 3. Analysis of student responses in interviews
4. 3. 1. Mental models of atomic structure
The qualitative analyses of this study show detailed exploration of student
perceptions and learning through analyzing student mental models of atomic structure.
Student models of atomic structure were qualitatively analyzed by two hierarchical order
schemes comprised of (a) four scientific models and (b) 13 levels of understanding (See
94
Table 3.9). Representative data were selected to describe the coded model for atomic
structure.
4. 3. 1. 1. Particle model (P) and levels of understanding (1/1 and 1/2)
As displayed in Table 3.9 and Table 4.14, it can be seen that a student having the
Particle model understands an atom as a solid or indivisible particle. Student models
coded as the Particle model were divided into two different levels (1/1 or 1/2) depending
on the ability to differentiate the relationships between atoms and molecules. Table 4.14
displays the criteria used to assess the student mental model of atomic structure as levels
1/1 and 1/2 for the Particle model.
Level of
Understanding
Criteria for Evaluating Level
1/1
A student understands an atom as a particle.
1/2
A student can differentiate atoms and molecules.
Atomic model
Particle model
(P)
Table 4.14: Criteria for analyzing mental models of atomic structure by levels of
understanding, 1/1 and 1/2, for the Particle model.
The following text was excerpted from KC’s pre-interview responses. The
researcher was coded as R. The ••• signifies time elapsed during interviews.
R: Then, what is an atom?
KC: The atom, it’s like the smallest piece of a molecule.
R: Then what is a molecule?
95
KC: Molecule … a lot of atoms.
R: Do you mean that atoms make a molecule?
KC: Yes. And molecules make compounds. (indicating student model in level 1/2)
…
R: Then, do you mean that atoms are the smallest piece?
KC: Yes.
R: Then, can you divide it further?
KC: Um…. I don’t think so. (indicating student model of the Particle model)
R: Then, could you define an atom again?
KC: Just the smallest piece of … the smallest particle that there is.
…
R: Do you have any pictorial image of an atom in your mind?
KC: Maybe like a circle.
R: Could you show that to me?
KC: I have no idea. … … … That’s my idea but smaller. (See Figure 4.6a.)
R: It looks small. You mentioned different types of atoms? Shape or what does differ?
…
R: So is it basically a circle?
KC: Yes.
R: How many atoms do you have?
KC: A lot. Like infinity… … I don’t know. A lot … ... Because there are a lot.
R: Do all of them have a circular shape?
KC: I think so.
KC: Um… … I don’t know. I think they are just a circle. They are just like that. (pointing to
Figure 4.6a.)
…
R: When you look at your atom, does it look like a circle on this paper? I mean what about 3dimensional shape of an atom?
KC: Um… It’s like a ball or watermelon. This one looks like a watermelon. (pointing to Figure
4.6a.)
96
a.
b.
c.
Note: KC’s diagram during the pre-interview, a. the ball or watermelon shape of an atom, b.
the structure of an element: bonded protons, electrons, and neutrons, c. the structure of an
element: nucleus and orbitals of protons, electrons, and neutrons
Figure 4.6: Example of student (KC) diagrammatic description of atomic structure during
pre-interview of the Particle model at the 1/2 level of understanding
R: So, do you mean that atoms are made up of protons, neutrons, and electrons?
KC: No. those are parts of atom. (pointing to Figure 4.6b.)
R: Parts of an atom?
KC: The proton is kind of an atom, neutron is kind of an atom, and electron is kind of an atom.
…
R: Then, based on all of your explanation, could you draw them, I mean, protons, electrons, and
neutrons?
KC: Draw them all together? Maybe they are just kind of, depending on what um….element you
are making. Maybe they just have like some in electrons, neutrons and they all form together
like that. But these have little circles too.
R: Could you put the specific names on your drawing?
KC: This one is a neutron. That one is a proton, and those are electrons. But I don’t know they
look like that. I think actually … (See Figure 4.6b.)
…
R: What are these small ones inside protons, neutron, and electrons?
KC: Those are atoms. (pointing to Figure 4.6b.)
R: O.k. these are atoms and this is neutron… o.k… then, what are these lines connecting all of
those?
KC: They are like bond, but actually….this is the nucleus and nucleus has…
R: Which one? And where is the nucleus?
KC: It’s the middle of the element.
R: What is an element?
97
KC: Like a copper… I really don’t know how to draw that. They have like circles like, another
circle is around them. Around the nucleus, there is another circle. I don’t know what kind of
atom this is. I’m just kind of making own my own.
R: Do you mean an element?
KC: Yes. I don’t know what element is this, this little picture would make. This is the nucleus
and it has atoms in it. And these are protons. I put the p for protons. And then these are neutrons.
And these are electrons. (See Figure 4.6c.)
…
R: And why did you put the different circles here? (pointing to 3 circles around nucleus in
Figure 4.6c.)
KC: Because they are on different orbitals
R: What are the orbitals?
KC: I think that they are rotating around the nucleus.
…
R: So, do you think that orbitals mean rotating around the nucleus?
KC: Yes. Kind of like the Earth and the Sun.
R: Do you mean the solar system between the Earth and the Sun?
KC: Yes, like these are the planets. They are just kind of spinning around it, and spinning
around, spinning around. (indicating the influence of Bohr’s model)
R: Then, you put three circles, why does this have three orbitals?
KC: Because protons, neutrons, and electrons all travel at different speeds.
KC imaged atomic structure as “maybe, like a circle” and “but smaller.” She
described the circle for atomic structure by the shape of “a ball” or “watermelon” in
Figure 4.6a. KC’s Particle model of an atom in Figure 4.6a. was coherently represented
in different diagrams (See Figure 4.6b. and 4.6c.) and verbal descriptions during the preinterview. She explained an atom as a spherical form of the smallest particle and she
differentiated the atom from a molecule or compound: “the atom, it’s like the smallest
piece of a molecule” and “molecule … a lot of atoms.” Data from KC’s pre-interview
reflect an example coded as the Particle model of an atom at the 1/2 level of
understanding. However, though there was no change in atomic structure as a solid
indivisible particle, her mental models of an element changed from Figure 4.6b. to Figure
98
4.6c. in order to explain the nucleus and orbitals. KC explained orbitals in Figure 4.6c. as
“kind of like the Earth and the Sun,” “kind of spinning around,” and “they are rotating
around the nucleus.” The orbital structure and explanation based upon the solar system
indicates the influence or evidence of Bohr’s model for atomic structure. This suggests
that KC has built a single mental model of atomic structure by combining the two models,
a Particle model for an atom and Bohr’s model for orbitals. KC’s pre-interview responses
were analyzed as a mixed model, the Particle model with Bohr’s orbitals, and it was
coded as Particle (Bohr) model or P(B) at the 1/2 level of understanding. Table 4.15
displays the analysis of KC’s mental models as represented by pre-interview responses: a
student mental model of atomic structure by scientific models (SM) and levels of
understanding (LU), number of models for an atom, change of models, and reasoning for
the change. Table 4.15 shows the change of models during the interview: from an initial
mental model of atomic structure (Mi) comprised of the Particle model (P) as drawn in
Figure 4.6a. to the between or transitional mental model of atomic structure (Mb)
comprised of Bohr’s orbital structure (B), and then, the final mental model of atomic
structure (Mf) comprised of the Particle model with Bohr’s orbital structure [P(B)] in
Figure 4.6c. The number of models was counted as 2 models as shown in Table 4.15.
99
Coded
name
Mental model
of atomic
structure
SM
LU
Number of
models for
an atom
Pre
KC
P(B)
1/2
2
Change of models
Mi
Mb
Mf
P
B
P(B)
Reasoning for the change
Atom as a particle shape, but
used Bohr’s Model for orbitals
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
Table 4.15: Analysis of student mental models as represented by KC’s pre-interview
responses.
4. 3. 1. 2. Bohr’s model (B) and levels of understanding (3/1, 3/2, and 3/3)
Table 4.16 displays the criteria for evaluating Bohr’s model at levels 3/1, 3/2, and
3/3. As explained in Table 4.16, students having Bohr’s model for atomic structure can
be divided into three different levels of understanding: levels 3/1, 3/2, and 3/3. At level
3/1, a student understands Bohr’s model including different levels of orbitals and orbiting
electrons around the nucleus; however, at this level, a student perceives the orbitals as a
set path for orbiting electrons and there is no indication of understanding of the concept
of orbitals related to “energy quantization” from quantum theory.
100
Level of
understanding
3/1
3/2
3/3
Criteria for Evaluating Levels
Atomic Model
A student understands the Nuclear model and different
levels of orbitals as a set path of electrons without
understanding energy quantization based on quantum
theory.
A student understands Bohr’s model and different
shapes of orbitals: modified Bohr’s orbital model
considering different shapes of orbitals without
understanding energy quantization based on quantum
theory.
A student understands Bohr’s model by understanding
energy quantization in quantum theory.
Bohr’s model
(B)
Table 4.16: Criteria for analyzing mental models of atomic structure by the levels of
understanding, 3/1, 3/2 and 3/3, for Bohr’s model.
Figure 4.7 introduces three selected examples of student models coded as Bohr’s
model at the 3/1 level of understanding. This study showed that students at this level
understood the atomic structure of the Nuclear model and different levels of orbitals as a
set path of electrons. Figures 4.7a. and 4.7b. represent KC’s model of atomic structure as
consistent with the Bohr’s model during the post-interview. KC explained atomic
structure with a centered nucleus and spinning electrons in different levels: “how they
spin around the nucleus” and “electrons orbit around nucleus.” “Spinning around” as
indicated by KC meant “rotating around the center with charges”. In a similar description
to that of KC’s, student, RZ, provides another example of student models in this category
as shown in Figure 4.7b. and Figure 4.7c. It was taken from RZ’s diagrams for the postinterview.
101
a.
b.
c.
Note: a. KC’s first diagram during the post-interview, b. KC’s second diagram during the postinterview, c. RZ’s diagram from the pre-interview
Figure 4.7: Examples of student (KC and RZ) diagrammatic descriptions of atomic
structure of Bohr’s model at the 3/1 level of understanding
The following text was excerpted from KC’s post-interview responses. Although
different levels of orbitals were described by KC (See Figure 4.7a. and Figure 4.7b.) and
RZ (Figure 4.7c.), they didn’t relate the orbitals of atomic structure to the level of
understanding of energy quantization based upon quantum theory. KC described the
levels as paths for electrons with different spinning (meaning rotating) direction: “this
level is like…they differently spin.” This reflects her level of understanding at the 3/1
level.
R: So, you have this as atomic structure in your mind, right?
KC: Umhum. Alright…these are electrons, they spin around outside of this which is a nucleus.
Those are protons and these are neutrons. (See Figure 4.7a.)
…
R: What are these circles? (pointing the circles around the nucleus in Figure 4.7a.)
KC: It’s how electrons, how they spin around the nucleus
102
R: What do you mean “spin around”?
KC: Like rotate around the center with their charges. This center is the nucleus.
R: What do you mean “with charges”?
KC: They can spin negatively or positively, just to be different directions.
R: Could you explain more about it?
KC: Um… o.k. they move, electrons orbit around nucleus…
…
R: You put 2 electrons on the first orbital and 4 electrons for the second orbital? (yes) why?
KC: Because I think I remember that the first level only can have 2, but I’m not sure. And the
second level would have to finish off the rest which 2-6 would be 4.
R: What do you mean by “level”?
KC: This level is like, … they differently spin. This one (pointing first orbital) spins one way,
and this one (second orbital) spins the other way.
Table 4.17 displays the analysis of student mental models as represented by KC’s
post-interview responses and RZ’s pre-interview responses. These responses were
analyzed as a single Bohr’s model at the 3/1 level of understanding.
Coded
name
Mental model of
atomic structure
SM
LU
Number of
models for
an atom
Post
KC
B
Mi
3/1
1
Pre
RZ
B
Change of models
B
Mi
3/1
1
Mb
B
Mf
B
Mb
Reasoning for the
change
No change
Mf
B
No change
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
Table 4.17: Analysis of student mental models as represented by KC’s post-interview
responses and RZ’s pre-interview responses.
103
4. 3. 1. 3. Bohr’s model (B) and level of understanding (3/2)
In level 3/2, a student understands the atomic structure of the Nuclear model and
different levels of orbitals as a set path of electrons. In addition, a student understands
different shapes of orbitals; however, the student does not have the concept of probability
for finding electrons and energy quantization to comprehend orbitals based on quantum
theory. Atomic structure at this level can be interpreted as a modification of orbital
shapes from the Quantum model into Bohr’s orbital structure as a set path.
Figure 4.8 represents two models of atomic structure coded as Bohr’s model at
the 3/2 level. Two students, MK and KT from Group 2, provided similar diagrams which
were classified as the modified Bohr’s model at the 3/2 level of understanding. MK’s and
KT’s modified Bohr’s model from the post-interview responses are displayed in Figures
4.8a. and 4.8b., respectively.
104
a.
b.
Note: a. MK’s diagram during the post-interview, b. KT’s diagram during the post-interview
Figure 4.8: Examples of student (MK and KT) diagrammatic descriptions of atomic
structure of Bohr’s model at the 3/2 level of understanding
The two students proposed their own models for atomic structure by considering
different shapes of orbitals within the context of Bohr’s model. Though different levels
and shapes of orbitals were represented in their models of atomic structure, they didn’t
relate the orbitals of atomic structure to the concept of energy quantization based on
quantum theory. The following text was excerpted from MK’s post-interview responses.
R: Then, how does the complicated atom look like?
MK: O.k. I will try. For complicated one, let’s see, this will be the nucleus, and your first orbital
is like this, that’s your s and that will hold two electrons? (See Figure 4.8a.)
105
•••
R: On top of that? What do you mean? The first s orbital? Could you show that to me?
MK: I need your hand, this is the nucleus. This would be the first one, first shell. And then, the
second shell, this is first shell, and the second shell would be on top of that, like that.
R: What about the electrons of the second shell?
MK: There are two of them…
R: Where are the electrons?
MK: Just floating around…
R: Floating? Following this line or?
MK: Like on the surface, following the surface.
R: Is this a certain path?
MK: Umhum.
R: What kind of a path?
MK: Just stays on this sphere
•••
R: You mentioned s, p, d, f. then what are they?
MK: That’s like the different shapes. (See Figure 4.8a.)
R: Different shapes of what?
MK: Orbitals.
R: Then what are orbitals?
MK: An orbital is where the electron is, that’s what it is.
MK explained an orbital as “where the electron is” and “that’s like the different
shapes.” By hand gesture describing the movement of electrons, he described floating
electrons over the surface following the paths, orbitals: “just floating around” and “like
on the surface, following the surface.” These various explanations with verbal, gestural,
and diagrammatic representations reflect his understanding of atomic structure at the 3/2
level. KT responded by a similar model in the same category to the post-interview. MK’s
and KT’s post-interview responses were analyzed as the Bohr’s model at the 3/2 level of
understanding. Table 4.18 displays the analysis of student mental models as represented
by MK’s and KT’s post-interview responses.
106
Coded
name
Mental model of
atomic structure
SM
LU
Number of
models for
an atom
Post
MK
B
Mi
3/2
Post
Change of models
1
Mb
B
Mf
B
Mi
Mb
Reasoning for the change
Modified Bohr’s Model
included the different
orbital shapes in Bohr’s
Model
Mf
Modified Bohr’s Model
included the different
B
3/2
1
B
B
orbital shapes in Bohr’s
Model
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
KT
Table 4.18: Analysis of student mental models as represented by MK’s and KT’s postinterview responses.
4. 3. 1. 4. Bohr’s model (B) and level of understanding (3/3)
In the developmental history of electronic atomic theory, Bohr developed his
orbital structure by applying the concept, “energy quantization” in order to explain
observations from line spectra. At this level of understanding, a student understands the
atomic structure of Bohr’s model and a student understands orbitals by relating the
concept, “energy quantization,” from quantum theory. In addition, a student can apply
this structure to analyze line spectra for hydrogen and helium. There was no student in
Group 2 whose model of atomic structure was coded at the 3/3 level of understanding.
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4. 3. 1. 5. Quantum model (Q) and levels of understanding (4/1, 4/2, 4/3, 4/4, and
4/5)
According to Table 3.9, a student having the Quantum model understands that an
electron doesn’t orbit on a set path. Student models coded as the Quantum model were
divided into five different levels (4/1 through 4/5) depending on the degree of
understanding of quantum theory related to atomic structure. Table 4.19 displays the
criteria for analyzing student mental models of atomic structure for the Quantum model
and levels (4/1, 4/2, 4/3, 4/4, and 4/5) of understanding.
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Level of
understanding
Criteria for Evaluating Levels
4/1
A student arranges electrons not on a set path but within
a certain area (or electrons within orbitals).
4/2
A student describes electrons in terms of or consistent
with the meaning of probability.
4/3
A student understands about different types and shapes
of orbitals (separate models for orbitals and atoms).
4/4
A student understands the different types and shapes of
orbitals (a combined or modified model for orbitals and
atoms).
4/5
A student understands the basic idea of quantum theory
(probability, wave function, and energy quantization)
and the modern picture of the atom and explains the
atom in terms of particles or waves.
A student explains the concept of probability and
orbitals in terms of quantum theory and integrates both
concepts into atomic structure.
Atomic
Model
Quantum
model
(Q)
Table 4.19: Criteria for analyzing mental models of atomic structure by levels of
understanding, 4/1, 4/2, 4/3, 4/4, and 4/5 for the Quantum model.
Figures 4.9 and 4.10 represent student models of atomic structure coded as the
Quantum model at the 4/1 level of understanding. At this level, a student arranges
electrons not on a set path of Bohr’s model but within a certain area defined as an orbital.
However, there is no indication that the student understands the concept of probability
for finding electrons related to quantum theory.
First, Figure 4.9 and the following text were taken from CE’s responses during
the post-interview. Her atom is represented by the nucleus, “just like a ball cluster,” and
109
electrons within 3-D spherical shape orbitals. “The sphere that holds the electrons” is
how she conceptualized the orbitals. CE described an orbital as a space for electrons,
which is identified as the Quantum model; however, in her model of atomic structure,
there was no indication of understanding the concept of probability for finding electrons
related to quantum theory. Three dimensional spherical models of an atom were
described in detail by using the example of fluorine and hydrogen in Figure 4.9, and by
using the analogy of a “donut ball” for the 1s orbital, inner sphere, and a “3-dimensional
donut” for the second 2s/2p orbital, outer sphere without the center ball.
Note: CE’s diagram during the post-interview
Figure 4.9: Example of student (CE) post-interview diagrammatic description of
atomic structure of the Quantum model at the 4/1 level of understanding
R: O.k. about an atom, could you describe it?
CE: This is the nucleus, and these are, that’s my picture of neutron, that’s a proton. It’s just like
a ball cluster. And then, you got this and this. And like, um…depending on what kind of atoms
it is, it is how many electrons and protons. So like this without these extra layers would be
110
helium and then, here, you have two more for the s and then, I don’t even know what the next.
What’s the next halogen? (See Figure 4.9)
…
R: What is this?
CE: Fluorine.
R: When I ask you what an atom looks like, is it like this? Is this in your mind?
CE: Um. Yes, this, but in 3-D, like I showed you before.
…
R: These two electrons, are these in this figure?
CE: Yes, here and here. That’s the 1s and we got the next orbital. (See Figure 4.9)
R: the same 3-D spherical shape?
CE: Umhum… And then this is 2s and 2p. 1, 2, 3, -7…
…
R: You mentioned an orbital, then, what is an orbital?
CE: It’s the sphere that holds the electrons.
…
R: Then, do you have two spheres?
CE: Yes, it’s like a donut ball and like a 3-dimensional donut. (Figure 4.9)
Also at the 4/1 level of understanding, there were students who demonstrated
mixed models with separate models for orbitals in addition to the Quantum model.
Although same students demonstrated the Quantum model at the 4/1 level of
understanding related to the question of orbitals, they explained or described atomic
structure consistent with the Bohr’s model or Bohr’s orbital structure. Figure 4.10
displays the mixed model, Quantum (Bohr) model or Q(B). VB’s model from the postinterview in Figure 4.10a. and HJ’s model from the post-interview in Figure 4.10c.
represent examples of the Quantum model in the 4/1 level. Figure 4.10b. and Figure
4.10d. were taken from two student (VB and HJ) post-interview responses as
descriptions for orbitals, respectively. The following text was excerpted from VB’s postinterview responses.
111
a.
b.
c.
d.
Note: a. VB’s diagram of an atom during the post-interview, b. VB’s diagram of
orbitals during the post-interview, c. HJ’s first diagram of an atom during the postinterview, d. HJ’s second diagram of an atom during the post-interview
Figure 4.10: Example of students (VB and HJ) post-interview diagrammatic
descriptions of atomic structure of the Quantum (Bohr) model at the 4/1 level of
understanding
R: what can you see?
VB: Oh, yes. Just a bunch of like, nucleus and bunch electrons, they are all kind of related to
each other. (See Figure 4.10a.)
…
R: This is a nucleus, (yes), then, keep going…
VB: Um, I don’t know what else is to say about it. Because electrons travel in orbitals. Except
orbitals depend on how heavy the nucleus is. So like, if it’s really heavy, they’re going to be
really small because the gravity pulls in, the gravity of the nucleus.
…
R: Could you explain the orbital again?
112
VB: That’s just levels at the electrons.
R: levels of what?
VB: the energy levels…
R: what do you mean by the energy level?
VB: That’s a really hard question. I think, I don’t know … I think that’s how many like… once,
it’s kind of like since there are six now, they all pull each other up to this orbital. So it’s like,
you can have five like here, go on till sixth one throw in. They all move up here. (See Figure
4.10b.)
…
VB: Because they can… It has to do with like reactivity or like what will react with. Like this,
you can’t…. The five electrons, they gets one when the atoms are stable, so it’s not stable if it
has not standing on stable stair.
…
R: Then, why do we need orbitals?
VB: To be able to explain it to somebody else how the electrons bond with other atoms.
To the question relating to orbitals, VB addressed “energy levels” to explain
orbitals: “that’s just levels at the electrons” and “the energy levels…” However, there
was no indication of understanding the meaning of “energy level” based on quantum
theory. To the question asking the meaning of “energy level”, she responded as “I don’t
know” and then, she related the concept to reactivity. Diagrams and verbal explanations
support the existence of Bohr’s model as her mental model for orbitals. Concerning the
existence of and relationships between two models, VB’s mental models were coded as
Quantum (Bohr) model or Q(B) at the 4/1 level of understanding. By relating orbitals to
energy levels and stability for reaction, VB expressed her understanding of atomic
structure by locating electrons within orbitals as the Quantum model and including the
concept of energy levels by using the analogy of stairs consistent with Bohr’s model.
According to VB’s model, when an atom does not have a “complete number of
electrons,” electrons stay in orbitals like Figure 4.10b. and the instability leads to a
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reaction or bonding with other atoms. When an atom has the “complete number,” which
is 6 electrons by her description, it stays on the orbitals and there will be no reaction like
Figure 4.10a.: “you can have five like here, go on till sixth one throw in, they all move
up here.” Figures 4.10c. and 4.10d. display HJ’s Quantum (Bohr) model or Q(B) at the
4/1 level of understanding. Figure 4.10c. represents HJ’s Quantum model with randomly
moving electrons in orbitals and Figure 4.10d. represents HJ’s orbital structure indicating
Bohr’s orbital structure.
CE’s post-interview responses were analyzed as the Quantum model (Q) at the
4/1 level of understanding and VB’s and HJ’s post-interview responses were analyzed as
the Quantum model with Bohr’s orbital structure or Q(B) at the 4/1 level of
understanding. Table 4.20 displays the summary of the analysis of student mental models
as represented by CE’s, HJ’s, and RZ’s post-interview responses.
114
Coded
name
Mental model of
atomic structure
SM
LU
Number of
models for
an atom
Post
CE
Q
Mi
4/1
1
Post
HJ
Q(B)
Change of models
Q
Mi
4/1
2
Post
Mb
B
Mi
Mf
Q
Mb
Modified orbitals as 1s, (2s, 2p),
(3s, 3p, 3d), 4s
Mf
Q
Mb
Reasoning for the change
To explain number of electrons,
used Bohr’s orbital structure,
but then, explained freely
moving electrons for atomic
structure of Quantum model
Mf
Modified Quantum model
included Bohr’s orbitals and
stability concept
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf= final mental model of atomic structure.
VB
Q(B)
4/1
2
Q
B
Q(B)
Table 4.20: Analysis of student mental models as represented by CE’s, HJ’s, and VB’s
post-interview responses.
4. 3. 1. 6. Quantum model (Q) and level of understanding (4/2)
At the 4/2 level of understanding, a student arranges electrons not on set paths of
Bohr’s model but within certain areas defined as orbitals. In addition, a student describes
electrons and orbitals, in terms of or consistent with, the meaning of the probability of
finding electrons. Related to the probability description, students at this level often
provide explanations about the Uncertainty Principle. The following text was excerpted
from TK’s pre-interview responses. TK’s atomic structure was described by her as “a
115
marble in the middle and then, just like, just kind of a field around it” and she explained
the field as orbitals, areas where randomly moving electrons can most likely be found.
Figure 4.7 represents an example of student models of atomic structure coded as the
Quantum model at the 4/2 level of understanding. Figure 4.11a. shows TK’s Quantum
model representing the concept of probability for finding electrons. Randomly moving
electrons in orbitals were displayed as arrows in Figure 4.11b.
R: Could you describe an atom?
TK: In my mind, I’m a very visual person, so like I like to see things, so if I were looking at this,
I will like to think that, it is the same color. I like to think of it just like as a tiny little grain seed,
I would say it’s a lot smaller. Kind of like what I think of it …
…
R: What is it?
TK: This is a real dense part and then this is kind of where the electrons are floating around. Put
that in my mind, that’s an atom.
R: Are there specific things here in your mind?
TK: I picture it as a sphere, yes, like a dense sphere.
R: what do you mean “dense sphere”?
TK: Like a marble, a marble in the middle and then just like, just kind of a field around it. Kind
of like where electrons are going. That’s always, I picture in my mind.
…
R: What is this? (pointing to the area around the dense nucleus in Figure 4.11a. and Figure
4.11b.)
TK: This is the area in… I can’t remember what this is called. This is the area which the
electron can be, it doesn’t actually like orbit. It just can be most likely found in this area.
R: You mean the area of what?
TK: Where the electron can be found.
…
R: What does the structure of an atom look like to you?
TK: There are lots of electrons like they are just, it will have more orbitals, more electrons
floating around randomly.
116
a.
b.
Note: a. TK’s diagram of an atom during the pre-interview, b. TK’s diagram of electrons
during the pre-interview
Figure 4.11: Example of student (TK) pre-interview diagrammatic descriptions of atomic
structure of the Quantum model at the 4/2 level of understanding
TK’s pre-interview responses were analyzed as the Quantum model (Q) at the 4/2
level of understanding. Table 4.21 displays the summary of the analysis of student
mental models as represented by TK’s pre-interview responses.
117
Coded
name
Mental model of
atomic structure
SM
LU
Number of
models for
an atom
Pre
TK
Q
Change of models
Mi
4/2
1
Q
Mb
Reasoning for the change
Mf
Q
Atomic structure concerned
the probability for finding
electrons
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
Table 4.21: Analysis of student mental models as represented by TK’s pre-interview
responses.
4. 3. 1. 7. Quantum model (Q) and level of understanding (4/3)
In the 4/3 level, a student understands the concept of probability for finding
electrons in the Quantum model and a student understands different types or shapes of
orbitals. However, the student is not able to construct the atomic structure including the
different shapes of orbitals as an atom. The following text was excerpted from CZ’s postinterview responses.
118
a.
b.
Note: a. CZ’s diagram of an atom with s orbitals during the post-interview, b. CZ’s
diagram of an atom with p orbitals during the post-interview
Figure 4.12: Example of student (CZ) post-interview diagrammatic descriptions of
atomic structure of the Quantum model at the 4/3 level of understanding
R: Do you mean, with this (referring to wave function for an s orbital), you can explain this
(Figure 4.12a.), and this (referring to wave function for a p orbital), you can explain this (Figure
4.12b.)?
CZ: Right, right, that you can you know, you have…
R: Separately?
CZ: Right, with this, it’s fairly easy to put them together, but with this, I mean you can look at a
wave function for something like this, but it’s not necessarily as clear as something like this. But
it’s more…it’s easier to think of this 3-dimensionally, and then you know, if you are bonding
this with something else, um … then, you can … you know, if you are bonding this with, say
another element that has an outermost, the outermost orbital is p orbital. You know, you can
look at the way that it’s going to have to be turned or twisted, so it fits to make correct bonding.
So, I guess, this is better. I guess with the s orbital, like we are talking about is a better way to
describe … what the orbitals look like and what the individual atom would look like, but then,
you get into more complicated structures. It’s better to describe what say a molecule has a whole
is going to look like because it’s just kind of complicated list for me, right now, to um … to kind
of correlate the, you know, like we talked about having an s, you know having 1s and 2s orbital.
R: then, what do you think about these two different diagrams as atomic structure?
CZ: I guess, the way I kind of think of… it is still… … … where you can take, you can still take,
say, you can still translate it and as 3 dimensional sphere, but now, it gets really difficult to draw
where the probabilities are. Because you know, this is going to translate. You could translate
this in a 3-dimensional sphere. If you wanted to, and just you know, shade the probability,
where the probability is highest. But then, you go ahead, you add that to it is where it gets
almost beyond my artistic ability to go ahead and draw that for you. Um … But you are going to
119
still have something that looks similar to this. Where you could still look at it and tell from, you
know the shading, where the electrons are most likely to occur. Um … but it’s going to be a
much more complicated geometry.
R: more complicated geometry, is it a totally different shape or kind of combined one including
s, p orbitals?
CZ: I’m not sure how you could draw that. I don’t…
R: do you think it should include the information?
CZ: Right … there should be someway to kind of put down where the electron, because things
in books, you know, they show you this and they show you wave functions and they describe
nodes, where there is, you know, there is no… probability of electrons.
Figure 4.12 represents student models of atomic structure coded as the Quantum
model at the 4/3 level of understanding. As can be seen in the two separate diagrams in
Figure 4.12 and the verbal descriptions during the post-interview, CZ constructed atomic
structure with s orbitals and with p orbitals separately. Both models indicated that CZ
understands the concept of probability for finding electrons related to quantum theory
(the term “probability” was addressed during the interview); however, he thought that
atomic structure would be more complicated and be beyond his artistic ability. Although
CZ didn’t develop a model combining the two orbitals for an atom, he predicted the
possibility of a complicated geometry for atomic structure: “there should be someway to
kind of put down where the electron is.” CZ’s post-interview responses were analyzed as
the Quantum model (Q) at the 4/3 level of understanding.
Table 4.22 displays the summary of the analysis of student mental models as
represented by CZ’s post-interview responses.
120
Coded
name
Mental model of
atomic structure
SM
LU
Number of
models for
an atom
Post
CZ
Q
Change of models
Mi
4/3
1
Mb
Q
Reasoning for the change
Mf
Q
Orbitals and an atom as
separate pieces of pictures,
not as a combined form:
showed s, p orbitals
separately as an atom
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
Table 4.22: Analysis of student mental models as represented by CZ’s post-interview
responses.
4. 3. 1. 8. Quantum model (Q) and level of understanding (4/4)
Figure 4.13 represents student models of atomic structure coded as the Quantum
model at the 4/4 level of understanding. In this level, a student understands the concept
of probability for finding electrons in the Quantum model and a student understands
different types or shapes of orbitals. In addition, the student constructed a model for an
atom by considering the different shapes of orbitals in atomic structure. In order to
explain the probability concept of finding electrons, she used the analogy of an Ohio
state map and her location (Figures 4.13b. and 4.13c.).
TK: like here is Ohio, you could say, I can most likely be found here which is my home or here
where I go to school just, that just is an idea where I could be found.
121
As can be seen in the diagram in Figure 4.13a., TK constructed her own atomic
structure combining different shapes of orbitals in an atom: “I know about the different
orbitals and shapes.” The description indicates that TK understood the probability
concept for finding electrons in orbitals and the different shapes of orbitals. In addition,
she constructed one atomic structure representing her understanding of the concept of
orbitals related to atomic structure and quantum theory. Moreover, TK constructed the
model by considering the potential effect of “repulsion” that is caused by electrons
within orbitals. Figure 4.13d. and Figure 4.13e. illustrated RZ’s atomic structure at the
4/4 level of understanding. In a similar way, RZ developed his own atomic structure at
the 4/4 level by combining all information that he apparently learned during the
chemistry course. Figure 4.13d. explains more about the concept of probability with
dotted lines. Figure 4.13e. was created to explain different shapes of orbitals for atomic
structure. TK and RZ revealed similar ways of understanding atomic structure. The
following text was excerpted from TK’s post-interview responses.
122
a.
b.
d.
c.
e.
Note: a. TK’s first diagram of an atom during the post-interview to explain the probability of
finding electrons and the different shapes of orbitals, b. TK’s second diagram of an atom
during the post-interview to explain the probability of finding electrons, c. TK’s diagram of
Ohio map analogy during the post-interview to explain the probability concept, d. RZ’s
diagram of an atom during the post-interview to explain the probability of finding electrons
and the different shapes of orbitals, e. RZ’s diagram of an atom during the post-interview to
explain the different shapes of orbitals
Figure 4.13: Example of students (TK and RZ) post-interview diagrammatic
descriptions of atomic structure of the Quantum model at the 4/4 level of
understanding
123
R: Do you mean that there were not many changes in your structure of an atom?
TK: Yes. Like I know about the different orbitals and shapes, I didn’t learn about the shapes
before, but um … basically the pictures are same.
R: Then can I see your picture again?
TK: o.k. we just have um… this is solid nucleus, but it actually has like for helium, two neutrons
and two protons. Very condensely packed and this is where most electrons are.
…
R: So, you are showing me a sphere.
TK: Yes. And this is where the two electrons are most likely to be found.
…
R: Then what is this sphere? I can see electrons, neutrons and protons. And what is this shaded
area?
TK: Um… it’s just like an electrical field.
R: what is the electrical field?
TK: I don’t know how to explain it. um … this is something where electrons are kind of they are
drawn to like the positive nucleus, so they just tend to go around.
R: Do you think there is something, not the real…
TK: It’s an idea pretty much. Like it is there, but it’s not something tangible like nucleus.
Nucleus is something tangible. Like the electrons are whole lot smaller, they don’t have nearly
as much as the masses in protons and neutrons, but like still kind of there, just like different…,
this orbital is something so we locate electrons, you know.
R: Do you mean that it’s kind of location?
TK: Yes.
R: Do you mean, kind of an area, not real something … can electrons be found here?
TK: Like here is Ohio, you could say, I can most likely be found here which is my home, or
here where I go to school just, that just is an idea where I could be found.
R: Maybe you can be found in Ohio, so this is the area…
TK: Where electrons could be found
…
R: You mentioned orbitals, what is it?
TK: Orbitals are just um, how can I say … how to explain… just um… They have
different shapes…
TK’s and RZ’s post-interview responses were analyzed as the Quantum model
(Q) at the 4/4 level of understanding. Table 4.23 displays the summary of the analysis of
student mental models as represented by TK’s and RZ’s post-interview responses.
124
Coded
name
Mental model of
atomic structure
SM
LU
Number of
models for
an atom
Post
TK
Q
Mi
4/4
1
Post
RZ
Q
Change of models
Q
1
Mf
Q
Mi
4/4
Mb
Q
Mb
Reasoning for the change
Constructed a model
combining different shapes of
orbitals as an atom
Mf
Q
From probability, constructed
a model combining different
shapes of orbitals as an atom
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
Table 4.23: Analysis of student mental models as represented by MK’s and RZ’s postinterview responses.
4. 3. 1. 9. Quantum model (Q) and level of understanding (4/5)
At this level, a student understands the basic idea of quantum theory (probability,
wave function, and energy quantization) and the modern picture of the atom and is able
to explain the atom in terms of particles and waves. The following text was excerpted
from LJ’s post-interview responses. LJ explained electron distribution or electron density
in terms of probability for finding electrons within certain areas. He used “photo snap
shot” analogy to explain the certain area and probability. This indicates that he developed
the Quantum model that explains the probability concept of finding electrons for orbitals
based on quantum theory.
125
R: Then, what is a nucleus?
LJ: I mean where the protons and neutrons are. The location would be, the middle, they are kind
of located in an almost like a sphere with this sphere. This would be the center.
R: Do you mean that is in the center of the sphere?
LJ: Um…not exactly sphere, but you know, it’s easy to think that way. And then this would just
be electron distribution.
R: Then, what about this line? Is this a real line?
LJ: No. but I mean that’s like, where you are most likely to find. It’s kind of the same concept as
I was talking about before. Like the atoms, electron cloud like, we have to draw line somewhere,
you know. It is most likely there.
R: o.k.
LJ: This would be like, this would be like time left photo instead of snap shot. You know, so I
think. … … If we are taking a snap shot, if we are possible to know the exact location of
electrons, it would be most likely all the electrons we can find would be within this area that we
drew.
LJ defined orbitals as “a kind of description of the probability” of where electrons
can be found or “electron density.” In addition, he added detailed explanations about the
mathematical representation of wave function and the shapes of orbitals or an atom.
Figure 4.14 is the graphical representation of his reasoning process for constructing
shapes of s orbitals from wave function. The concept of Pauli’s exclusion principle and
wave/ particle duality were mentioned. The concept of energy quantization related to
orbitals also was addressed. Figures 4.14 represents student models of atomic structure
coded as Quantum model at the 4/5 level of understanding.
R: what is an orbital?
LJ: Orbital is just, you know, the, it’s kind of the path that the electrons take, but not…
R: the path? Is it different meaning with your explanation of the electron density?
LJ: It’s, the orbital is really kind of just like a … How would you say, it’s kind of description of
the probability of where … probably be … It’s not necessary their path, you know what I mean?
126
Note: LJ’s diagram of atomic structure related to wave function
during the post-interview
Figure 4.14: Example of student (LJ) post-interview diagrammatic descriptions of
atomic structure of the Quantum model at the 4/5 level of understanding
Figure 4.14 and the following text shows LJ’s Quantum model descriptions for
orbitals using the wave function of the probability for locating electrons and their
distance from the nucleus. The probability was explained in detail by using an example
with percentage of the area under curve of a graph.
R: then, do you think both of the electron density and the orbital as the same meaning?
LJ: um…yes, I could say pretty much. I mean the orbital would be like a description of where it
would be likely. A large chance in that orbital would be most concentrated, I think or likely to
be found.
R: then, what does the p orbital mean?
LJ: The p orbital, the p, I mean just describing certain shape of this, you know, this wave
function. (See Figure 4.14)
R: what is the wave function?
LJ: um…what is wave function…. I know you’re probably asking it to wrong person. But I
think it’s just a mathematical explanation of the shape of the orbital, I’d say.
…
127
LJ: I guess it may be like that. And this is like the density. You know? So, as related to distance
from, I think it’s distance. (See Figure 4.14)
R: from?
LJ: from the nucleus, from the center, the nucleus, I don’t know.
R: then, do you mean that this origin (0, 0) is the position of the nucleus?
LJ: right.
R: then, the distance from here or here, what does this mean in an atom? And what does this and
that axis mean?
LJ: this would be what, o.k…..so let’s…. I mean this would be…..um….this would be the
probability of finding an electron. And this would be distance from nucleus, you know. The
farther you are away the less they will affect. That you will find.
…
R: About this mathematical representation of the wave function, could you explain more about
these two of this function and orbitals?
LJ: I mean like, for example, we pick the spot where like, if we….under this curve, we could
say what’s 90% of the area of this curve, 80% of something… O.K. Let’s say it’s here. This
represents 80% area. This distance right here would be this distance right here.
R: so do you mean that most of electrons are distributed here?
LJ: Right.
R: and then decreases like this graph?
LJ: and decreases, you know, I mean, infinity of course.
R: infinity?
LJ: yes.
With regard to quantum theory, LJ explained the concept of “energy
quantization” by using the analogy of the units of money or steps: “it can only come in
certain chunks” and “kind of walking on steps.”
LJ: I mean, because basically, because this sphere is not representing individual atom, it’s
representing the overall, you know, because this, say this is, you know, 1s, say it’s2. I mean, so
we got 2 electrons, we’ll maybe like….
R: why 2 electrons?
LJ: why 2 electrons? Because of whatever who’s ever theory say that you can have 2 electrons
in….I don’t know… because they are about to spin…
R: what do you mean by ‘spin’?
LJ: the electrics, the opposite, they are rotating, I don’t know.
R: What do you mean by rotating?
LJ: um…if you think of it, like the earth something like spherical particles
R: So, do you think electrons as spherical particles?
128
LJ: In this case, yes. I mean, you really can’t look at it as either one or the other. To our best
understanding, it has properties of both a wave and a particle. You know, it’s a wave particle.
R: In this case?
LJ: I mean I think that would make sense because it would be kind of hard to explain spinning
based on a wave, um…. You know. But then, it would be kind of hard to explain distribution
based on just two particles, you know, they can’t be everywhere at once, but the more we learn
about, you know, like molecular orbital theory and hybridization, they kind of are, you
know….I mean they are moving so fast who to say where exactly they are, so.
R: 1s, 2p, 3p… then, what do you mean with the number, 1, 2, and 3?
LJ: The one, that’s just the quantum energy level.
R: what do you mean ‘quantum energy level’?
LJ: it just well, I mean, before the quantum theory, energy is quantimized…I don’t know exact
word…
R: quantized?
LJ: Quantized, yes. Quantized.
R: what do you mean “quantized”?
LJ: it means it can only come in like certain chunks, you know what I mean? There is no like,
kind of walking on steps. You know. Either on step 1 or step 2, you can’t like, nothing in the
middle.
R: what is this step for? Could you explain more?
LJ: Like…like a…think, I mean think about money, I mean if you buy something, you know,
o.k. you can spend a dollar, you can spend 50 cents, um, but when you get down into the
smallest amount of money that you can spend. Any one time is a penny. Because you can’t
break a penny into further, you know, smaller money. So, I mean, this would be like, for
example, we are talking here 1, 2, 3, we are talking about energy, for example, the energy
R: you mean quantized chunk of energy?
LJ: right, so this is, you know, I don’t know, I don’t know the exact mathematics behind it. I
mean I don’t think like the two quantum level is exactly twice the one. I don’t think that’s the
case. Anyway, you’re either 1, either 2, or either 3…
R: but do you mean the energy is different by the number?
LJ: sure, sure. If we have 1s and 2s, 2s has higher energy.
As can be seen in the diagram of Figure 4.15, LJ first, explained the concept of
the probability of finding electrons by relating orbitals and then, constructed his own
atomic structure by combining different shapes of orbitals as an atom as previously was
described in TK’s and RZ’s diagrammatic representations. LJ was able to explain the
shape of orbitals by interpreting the mathematical and graphical meaning of the wave
function. Moreover, he extended his model by applying the concept “hybridization of
129
orbitals.” Figure 4.15 represents LJ’s atomic structure as further developed by
considering hybridization of s and p orbitals. “sp hybridization” which was explained in
detail by using representations of the wave function.
Note: LJ’s diagram of atomic structure considering hybridization of
s- and p-orbitals in the post-interview responses
Figure 4.15: Example of student (LJ) post-interview diagrammatic descriptions of atomic
structure of the Quantum model at the 4/5 level of understanding
R: Then, is it together? O.k., then, if I have, maybe, 16 electrons, how can you draw the atomic
structure of the 16 electrons?
LJ: basically, I mean, I think for what I’ve learned so far, the most clear explanation is with the
molecular orbital theory. Um…that will just basically be taking, you take this 3-d
representations to figure out all the 3-d representations of these, you know, all the orbitals are
included and I know it probably better to put them on the computer. You know and like to put
them together and then, I guess, according to like molecular orbital theory, like theory which
one was combined to form hybrid orbitals and then, that will change the shape of
the…eventually…
R: how?
LJ: well, I mean sometimes like, I mean, combine and there is, you know, two waves…
R: combining what?
130
LJ: we are combining two or more orbitals….um…and their overall shape, you know, just
distribution of electrons will….
R: how?
LJ: um…like for example, um….that would be a good example…um…I don’t know…
um…like….I mean like symbol like sp hybrid orbital is basically accommodation of s and p.
You know, so if you look at the wave functions, you know, I mean, like where you got to here is
let’s say, um…you know…this is 1…um….. this is the s….
R: you mean combining wave function?
LJ: right, right. And this is, you know, this is like the….I don’t know. I don’t know how I can
do this p orbital, right? this is like…
LJ’s post-interview responses were analyzed as the Quantum model (Q) at the 4/5
level of understanding. Table 4.24 displays the summary of the analysis of the student
mental models as represented by LJ’s post-interview responses.
Coded
name
Mental model of
atomic structure
SM
LU
Post
Number of
models for
an atom
Change of models
Mi
Mb
Reasoning for the change
Mf
Constructed a model
combining different shapes of
Q
4/5
1
Q
Q
orbitals as an atom and then,
considered hybridization of s
& p orbitals
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
LJ
Table 4.24: Analysis of student mental models as represented by LJ’s post-interview
responses.
131
4. 3. 1. 10. The summary of the analysis of student mental models of atomic
structure from interviews
The pre- and post-interview analysis of scientific models and levels of
understanding in Table 4.25 includes 20 students. Of these 20 students, 5 had only preinterview data. This table includes student mental models of atomic structure, number of
models representing atomic structure, changes of models during interviews, and
reasoning for the changes.
132
Coded
name
Mental model of
atomic structure
SM
LU
Number
of
models
Pre
B
KF
Mi
3/1
1
Post
B
1
Pre
EJ
4/1
2
Post
Pre
Q(B)
4/1
2
Mb
B
Mi
3/1
Q(B)
Change of models
Mf
B
Mb
B
B
3/2
1
B
Made modification of orbital
names, not shapes, arrange orbitals
by the order of (1s), (2s, 2p), (3s,
3p, 3d)
Pre-only
Mi
Mb
Mf
Q
B
Q(B)
Mi
Mb
Mf
Mi
Mb
Mf
Q
B
Q
Mi
Mb
Mf
Pre
Q(B)
CE
4/1
2
Post
B
Bohr’s model
Mf
MK
Post
Reasoning for the change
B
Mi
Mb
Mf
Q
B
Q
Mi
Mb
Mf
Quantum model with Bohr’s orbital
structure
Electrons on a path as Bohr’s
orbitals, then back to randomly
moving electrons
Modified Bohr’s model included
the different orbital shapes in
Bohr’s Model
Include Bohr’s orbital structure, but
not clear
Modified orbitals as 1s, (2s, 2p),
(3s, 3p, 3d), 4s
Note: SM=scientific model. LU=levels of understanding. Mi=initial mental model of atomic
structure. Mb=between mental model. Mf=final mental model of atomic structure.
Q
4/1
1
Q
Q
Continued
Table 4.25: The analysis of student mental models of atomic structure as represented in
the pre- and post-interview responses.
133
Table 4.25 continued
Pre
Q
WT
Mi
4/4
1
Post
Q
1
Pre
SJ
B
1
Post
Pre
KT
1
Post
3/2
1
Pre
Q
Mb
Mb
Mi
3/1
B
Mb
B
Mi
1
Mf
Q
Constructed a model combining
different shapes of orbitals as an
atom
Mf
Pre-only
B
Bohr’s model
Mf
B
B
Mi
Mf
B
B
Q
4/5
1
Bohr’s model
Modified Bohr’s model included
the different orbital shapes in
Bohr’s model
Mf
Q
Q
Mi
Mf
LJ
Post
Constructed a model combining
different shapes of orbitals as an
atom, but not clear at this stage
Mf
Mi
4/5
Mf
Q
Q
Mi
3/1
B
Q
Mi
4/5
Mb
Q
Q
From probability, constructed a
model combining different
shapes of orbitals as an atom, but
not clear at this stage
Constructed a model combining
different shapes of orbitals as an
atom and then, considered
hybridization of s & p orbitals
Continued
134
Table 4.25 continued
Pre
B
RZ
Mi
3/1
1
Post
Q
1
Pre
MD
Q
1
Mb
Q
Mf
Q
From probability, constructed a
model combining different
shapes of orbitals as an atom
Mf
Pre-only
Q
Mi
Mb
Mf
Pre
Mi
Mb
Mf
4/2
Q
1
4/3
Q(B)
Q
Mi
1
Pre
4/3
2
4/3
1
Q
Mb
Q
Mi
Post
Q
Mb
Post
Post
BM
Mf
B
Q
Mi
4/3
Q
CZ
B
Mi
4/4
Mb
Mf
Q
Mb
Orbitals and an atom as separate
pieces of pictures, not as a
combined form: showed s, p
orbitals separately as an atom
Mf
Q
B
Q(B)
Mi
Mb
Mf
Q
Understand the concept of
probability
Q
No combined picture and had
separate pictures for an atom and
different shapes of orbitals, still
had Bohr’s orbital structure
From probability, constructed a
model combining different
shapes of orbitals as an atom, but
not clear at this stage
Continued
135
Table 4.25 continued
Pre
Q(B)
Mi
4/2
2
Post
LT
Q(B)
4/4
2
Pre
Q
TK
4/2
1
Post
Q
1
Pre
2
Post
HJ
Q(B)
Q
Q
Mi
Mb
Mf
B
Q
Q(B)
Mi
Mb
Mf
Q
Q
Mb
Q
4/1
2
Mb
Bohr’s Model as simple
representation, and then,
addressed different orbital
shapes, tried to construct a
model combining different
shapes of orbitals as an atom,
but not clear
Atomic structure concerned
the probability of finding
electrons
Constructed a model
combining different shapes
of orbitals as an atom
Mf
Q
B
Q(B)
Mi
Mb
Mf
B
Electrons in path like orbits
(related to the solar system)
and then, randomly moving
electrons
Mf
Q
Mi
4/1
Mf
B
Mi
4/4
Q(B)
Mb
Q
Modified the Quantum
Model by putting electrons
on a path- like circle within
orbitals
Explained number of
electrons, using Bohr’s
orbital structure, but then,
explained freely moving
electrons for atomic structure
of the Quantum Model
Continued
136
Table 4.25 continued
Pre
TH
B
Mi
3/1
Mb
B
Mf
Pre-only
B
Bohr’s model
Post
Mi
Mb
Mf
Pre
Mi
Mb
Mf
B
3/1
2
Q
B
B
Mi
Mb
Mf
BJ
Post
B
3/1
1
Pre
HD
B
B
Mi
3/1
Mb
B
B
Modified Bohr’s model, name
Bohr’s orbitals by the order of
1s, 2s, 2px, 2py, 2pz, …
Mf
Pre-only
B
Bohr’s model
Post
Mi
Mb
Mf
Pre
Mi
Mb
Mf
Q
B
Q
Mi
Mb
Mf
Q
B
Q(B)
Mi
Mb
Mf
P
B
P(B)
Mi
Mb
Mf
Q(B)
4/1
2
VB
Post
Q(B)
4/1
Pre
KC
P(B)
1/2
Post
B
3/1
2
B
B
137
First showed electrons
surrounding nucleus within a
membrane, but by responding to
orbitals, showed Bohr’s model
Explained orbital as a path of
electrons and then changed to no
path
Modified the Quantum model by
including Bohr’s orbitals and
stability concept
Atom as a particle shape, but
used Bohr’s model for orbitals
Bohr’s model
4. 3. 2. Changes of mental models of atomic structure
Changes in student mental models describe student conceptual development for
understanding atomic structure and learning processes for constructing their own models
of atomic structure. Data were analyzed by two criteria: four scientific models and 13
levels of understanding of atomic structure. According to the framework in Table 3.9,
interview responses from 20 students in Group 2 were analyzed. Because 5 students did
not participated in the post-interview, pre- and post-interview responses from 15 students
were compared in detail.
Table 4.26 compares the number of student mental models of atomic structure for
students with both pre- and post-interview responses by scientific models.
Scientific Model
P
P(B)
N
B
Q(B)
Q
Total
Number of student models
in the pre-interview
0
1
0
4
6
4
15
Number of student models
in the post-interview
0
0
0
5
3
7
15
Note: P=Particle model. P(B)=Particle model with Bohr’s orbital structure. N=Nuclear model,
B=Bohr’s model. Q(B)=Quantum model with Bohr’s orbital structure. Q=Quantum model.
Table 4.26: Number of student mental models of atomic structure for students with preand post-interview responses by scientific models.
138
As can be seen in Table 4.26, for the Quantum model which is considered to be
the instructor’s model and the model to be targeted and learned in this chemistry course,
the comparative analysis shows an increased number of students (from 4 or 27% to 7 or
47%) who developed the Quantum model by the end of the course. There were also a
number of students who had mixed models with two models such as the Particle model
with Bohr’s orbital structure P(B) and the Quantum model with Bohr’s orbital structure
Q(B). This number from the pre-interview to the post-interview responses decreased
from 7 or 47% to 3 or 20%. As can be seen from the data in Table 4.26 and Figure 4.16,
4 students showed Bohr’s model in their pre-interview responses and the number
increased to 5 in the post-interview responses. Concerning the single and mixed models
involving Bohr’s models, the number of student models influenced by Bohr’s model
changed from 11 or 73% to 8 or 53%. Although the number decreased in the postinterview responses, this study shows a persistent influence of Bohr’s model on student
mental models of atomic structure. The comparison of pre- and post-interview response
for atomic structure is displayed in Figure 4.16.
139
Student Models from Interview responses
by Scientific Model
8
Number of Students
7
6
5
4
3
2
1
0
P
P (B)
N
B
Q (B)
Q
Scientific Model
Pre-Interview (by model and with 15 students)
Post-interview (by model and with 15 students)
Figure 4.16: Number of student mental models of atomic structure from the pre- and
post-interview responses by scientific model
Student responses to the pre- and post-interviews were coded by levels of
understanding of atomic structure (See Table 3.9) and then, the number of students at
each level was counted and compared in Table 4.27. The 13 levels reflect the hierarchical
order of the concept “atomic structure.” From the 15 students in Group 2 who
volunteered for and participated in the pre- and post-interviews, there were no students
whose mental models of atomic structure were coded at the 1/1, 2/1, 2/2, 2/3, and 3/3
levels of understanding. Because of this situation, those levels are not displayed in Table
4.27.
140
Level of
Understanding
1/2
3/1
3/2
4/1
4/2
4/3
4/4
4/5
total
Number of students
in pre-interview
1
4
0
4
3
1
1
1
15
2
15
Number of students
0
3
2
3
0
2
3
in post-interview
Note: the levels 1/1, 2/1, 2/2, 2/3, and 3/3 are not displayed in this Table.
Table 4.27: Number of student mental models of atomic structure in the pre- and postinterview responses by level of understanding.
According to student responses in the pre-interview, the majority of students (11
or 73%) exhibited mental models of atomic structure based on (a) Bohr’s model at level
3/1 without understanding “energy quantization” for the concept “orbitals” or (b) the
Quantum models at the levels 4/1 and 4/2 with or without understanding the concept of
probability for finding electrons. Few students (3 or 20%) were determined to be at level
4/3 and above. This suggests that students showed a lack of understanding about orbitals
in the pre-interview responses. Figure 4.17 shows the number of student mental models
of atomic structure from the interview responses by level of understanding.
141
Student Models in Interviews
by Level of Understanding
Number of Students
5
4
3
2
1
0
1/2 3/1 3/2 3/3 4/1 4/2 4/3 4/4 4/5
Level of Understanding
Pre-interview (by level with 15 students)
Post-interview (by level with 15 students)
Figure 4.17: Number of student mental models of atomic structure in the preand post-interview responses by level of understanding
Table 4.28 represents the details describing types of changes of student mental
models of atomic structure from the pre- and post-interview responses by scientific
model and level of understanding. Table 4.28 combines all information related to student
mental models of atomic structure and the details of the individual changes as
represented by the interview responses. The change between pre- and post-interview
responses was marked by arrows.
142
Coded
name
1/2
2/1
2/2
2/3
3/1
3/2
3/3
4/1
4/2
4/3
4/4
4/5
Q
Q
B
B
KF
EJ
Q(B)
MK
B
Q(B)
Q(B)
Q
CE
WT
SJ
B
KT
B
B
Q
Q
LJ
RZ
B
Q
MD
Q
CZ
Q
Q
Q(B)
Q
BM
LT
Q(B)
Q(B)
TK
Q
Q
Q(B)
Q(B)
HJ
TH
B
BJ
B
B
HD
B
Q(B)
Q(B)
VB
KC
P(B)
B
Table 4.28: Change of student mental models of atomic structure in the pre- and postinterview responses by scientific model and by level of understanding.
143
In the comparison of the pre- and post-responses to interviews, 5 students
participated only in the pre-interview. When the pre-responses were compared to the
post-responses for the remaining 15 students, data from this study showed more students
from the post-interviews with mental models in the advanced levels of 4/3, 4/4, and 4/5
(20% → 47%) than from the pre-interviews. The change suggests that more students
acquired an understanding related to different shapes of orbitals during this course and
developed their own atomic models combining the probability concept for finding
electrons and different shapes of orbitals for atomic structure. The comparisons of the
number of students at each level of understanding for the pre- and post-interview
responses are displayed in Figure 4.17.
Table 4.29 shows a summary of the types of changes illustrated in Table 4.28.
Table 4.29 displays the changes of student models of atomic structure from pre- to postinterviews by levels of understanding. The -, =, and + signs mean decrease in level, no
change in level, and increase in level of understanding.
Seven students showed an increase in their levels of understanding, 7 students
made no changes in their understanding, and 1 student (MK) decreased his level of
understanding. Two of the students who remained at the same level of understanding
progressed from a mixed model [Q(B)] to a single (Q) model (See CE And BM in Table
4.28).
144
∆Post –Pre
- (1)
= (7)
+ (7)
Type of changes
4/1 → 3/2
(1)
3/1 → 3/1
(2)
1/2 → 3/1
(1)
4/1 → 4/1
(3)
3/1 → 3/2
(1)
4/3 → 4/3
(1)
3/1 → 4/4
(1)
4/5 → 4/5
(1)
4/2 → 4/3
(1)
4/2 → 4/4
(2)
4/4 → 4/5
(1)
Table 4.29: Change of student mental models of atomic structure from the pre- and postinterview responses by level of understanding.
When the pre- and post-responses to interviews were compared, students at level
3/1 and level 4/1 except for one student (RZ) made little change in their level of
understanding after experiencing the course instruction. This suggests that these students
did not understand quantum theory related to atomic structure and remained primarily at
level 3/1 and level 4/1 after 10 weeks of instruction. These two levels include students
using Bohr’s model without understanding “energy quantization” and the Quantum
model without the concept of “probability” related to quantum theory. Understanding
quantum theory related to atomic structure is a major criteria that helps students to be
able to develop their levels of understanding above the 4/2 level to 4/3 through 4/5 levels
of understanding, which was considered to be the target model of this course. Five
students of the 7 students who increased their levels of understanding achieved at the 4/3
or higher level of understanding. The number indicates that these five students developed
the target model of atomic structure explaining the concept of “probability” and
145
“different shapes of orbitals” which was the goal of the instruction. Except for one
student (RZ) who had made major progress in developing his model of atomic structure,
data revealed that four students who already had the Quantum model at the 4/2 or higher
level of understanding in the pre-interview responses achieved the target model of this
course. There was one student (MK) who decreased his level of understanding from the
Quantum model at the 4/1 level of understanding to Bohr’s model of the 3/2 level of
understanding.
Although two students (CE at the 4/1 level and BM at the 4/3 level) stayed at the
same level of understanding for both their pre- and post-interview responses, they also
made improvement by constructing a single model from the mixture of two models for
atomic structure, changes from Q(B) to Q. When these two students are included among
those who progressed toward the target model, nine students gained positively and five
students showed no changes toward constructing desired mental models of atomic
structure.
A student, MK, showed a decreased level in the post-interview responses. Figure
4.18 shows MK’s mental models of atomic structure as represented in the pre- and postinterview responses. Figures 4.18a. through 4.18d. excerpted from MK’s pre-interview
responses and Figures 4.18e. and 4.18f. were taken from his post-interview responses.
146
a.
b.
c.
e.
d.
f.
Note: a. the structure of carbon (Mi-Quantum model during the pre-interview), b. the solar
(during the pre-interview) system (Mb), c. the structure of carbon (Mb-Bohr’s model during the
pre-interview), d. the structure of carbon (Mf-Quantum model during the pre interview), e.
orbitals (Mb-during the post-interview), f. atomic structure (Mf-Bohr’s model in the postinterview)
Figure 4.18: Comparison of MK’s mental models of atomic structure in the pre- and
post-interview responses
First, in the pre-interview, MK explained atomic structure by the Quantum model
at the 4/1 level of understanding: nucleus + randomly moving electrons around the
147
nucleus. Figure 4.18a. was his initial model for a carbon atom (Mi), which is coded by
the Quantum model at the 4/1 level of understanding. Though he did not address the term
“probability,” the place for electrons was described as the probability concept. Then, in
order to explain the concept of orbitals, he remembered the solar system (See Figure
4.18b.) and by extending the diagram of the solar system, he drew another diagram for
the carbon atom (See Figure 4.18c.). The structure including orbitals in Figure 4.18c.
indicates that MK has a mixed model with two separate models for an atom and orbitals.
This resulted in his mental model of atomic structure to be coded by the Quantum model
including Bohr’s orbital structure or Q(B) at the 4/1 level of understanding. Finally, he
brought the Quantum model including randomly moving electrons back to his model of
atomic structure (Mf).
Second, in the post-interview, though MK described the different shapes of
orbitals in Figure 4.18e., his model for orbitals does not reflect the probability concept
for finding electrons related to quantum theory but it is described as a set path for
moving electrons around the nucleus. Although he had the probability concept at the
beginning of this course, rather than developing the elements of the Quantum model that
he had as a previous conception in his pre-interview responses, he extended his
perception oriented toward Bohr’s orbital structure to construct a modified Bohr’s model
at the 3/2 level of understanding. Figure 4.18f. shows MK’s model for atomic structure
that includes different shapes of orbitals within Bohr’s model.
148
Based upon the interview responses, most of the students who had Bohr’s model
made little or no change during the course except RZ. RZ showed major improvement
during the quarter from the 3/1 level to the 4/4 level of understanding of atomic structure.
Figure 4.19 displays RZ’s mental models of atomic structure as represented in pre- and
post interviews.
a.
b.
c.
d.
Note: a. Bohr’s model during the pre-interview (face view), b. Bohr’s model during the preinterview (side view), c. first Quantum model during post-interview, d. second Quantum
model during the post interview)
Figure 4.19: Comparison of RZ’s mental models of atomic structure in the pre- and postinterview responses
149
RZ described his atomic structure, Figures 4.19a. and 4.19b., during the preinterviews and those are identified as Bohr’s model at the 3/1 level of understanding,
which is supported by has explanation for orbitals, “the path of the electron takes.”
R: O.k. what is this circle?
RZ: that’s the orbits of the electrons when they are going around, I don’t really know why
they’re going around, but …
…
R: then, what is the orbital?
RZ: the path of the electron takes.
R: so, this path? This path is the orbital? (See Figure 4.19a.)
RZ: Yes. …well.. yes…one of these would be an orbital.
In the post-interview response, RZ commented on his model during the preinterview as “Bohr’s model of an atom which isn’t right.” RZ showed his understanding
of the probability concept explaining “orbitals” or “electron density.” “Electron density”
was meant as “the probability finding any electron in a certain area” and “orbitals” were
defined as “a space that you would find an electron in.” The probability was represented
by the dotted orbital structure in Figure 4.19c. Figure 4.19d.illustrates his atomic
structure as represented in the post-interview. The models are classified as the Quantum
model at the 4/3 level of understanding of atomic structure. The following text was
excerpted from RZ’s post-interview responses.
R: Yes, what kind of change have you had since the first interview?
RZ: Um…well…I noticed what I was doing before was called the Bohr’s model of an atom
which isn’t right.
150
R: who said?
RZ: Um…well, I thought I figured who was. They postulated some kind more complicated…I
liked Bohr model a lot better after going through chapter 6 because it’s so confusing wave
functions. Ah…I’ve always thought of even electrons as a particle like a piece of matter itself.
…
R: At the beginning, when I ask you about an atom, how does it look like in your mind? Is it still
same or different with the previous one?
RZ: It’s different. Whenever I think of an atom and its orbitals, I see … uh … this would be
protons. Protons and the nucleus is still the same. It’s always going to be the same. We will go
ahead and do. And there is a …
R: Is this neutron?
RZ: Yes, and then, what we have out here, um… would be electron density.
R: What is electron density?
RZ: It’s the probability finding any electron in a certain area.
…
R: What is the orbital?
RZ: It’s a space the…um…you would find an electron in.
4. 3. 3. Analysis of alternative models of atomic structure as represented in interview
responses
Two different schemes in Table 3.9 classified types of student mental models of
atomic structure by four scientific models and by 13 hierarchical levels of understanding.
According to curriculum guides, text materials and instructor’s notes, the Quantum
model at the 4/3 through 4/5 levels of understanding was considered as the instructor’s
target model of this CHEM 121 course. Based on the target model of this course,
students of this introductory college chemistry course were expected to understand the
basic idea of quantum theory (probability, wave function, and energy quantization), to
construct the modern picture of an atom, and to explain the atom in terms of particles or
waves. With regard to the basic idea of quantum theory related to atomic structure,
students begin to show their understanding related to quantum theory from the level 4/2
and higher. Level 4/2 is the required level of understanding for the concept of probability
151
to explain orbitals; however, the level of student understanding needed for different
shapes of orbitals involves levels 4/3 and higher. Students at level 4/4 are able to create
an atomic structure by combining the probability and different shapes for orbitals. At
level 4/5, students are expected to explain atomic structure by relating quantum theory
such as wave function, energy quantization, Pauli’s exclusion rule, uncertainty principle,
and particle/wave duality. Based upon this progression, this study explored levels of
understanding from 1/1 through 4/2 in detail to analyze alternative models of atomic
structure as represented in interview responses.
4. 3. 3. 1. Particle model and the 1/2 level of understanding
Figure 4.20 shows an example of student diagrammatic descriptions identified as
the Particle model. KC described an atom as a particle having a ball or watermelon shape
during the pre-interview. KC’s orbital structure in Figure 4.16 includes protons, neutrons,
and electrons around the center or nucleus like Bohr’s model of orbiting electrons around
the nucleus. Three particle atoms are arranged inside the protons, neutrons, and electrons.
The atoms were explained as a solid particle that can not be divided into smaller particles.
152
Figure 4.20: Example of student (KC) alternative models of atomic structure during preinterview for the Particle model at the 1/2 level of understanding
4. 3. 3. 2. Bohr’s model and the 3/1 level of understanding
During the post-interview, KC developed her atomic structure that was composed
of the nucleus and rotating or spinning electrons around the nucleus. Her description of
an atom was classified as Bohr’s model explaining orbitals as a set-path for electrons.
Figure 4.21 shows examples of KC’s alternative models of atomic structure during the
post-interviews for Bohr’s model at the 3/1 level of understanding (KC’s atomic
structure viewed in different angles). KC visualized spinning electrons to be the same as
rotating electrons. Each orbital for rotating particles was represented by arrows to
describe different spinning directions and charges. Her idea did not extend into the
Quantum model. The following text was excerpted from KC’s post-interview responses.
153
R: What is it?
KC: It’s how electrons, how they spin around the nucleus
R: What do you mean ‘spin around’?
KC: Like rotate around the center with their charges. This center is the nucleus
…
R: What do you mean ‘charged’? Could you explain it again?
KC: They can just spin in different direction.
R: Different direction?
KC: If they were negative, they could spin like clockwise, if they were positive, they can spin
counterclockwise, I don’t really….
R: Then, you mean electrons can be positive?
KC: No. no. they can’t. ….. Maybe, they spin in the same way
R: They are spinning in the same direction?
KC: Yes, all these on this orbital would all be spinning the same direction around the nucleus.
R: If this atom has a different orbital, what will happen?
KC: The next one, draw another one….. (See Figure 4.21a.) This is a very good number to
guess. They are just there and these ones….taking spin different way. But I thought the spins
had…maybe, spins have negative and positive charges because I think that these one spinning in
different way than these ones.
…
R: Do you remember anything about quantum?
KC: I wasn’t good at that section. That was one that I had bit of trouble with.
R: Why do you think?
KC: Because I didn’t read good enough. I read it, but I should have read it into a little more, I
think because just the concept wasn’t sticking with me well.
R: Is it related to this atomic structure or not?
KC: Um….. oh my gosh….. I think so…I don’t remember.
a.
b.
Note: a. face view, b. side view
Figure 4.21: Example of student (KC) alternative models of atomic structure during
post-interview for Bohr’s model at the 3/1 level of understanding
154
4. 3. 3. 3. Bohr’s model and the 3/1 level of understanding with marked quantum
numbers
Figure 4.22 represents examples of student (BJ and KF) alternative models of
atomic structure during post-interview for Bohr’s model with quantum numbers at the
3/1 level of understanding. BJ and KF developed the Bohr model concept for atomic
structure at the 3/1 level of understanding as illustrated in Figures 4.22a. and 4.22c.,
respectively. Figures 4.22b. and 4.22d. represent side views or perspectives from
different angles.
a.
b.
c.
d.
Note: a. face view (BJ’s atomic structure), b. side view (BJ’s atomic structure), c. face view
(KF’s atomic structure), d. side view (KF’s atomic structure)
Figure 4.22: Example of students (BJ and KF) alternative models of atomic structure
during post-interview for Bohr’s model at the 3/1 level of understanding with quantum
numbers
155
As can be seen from the Figure 4.22, both BJ and KF understood orbitals as a setpath for rotating electrons. The following text is excerpted from BJ’s post-interview
responses. According to BJ’s explanation, she described the structure of an atom in
Figure 4.22a. in terms of orbitals (s, p, d, and f) and sub-shells (px, py, pz). However,
there is no indication that she understood the quantum numbers and electron
configuration in relation to the concept of orbitals based on quantum theory. Rather than
constructing the Quantum model, BJ modified Bohr’s model at the 3/1 level of
understanding by using orbitals and sub-shells with electron configuration. Figure 4.22a.
shows that orbitals and sub-shells in BJ’s diagrammatic representation were not
distinguished.
R: Could you show that to me?
BJ: O.k. alright, you have your nucleus again. We can draw, the + is proton, the 0 is neutron,
and that’s not actually there, that’s just what I put there to hold it together. Um…but then
around, you have orbitals, you have electrons floating around and each orbital can only have 2
electrons, and you can have like s, p, d, and f orbital. And each of those have like sub orbitals,
and so like this first will be s orbital and then next orbital out would be px and then you have py,
pz, and then you do the same thing with d and then f. Just depends on where the atom is in the
periodic table as to how far you go out.
…
R: What is electron configuration?
BJ: They just tell you where the electron is like which sub-shells and orbitals kind of stuff.
R: What are sub-shells?
BJ: Like if you have your p orbital, your sub-shell is going to be your x, y, and z. That’s the subshell of the p orbital.
KF used quantum numbers to explain orbitals of his atomic structure in a way
similar to BJ’s model. However, KF understood Bohr’s model and explained orbitals as a
156
set path of electrons. In regard to quantum numbers, he remembered principle and
azimuthal quantum numbers, but didn’t understand the meaning of those numbers based
on quantum theory related to atomic structure. The following text was excerpted from
KF’s post-interview responses. To the question about the meaning of “quantum or
quantized,” he recalled the concept of quantum number, but his response was “I don’t
know where they came… I’m not sure… I wish that I can explain…” Figure 4.22c.
indicates that he differentiated the principle numbers (1, 2, and 3) by different levels (or
sizes) of orbitals. However, the azimuthal numbers were marked on the same orbitals and
there was no difference in azimuthal quantum numbers (s, p, d, and f).
R: then, could you show the atom to me ?
KF: um, the picture in my mind is the nucleus, the protons and neutrons in here and then the
electrons orbiting it.
…
R: what is the meaning of quantized or quantum?
KF: All the quantum numbers are… Here is spin quantum number, azimuthal quantum
number…and principle and one more, but I don’t remember it. So, basically tells like the
behavior of the atom or electron, so.
R: then, you mean, are the quantum numbers related to atoms?
KF: umhum … This one is like called l and s, p, d, and f and… so that’s what that is now. S, p, d,
and f, that is like for hydrogen and it would be, like that’s the electron thing for that. So, there is
one electron here. Um, so since that’s 1s, principle quantum number for that would be number 1.
…
R: let’s start with principle quantum number. What does number 1, 2, 3…mean?
KF: you can go all the way like to fill electron things, like each one has certain pattern that it
had to be filled in, so 1s2 2s2…
R: could you explain this by using your atomic structure?
KF: I don’t know where they came…
…
R: what does this number 1, 2, 3… mean? And what is the meaning of s, p, d…?
KF: o.k. like on the periodic table. ………………………………… O.k. these are all ss and
these are all ps, these are all ds, and these are fs.
…
R: what is the s, p, d, and f? Are they different?
KF: um…it will not, but… I don’t really know how they are different. Um… other than like the
quantum number like that
157
R: quantum number?
KF: that makes some difference.
R: Then, what is quantum number?
KF: I’m not sure. Um…..I wish that I can explain, but…boy……. I don’t really know. um. It’s
just the way that categorized, I think, but I’m not sure
4. 3. 3. 4. Bohr’s model and the 3/2 level of understanding with different orbital
shapes
Students having this alternative model showed their understanding using Bohr’s
model with a centered nucleus and orbiting electrons combined with the different shapes
of orbitals as a set-path. MK and KT created their own modified Bohr’s model by
including different shapes of orbitals in this category. However, there was no indication
of understanding of the meaning of the Quantum model. Figure 4.23 displays examples
of student alternative models of atomic structure during the post-interview for the Bohr
model at the 3/2 level of understanding. Figures 4.23a. and 4.23b. show two alternative
models of the modified Bohr’s model explaining different orbital shapes. In the preinterview, KT showed Bohr’s model at the 3/1 level of understanding as his model for
atomic structure and he developed his mental model implementing the different orbital
shapes into the Bohr’s model framework in the post-interview. On the other hand, MK
had two separate models for atomic structure including Bohr’s model orbital structure
with his Quantum model at the 4/1level of understanding. In his case, the orbital
structure became clearer with the different shapes and he returned to Bohr’s model at
level 3/2 rather than keeping his Quantum model at the 4/1 level of understanding.
158
(a)
(b)
Note: a. MK’s atomic structure, b. KT’s atomic structure
Figure 4.23 Example of students (MK and KT) alternative models of atomic structure
from post-interview responses for Bohr’s model at the 3/2 level of understanding
4. 3. 3. 5. Quantum model with Bohr’s orbital structure at the 4/1 level of
understanding
VB and HJ showed mixed models of different combinations for atomic structure
depending on the questions and interactions during the interviews. First, to the question
about atomic structure, both described electrons “around the nucleus” without assigning
electrons to a set-path, which classifies their model as the Quantum model at the 4/1 level
of understanding. Second, in addition to the atomic structure identified as the Quantum
model at the 4/1 level of understanding, they used Bohr’s atomic structure for the
question asking about orbitals. Figure 4.24 displays examples of student alternative
models of atomic structure identified by category of Quantum model with Bohr’s orbital
159
structure or Q(B) at the 4/1 level of understanding. Figures 4.24a. and 4.24b. represent
VB’s atomic structure and Figures 4.24c. and 4.24d. represent HJ’s atomic structure.
Figures 4.24a. and 4.24c. represent the Quantum model and Bohr’s orbital structure is
displayed in Figures 4.24b. and 4.24d.
a.
b.
c.
d.
Note: a. VB’s atomic structure, b. VB’s orbitals, c. HJ’s atomic structure, d. HJ’s orbitals
Figure 4.24 Example of students (VB and HJ) alternative models of atomic structure
from the post-interview responses for the Quantum model with Bohr’s model at the 4/1
level of understanding
4. 3. 3. 6. Quantum model with marked quantum numbers at the 4/1 level of
understanding
During the post-interview, CE developed the Quantum model with quantum
numbers at level 4/1 of understanding by explaining an orbital as “a sphere that holds the
electrons.” CE’s orbitals in Figure 4.25 were labeled by lists of quantum numbers such as
1s, 2s, 2p, 3s, 3p, and 3d. However, there was no indication of understanding the
160
meaning of probability and quantum numbers for orbitals based on quantum theory.
Figure 4.25 displays CE’s alternative model of atomic structure during the post-interview
identified as the Quantum model with quantum numbers at the 4/1 level of understanding.
This alternative model indicates the lack of understanding about the meaning and
different shapes of orbitals related to quantum theory. In Figure 4.25a., she arranged the
quantum numbers for orbitals by assigning separate orbitals for each azimuthal quantum
number (s, p, d, and f) in the order of 1s, 2s, 2p, 3s, 3p, 3d, and 4s. In Figure 4.25b., she
divided orbitals by the principle quantum number (1, 2, 3, …) and combined the
azimuthal quantum number with the same principle number as a group such as 1s, (2s,
2p), (3s, 3p, 3d), and 4s.
The discrepancy between Figures 4.25a. and 4.25b. was compromised with
permanent lines by principle numbers: “I guess like this line isn’t as permanent as like
this line.” The modified idea was illustrated by the black thick line on the atomic
structure in Figure 4.25a. The following text was excerpted from CE’s post-interview
responses.
161
a.
b.
Note: a. Quantum model with quantum numbers (by the order of 1s, 2s, 2p, 3s, 3p, 3d, and
4s), b. Quantum model with quantum numbers (by the modified order of 1s, 2s & 2p)
Figure 4.25: Example of student (CE) alternative models of atomic structure from the
post-interview responses for the Quantum model at the 4/1 level of understanding with
quantum numbers
R: O.k. Then, the electrons here and there, are they different each other? (See Figure 4.25)
CE: No.
R: Then, how about these two? (See Figure 4.25a.)
CE: These two are the same essentially. They are the 1s and then, but these, there’s like this one
and this one will be the s and these 5 are the p.
R: How can you tell this as s and the other one as p?
CE: That’s something I don’t know and that’s like um … like for … also for these, ones that
have d, there’re four, if they’re filled and so I don’t know how you draw that. Because … then,
3d would be before the 4s. … I guess next one is…
R: What is 3d?
CE: O.K. you do. This is all protons and neutrons and then, you draw … 1s, 2s, 2p, … Here it is.
… 3p and then … I don’t know how you…because how would you draw for like Ti, you do 4s,
no, um… 3d and then 4s, but then, … … you fill this before you fill that.
…
R: Here, in this drawing, you separated p with s. It’s different with the previous structure having
2s and 2p in the second orbital. Could you explain it more?
CE: Because that’s the order they fill.
R: Then, how can you connect these two?
CE: Um …well … … um … … I don’t know. I guess like this line isn’t as permanent as like
this line. These lines will be wall as you change numbers.
…
R: Did you learn or know some about quantum theory…?
162
CE: Quantum numbers
R: O.k. what is it?
CE: Let’s see. Uh…quantum numbers were…oh…o.k. Um… the outer shell is 2, and so the
quantum number is 2. The principle quantum number and then the azimuthal quantum number is
the p, so it would be…1, 2, 3, s, p, d, f, so it’s one.
R: What is the meaning of quantum or quantized? Why do you need this number?
CE: Um… I don’t know.
R: Do you think that is related to your drawing or not?
CE: Yes, well, if they tell you quantum number, then, you can figure out what the outer shell is.
4. 4. Mental models of atomic structure as represented by different assessments
Each assessment represents student mental models of atomic structure in different
ways. Various types of information were collected for getting more or better information
to infer student mental models. Data, as represented in different assessments, were
collected to analyze student perceptions of atomic structure. Because thirteen students
from Group 2 participated in all of the pre- and post-interview responses and pre- and
post-questionnaire responses, data from those 13 students were analyzed in detail. Preand post-responses to the questionnaire, achievement on the 34 items related to atomic
structure, and course grades were compared with the mental models constructed from the
interview responses analysis.
4. 4. 1. Comparative analysis of student responses to questionnaires and interviews
The agreement between responses from the questionnaires and the interviews was
calculated by percentage and reported in Table 4.30. As can be seen in Table 4.30, the
determination of mental models for atomic structure results in a greater degree of
agreement for data representations of the scientific models than levels of understanding.
163
Especially, there was a particularly large discrepancy for student level of understanding
as determined by post-response comparisons from the questionnaire and interview data.
Interview and
Questionnaire
Criteria
Number of
corresponding models
Pre-response
Post-response
SM
LU
SM
LU
9
9
11
5
Percentage of
69.2
69.2
84.6
38.5
corresponding models
Note: SM=scientific models. LU=level of understanding. Number of student responses=13.
Table 4.30: The number and percentage of agreement between questionnaire and
interview classification of scientific model and level of understanding for mental models
of atomic structure.
The notable increase in agreement from the pre-questionnaire and pre-interview
scientific models to the post-questionnaire and post-interview scientific models may be
due to the use of diagrams for this purpose as a part of the chemistry course. Considering
the dependence of scientific models on diagrammatic representation, this may indicate
that students better understand or remember diagrammatic models during the course. In
addition, participation in the pre-assessments may have helped the students to express
their diagrammatic representation of scientific models more clearly.
164
Concerning the decreased correspondence between two post-assessments for level
of understanding, the detailed analysis of the interview assessment provided the
opportunity for the interviewer to get a more in-depth understanding of the student
perception of atomic structure than the questionnaire format. In addition, the interview
process itself may have helped students to think more analytically about their perceptions
and knowledge of atomic structure.
Table 4.31 displays student models of atomic structure analyzed from
questionnaire and interview responses. In addition, the percent achievement on the 34
items related to atomic structure and the course letter grade are also included. Student
models of atomic structure as determined from the questionnaires and interviews were
analyzed by scientific models and levels of understanding.
165
Coded
name
KF
MK
CE
WT
KT
RZ
BM
LT
TK
HJ
BJ
VB
KC
Analysis
criteria
Mental model of
atomic structure
(questionnaire)
Pre
Post
Mental model of
atomic structure
(interview)
Pre
Post
SM
B
B
B
B
LU
3/1
3/1
3/1
3/1
SM
B
B
Q(B)
B
LU
3/1
3/1
4/1
3/2
SM
Q(B)
Q
Q(B)
Q
LU
4/1
4/1
4/1
4/1
SM
Q
Q
Q
Q
LU
4/2
4/4
4/4
4/5
SM
B
B
B
B
LU
3/1
3/1
3/1
3/2
SM
B
Q
B
Q
LU
3/1
4/3
3/1
4/4
SM
Q
Q
Q(B)
Q
LU
4/2
4/2
4/3
4/3
SM
B
B
Q(B)
Q(B)
LU
3/1
3/2
4/2
4/4
SM
Q(B)
Q
Q
Q
LU
4/2
4/2
4/2
4/4
SM
Q(B)
Q(B)
Q(B)
Q(B)
LU
4/1
4/1
4/1
4/1
SM
B
B
B
B
LU
3/1
3/1
3/1
3/1
SM
Q(B)
Q(B)
Q(B)
Q(B)
LU
4/1
4/1
4/1
4/1
SM
P(B)
Q(B)
P(B)
B
LU
1/2
4/1
1/2
3/1
% of correct
responses to 34
items
%
course grade
67.6
C+
70.6
C
70.6
C+
64.7
C+
94.1
A
88.2
A
64.7
B-
67.6
C+
85.3
A-
67.6
C+
38.2
C
55.9
C+
52.9
C+
Class
achievement
Table 4.31: The analysis of 13 student mental models of atomic structure as represented
in the interview and questionnaire responses to the course exam items related to atomic
structure and to the course grade.
166
For the comparison of student models as represented in questionnaire and
interview responses, student responses on those assessments were compared by scientific
models and levels of understanding of atomic structure. Figure 4.26 displays the number
of student mental models of atomic structure in the pre- and post-questionnaire and preand post-interview responses by scientific models. Data from the pre- and postquestionnaire responses were compared and illustrated in Figure 4.26a. and data from the
pre- and post-interview responses were compared and illustrated in Figure 4.26b. In the
comparison of the pre- and post-responses in Figures 4.26a. and 4.26b., both assessments
represent conceptual development by displaying the changes of student models toward
the Quantum model. The questionnaire results did not show much change in relation to
the mixed model, Q(B) during the course (4 students in pre-responses and 3 students in
the post-responses). The interview responses on the other hand provided more
information of change as represented by the decrease in the number of students with the
mixed model [Q(B)] from pre- (6 students) to post-interview (3 students) along with the
increase of students with the Quantum model (Q) from pre- (2 students) to post-interview
(5 students).
167
Student Models from Interview Responses
by Scientific Model
7
7
6
6
Number of Students
Number of Students
Student Models from Questionnaire
Responses by Scientific Model
5
4
3
2
1
5
4
3
2
1
0
0
P
P (B)
N
B
Q (B)
P
Q
P(B)
N
B
Q(B)
Q
Scientific Model
Scientific Model
Pre-Questionnaire (by model with 13 students)
Pre-interview (by model, 13 students)
Post-interview (by model, 13 students)
Post-questionnaire (by model with 13 students)
a.
b.
Note: a. analysis of the questionnaire responses, b. analysis of the interview responses
Figure 4.26: Number of student mental models of atomic structure in the pre- and postquestionnaire and the pre- and post-interview responses by scientific model
Figure 4.27a displays the changes in the number of student mental models of
atomic structure from the pre- and post-questionnaire responses by level of
understanding. Figure 4.27b. displays changes in the numbers of models of atomic
structure from the pre- and post-interview responses by level of understanding. Both
assessments display increased numbers at the higher levels of understanding toward the
Quantum model. The analysis of the interview responses results in more precise shifts in
levels consistent with the Quantum model than did the questionnaire responses. This is to
be expected due to the opportunity to have students elaborate on their perceptions and
168
thinking processes during the interview sessions. During the interviews, the more in
depth descriptions by the students allowed for a more precise identification of the student
models and distinctions necessary for better identification of levels and shifts between
levels of understanding related to the Quantum model.
Student Models from Questionnaire
Responses by Level of Understanding
Student Models from Interview Responses
by Level of Understanding
5
6
Number of Students
Number of Students
7
5
4
3
2
1
0
4
3
2
1
0
1/2 3/1 3/2 3/3 4/1 4/2 4/3 4/4 4/5
1/2
Level of Understanding
3/1
3/2
3/3
4/1
4/2
4/3
4/4
4/5
Level of Understanding
Pre-interview (by level, 13 students)
Post-interview (by level, 13 students)
Pre-Q uestionnaire (by level with 13 students)
Post-Q uestionnaire (by level with 13 students)
a.
b.
Note: a. analysis of the questionnaire responses, b. analysis of the interview responses
Figure 4.27: Number of student mental models of atomic structure in the pre- and postquestionnaire and the pre- and post-interview responses by level of understanding
169
4. 4. 2. Cluster analysis of student mental models by q methodology
Thirty-four questions related to atomic structure were selected from the multiplechoice course examinations (mid-term 1, mid-term 2, and final exam). Q-factor analysis
was completed to determine what clusters of the 20 interviewed students would result
from this correlation analysis. This analysis produced three principal components for the
interviewed students. Because LT was not included in any of the three principal
components, the results are based on 19 students. Table 4.32 displays the component
loadings for the students on each of the three clusters along with the percent of variance
for each component. As indicated in Table 4.32, 7students (KF, EJ, MK, CE, WT, SJ,
and KT) comprised the first cluster, 5 students (LJ, RZ, MD, CZ, and BM) comprised the
second cluster, and 7 students (TK, HJ, TH, BJ, HD, VB, and KC) comprised the third
cluster.
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Coded name
KF
EJ
MK
CE
WT
SJ
KT
LJ
RZ
MD
CZ
BM
LT
TK
HJ
TH
BJ
HD
VB
KC
Percent of
Variance
Component Loading
1
2
3
.742
.718
.590
.530
.520
.519
.433
.804
.794
.774
.557
.495
.696
.657
.638
.633
.575
.502
.492
23.13
11.78
10.55
Note: Number of persons=20. Number of items=34. Sample=Group 2.
Table 4.32: Student loadings on the three-component rotated solution resulting from the
person by item principal components analysis for Group 2.
During the interviews, the more in depth descriptions by the students allowed to
form a more precise identification of the student models and distinctions necessary for
better identification of levels. Student background information and mental models of
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atomic structure as inferred from the interview analysis were used to characterize the
clusters of student groups resulting from the principal components analysis. Table 4.33
displays the three principal components along with information used to characterize each
cluster. Component loading of 0.400 or less were not included in Tables 4.32 and 4.33.
Because LT did not have a loading above 0.400 on any of the 3 components and 5 of the
student interview volunteers did not complete both the pre- and post-interviews, the
resulting analysis sample was comprised of 14 students. Table 4.33 displays the principal
component loadings and student background information including gender, course grade,
and atomic structure related achievement. Table 4.33 also includes the student mental
models of atomic structure related to scientific models and levels of understanding as
determined from the interview responses.
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Coded
Name
Gender
% of correct
responses to
34 items
Course
Grade
Scientific
Model
(Pre : Post)
Level of
understanding
(Pre : Post)
KF
M
67.6
C+
B
B
3-1
3-1
.742
MK
M
70.6
C
Q(B)
B
4-1
3-2
.590
CE
F
70.6
C+
Q(B)
Q
4-1
4-1
.530
WT
M
64.7
C+
Q
Q
4-4
4-5
.520
KT
M
94.1
A
B
B
3-1
3-2
.433
LJ
M
88.2
A
Q
Q
4-5
4-5
.804
RZ
M
88.2
A
B
Q
3-1
4-4
.794
CZ
M
91.2
A
Q
Q
4-2
4-3
.557
BM
M
64.7
B-
Q (B)
Q
4-3
4-3
.495
TK
F
85.3
A-
Q
Q
4-2
4-4
.696
HJ
F
67.6
C+
Q(B)
Q(B)
4-1
4-1
.657
BJ
F
38.2
C
B
B
3-1
3-1
.633
VB
F
55.9
C+
Q(B)
Q(B)
4-1
4-1
.502
KC
F
52.9
C+
P(B)
B
1-2
3-1
.492
Component Loading
CP1
CP2
CP3
Table 4.33: Component analysis by gender, atomic structure related percentage
achievement, course grade, mental models of atomic structure from interview responses,
and component loadings.
The composition of the components by gender was noticeably different. Although
there is one more male (M) than female (F) student included in the overall sample
component 1 (CP1) as can be seen in Table 4.32, this cluster was balanced combination
in terms of gender with four males and three females. Component 2 (CP2) is composed
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of all male students and component 3 (CP3) is composed of almost female students
except HD who didn’t respond to the post-interview.
The course grade was calculated by assessing student performance in three
multiple-choice examinations (mid-term 1, mid-term 2, and final exam), six take-home
quizzes, and ten lab activities. Table 4.33 includes course grades from A through D+.
Most students in component 1 except KT (grade A) received grades of C or C+. Students
in CP2 achieved higher grades of A or A- except a student, BM who received a B-. CP3
shows a wide range of grades from A- through D+.
Student mental models of atomic structure as coded by scientific model from the
interview are presented for the three clusters of students. Table 4.33 shows the number of
students who were classified by category of scientific model and level of understanding
by component. According to the data in Table 4.33, there were minor differences
between CP1 and CP3. However, CP2 included more students who developed Quantum
models and higher levels of understanding for atomic structure in post interview
responses. As can be observed in Table 4.33, all of the students in CP2 ended up with the
Quantum model at levels of understanding ranging from 4/3 to 4/5. In the post-interview
responses, the CP1 group showed a decrease in the number of students who
demonstrated a mixed model of two models for atomic structure as represented by Q(B).
In the post-interview responses, students in CP 1 showed more changes in the number of
students in levels of understanding than students of CP3.
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CP1 is comprised of mostly male students with a moderate level of atomic
structure achievement and course grades in the C range. The pre-conceptions of atomic
structure can be characterized as including aspects of the Bohr model. Changes in
perceptions of atomic structure can be characterized by little or no change with some
evidence of movement to a lower level of understanding.
CP2 is comprised of all male students with high levels of atomic structure
achievement and course grades in the A - B range. The post-conceptions of atomic
structure can be characterized by a predominance of the Quantum model at he higher
levels of understanding. Changes in perceptions of atomic structure can be characterized
by noticeable improvement to the higher levels of understanding related to the Quantum
model.
CP3 is comprised of all female students with a broad range of atomic structure
achievement and course grades in the C or below range. The conceptions of atomic
structure can be characterized as predominantly mixed models. Little or no changes in
models for atomic structure were evident.
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CHAPTER 5
CONCLUSION AND DISCUSSION
5. 1. Objectives of this study
The nature of matter based upon atomic theory is a principal concept in science;
hence, how to teach and how to learn about atoms is an important subject for science
education. To this end, this study explored student mental models of atomic structure at
the educational level of introductory college chemistry. This study provides information
about student perceptions of atomic structure and how students learn about this concept.
The changes in student mental models serve as a valuable resource for comprehending
student learning processes and conceptual development.
First, student mental models of atomic structure in college chemistry were
explored by examining four scientific models that have been developed throughout the
history of science: the Particle model, the Nuclear model, the Bohr model, and the
Quantum model. In the development of atomic theories, various atomic models have
been used to explain or support scientific observations and the nature of an atom. By
continual refinement, atomic models have changed throughout science history. The
developmental history of atomic theory, when examined in chronological order, presents
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a hierarchy of models. In this respect, the Quantum model is currently accepted in the
scientific community and it is taught as a scientific model for atomic structure within the
school curriculum. However, past models such as the Particle model by Dalton, Nuclear
model by Rutherford, and orbital structure model by Bohr are still in use in school
curricula. This study used the four scientific models to specify criteria for coding student
mental models of atomic structure. The data collected for this study inform student
perceptions of atomic structure and also indicate the presence of some influence of
scientific models on student mental models and learning. This study reports that concepts
or diagrams of the Nuclear or Bohr’s model appeared in student mental models (in both
pre- and post-responses to questionnaires and/or interviews). In addition, there were
students who had mixed models comprised of two separate models for atomic structure.
Second, thirteen levels of understanding of atomic structure which were derived
from curriculum guides were used to assess student mental models (See Table 3.9).
These levels represent developmental orders of the concept of “atomic structure” in detail.
In this study, student responses to pre-questionnaires and pre-interviews represent their
previous conceptions and their learning of atomic structure by level of understanding.
Changes of mental models were determined by comparing the level of understanding
between the pre- and post-responses. The data revealed various types of alternative
models and patterns relating to learning about atomic structure.
Third, the mental models that students described provided indirect information
that was used to infer the nature and construction of student models. Various assessments
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such as course examinations, questionnaires, and interviews were used to map out
student perceptions of atomic structure. In particular, the student responses to
questionnaires and interviews were assessed and used to represent student mental models
of atomic structure. There were primarily two criteria of the student mental models that
were compared: four scientific models and 13 levels of understanding. All assessments
were compared to each other in various ways. Student mental models, as represented in
questionnaires and interviews, were compared. Comparative analysis between student
mental models from interviews and students’ responses to atom-related questions from
course examinations were explored for similarities and differences.
5. 2. Description of research method
5. 2. 1. Sampling
Data was collected from students who were taking the first course of a three
course series of introductory chemistry courses in 2004. Responses to course
examinations (two mid-term examinations and a final examination), pre- and post-course
questionnaires, and pre- and post-course interviews were the primary sources of
information used to analyze student mental models of atomic structure. Six hundred
thirty-three students were enrolled in this course and their course assessments were
collected. Twenty students volunteered for the pre-course interview and fifteen of the
twenty students returned for the post-interviews. Among the 20 interview volunteers, 18
students completed both pre- and post-questionnaires. A total of 13 students participated
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in all pre- and post-questionnaires and interviews. Data from these 13 students were used
to compare student questionnaire and interview responses. Because one student was not
included on any of the components from the q-factor analysis, 14 student mental models
from the 15 interview respondents were further explored.
Assessment
Questionnaire
analysis
Interview
analysis
Questionnaireinterview
comparison
Number of students who
participated in assessment
18
15
13
Q-factor analysis
with models
identified from
interview
14
Table 5.1: Number of students who participated.
5. 2. 2. Assessments
5. 2. 2. 1. Course assessments
In order to evaluate student conceptual understanding of atomic structure as
represented by the responses to the course assessments, test items related to atomic
structure were selected from the three multiple-choice examinations. Discussion with
experts and examination of curriculum guides for the content analysis resulted in the
selection of 34 items related to “atomic structure.” Percent achievement on the items
related to atomic structure was examined. In addition, the responses to the selected 34
items were further explored by q methodology in order to understand the identifying
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characteristics of the interview sample clusters of students in relation to their mental
models of atomic structure and other defining traits.
5. 2. 2. 2. Questionnaires
Pre- and post-questionnaires asking students about atomic structure were
implemented at the beginning and the end of the ten-week quarter. These questionnaires
required students to provide written and diagrammatic or graphic descriptions of atomic
structure. These questionnaires also asked for a definition of an atom and a description of
orbitals. In order to compare the questionnaire responses with the interview data, the
responses of the group of 20 students who had volunteered for the interviews were
selected and further explored. Of the 20 students who responded to the pre-questionnaire,
18 responded to the post-questionnaire. The pre- and post-responses from the 18 students
were examined by the schemes designed to characterize their mental models of atomic
structure. Four scientific models and thirteen levels of understanding were used as the
criteria to describe student mental models of atomic structure as represented by their
questionnaire responses. In order to better understand the conceptions of students who
had a mixed model comprised of two separate models for atomic structure (one as atomic
structure and the other as atomic structure related to orbitals), student responses were
coded by a mental model of atomic structure (Ma) and a mental model for orbitals (Mo),
respectively. The resulting student models for atomic structure from the pre- and postquestionnaires were compared.
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5. 2. 2. 3. Interviews
In order to analyze student models of atomic structure as represented by the
student-researcher interactions during the interviews, the same two schemes were used:
(a) the defining characteristics of the four scientific models and (b) 13 levels of
understanding that were used with the questionnaire responses. To better understand
students who demonstrated a mixed model comprised of two separate models for atomic
structure (such as one for an atom and a different one for the atomic structure of orbitals),
all changes in student responses during the interviews and models for the description of
atomic structure were analyzed. For ease of use, student responses during interviews
were coded by Mi, Mb, and Mf. Mi represented the student initial mental model of atomic
structure; the code Mb was used to represent the intermediate or between model of atomic
structure; and Mf was used to represent their final mental model of atomic structure.
Among the 20 pre-interview volunteers, fifteen students returned for the post-interview.
The models for atomic structure from the pre- and post-interviews were compared for
these 15 students to investigate any changes.
5. 3. Research findings by research question
Because the interview analysis was considered to provide a more in-depth
description of student models leading to a more precise and accurate representation of
scientific models and levels of understanding related to atomic structure, student models
from the interview analysis were used to explore the changes in models, the interaction
181
with other defining variables, and the characteristics of student clusters achieved by q
methodology.
5. 3. 1. How do student mental models of atomic structure, as represented by responses
to an open-ended interview, compare to the scientific models of atomic structure?
Because fifteen students participated in both pre- and post-interviews, the
following results were based on this group of 15 student interview responses.
The student mental models of atomic structure compared to scientific models
from the pre-interview responses revealed Bohr’s models (B) for four students, Quantum
models (Q) for another four students, and a mixed model with two separate models of
atomic structure for seven students [one with P(B) and six with Q(B)]. Five students had
Bohr’s models, seven students had Quantum models, and three students had the mixed
model Q(B) as determined by their post-interview responses.
The number of students in categories of P(B), B, and Q(B) represented a large
proportion of the group for both the pre- and post-interview responses. Concerning the
mixed model with Bohr’s orbital structure, this study shows that many students (73.3%
in the pre-interview) had a preconception of Bohr’s model or Bohr’s orbital structure as
part of their model for atomic structure. The post-interview data indicates that students
may have learned to understand orbitals as part of atomic structure through the CHEM
121 course.
182
5. 3. 2. How do student mental models of atomic structure, as represented by responses
to an open-ended interview, compare to the levels of understanding of atomic
structure?
Student models as characterized by levels of understanding showed the
distribution of levels of understanding of atomic structure from level 1/1 through 4/5. In
the pre-interview, the analysis of levels of understanding showed a general distribution of
4 students at level 3/1, 4 students at level 4/1, and 3 students at level 4/2 and there was
one student at each level 1/2, 4/3, 4/4, and 4/5. For the post-interviews, there were 3
students at level 3/1, 2 students at level 3/2, 3 students at level 4/1, 2 students at level 4/3,
3 students at level 4/4, and 2 students at level 4/5.
5. 3. 3. What alternative models of atomic structure are represented by responses to the
interviews?
The Quantum models at levels 4/3, 4/4, and 4/5 were considered as the
instructor’s target model for this course according to the curriculum guides. Therefore,
the models from levels 1/1 through 4/2 were considered as alternative models. Within
these levels, this study revealed several patterns of responses identified as alternative
models.
Alternative model 1. A student described an atom as a particle that cannot be
divided into sub-particles. Atomic structure was described as “a ball” or “watermelon.”
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Alternative model 2. Students described Bohr’s model at the 3/1 level of
understanding. For this type of model, students drew atomic structure with the nucleus in
the center and orbiting electrons in orbitals. These students showed no indication of
understanding the meaning of and different shapes for orbitals; however, there were two
students (BJ and KF) who marked quantum numbers such as 1s, 2s, 2p, 3s, 3p, and 3d in
their atomic structure diagrams. Further analysis of these two student models revealed no
evidence indicating an understanding of the meaning of the quantum numbers as related
to quantum theory or orbitals. Rather than understanding the meaning of quantum, they
tried to relate the idea to the periodic table and electron configuration to find valence
electrons and to explain bonding.
Alternative model 3. Two students (MK and KT) showed Bohr’s model at the 3/2
level of understanding. This model indicated that the students knew about different
shapes of orbitals (s, p, d, and f); however, their understanding was based upon Bohr’s
orbital structure which describes a set path for electrons, and there was no indication that
they understood Quantum models of atomic structure in relation to the probability of
finding electrons.
Alternative model 4. There were seven students in the pre-interviews and 3
students in the post-interviews who showed a mixed model involving two separate
models for atomic structure. They reflected the Quantum model at the 4/1 level of
understanding as their atomic structure by arranging electrons within orbitals or within a
certain area; however, in reference to orbitals, they had the image of Bohr’s orbital
184
structure as a separate model. Of particular interest in these mixed models was student
(VB) who developed her own model for atomic structure. She modified her Quantum
model that explained the presence of electrons in terms of probability by combining
concepts of Bohr’s orbital structure and stability. When an atom has a “complete
number” of electrons for an orbital (she explained the complete number as 2 for the first
orbital and 6 for other orbitals), the electrons will be on the orbital path, which means
that the atom will then be stable and there will be no reaction between atoms. But when
the atom doesn’t have the “complete number,” electrons will move around within the
orbitals and they will be involved in reactions with other atoms.
Alternative model 5. One student (CE) reflected the Quantum model at the 4/1
level of understanding with labeling lists of quantum numbers such as 1s, 2s, 2p, 3s, 3p,
and 3d for orbitals. There was no indication of understanding of the meaning of the
quantum numbers in relation to quantum theory or orbitals.
5. 3. 4. How do student mental models of atomic structure, as represented in openended interview responses, change after experiencing the introductory college
chemistry course?
1) In the pre-interview, the general distribution of the students showed mainly 4
students at level 3/1, 4 students at level 4/1, and 3 students at level 4/2 of understanding
and in the post-interview, although the number does not reflect individual changes, data
shows general shifts of levels toward higher levels of understanding (4/3, 4/4, and 4/5).
185
In the post-interview, the number of Quantum models increased and the number of
students revealing a mixture of two models was decreased from 7 to 3. The comparative
analysis between the pre- and post-interview responses shows improvement toward the
advanced or higher levels of understanding. The changes in student perceptions were
toward development of higher level models of atomic structure or in the development of
a single mental model relating two separate models for atomic structure. Data illustrates
students’ better understanding of the concept of probability for finding electrons and
different shapes of orbitals as the structure for an atom.
2) This study supports the influence of Bohr’s model on developing student
mental models of atomic structure, in particular, for the orbital structure. Counting the 6
students who had the mixed models with Bohr’s orbital structure, 10 students out of 15
showed Bohr’s model or Bohr’s orbital structure for atomic structure in their preinterview responses. Among the 10 student models from the pre-interview, only 3
students expressed their model with no Bohr’s orbital structure in the post-interview
responses and the 7 students remained without changes in their models. One student (RZ)
who had Bohr’s model from the pre-interview developed the Quantum model without
Bohr’s model or Bohr’s orbital structure as can be seen in the post-interview. Two
students (CE and BM) who had the Q(B) model developed the Quantum model without
Bohr’s model or Bohr’s orbital structure. One student (MK) having the Q(B) model
reverted back to Bohr’s model by modifying the orbital structure within the Bohr’s
186
orbital structure. This change supports the influence of Bohr’s models as well as the
influence of preconception.
3) The analysis based upon pre-interview responses showed that the distribution
of the number of students at the levels of understanding consistent with Bohr’s model of
atomic structure did not change for the post-questionnaire except for one student (RZ).
From the interview responses for atomic structure, RZ made a major improvement from
Bohr’s model at the 3/1 level to the Quantum model at the 4/4 level of understanding.
4) Data revealed that students at the Quantum levels of understanding made
progress by increasing the level of understanding to more closely represent the target
model by the end of the course. On the other hand, there were few changes in models for
students who had Bohr’s model as their preconception. This study suggests that students
who developed Bohr’s model as a preconception did not make noticeable progress
toward the advanced model or Quantum model nor achieve a higher level of
understanding related to this course experience.
5. 3. 5. How are the student perceptions of atomic structure as represented by
questionnaires and interviews related to each other?
1) The interview assessment better identified student models which were
comprised of mixed models of different models. Pre-interview analysis revealed 7
students who had the mixed models for atomic structure and pre-questionnaire analysis
revealed 5 students with the mixed models. Both assessments of the post-responses
187
showed that students made improvement not only by elevating the models but also by
making a single model from a mixed one for atomic structure. Post-interview analysis
revealed 3 students with the mixed models and the post-questionnaire analysis also
revealed 3 students with the mixed models.
2) In the comparison of the questionnaire and interview responses, there is greater
variability in the post-interview response in terms of levels of understanding. Analysis
shows that the post-interview responses better revealed advanced levels of understanding
than the post-questionnaire responses. This may be due to the situation that interview
assessments can allow analysis of student levels of understanding, particularly, changes
and improvement to higher levels, in more detail.
3) Scientific models are better described for and by students through
diagrammatic representations, the increased agreement in the post-responses may
indicate that students developed clear diagrammatic representations for atomic structure
or better understood their diagrammatic representations during the chemistry course. It is
also likely that student participation in the pre-questionnaire and pre-interview processes
may have helped students to think or remember their diagrammatic representations for
atomic structure.
5. 3. 6. What are the defining characteristics of students who are clustered together as a
result of the Q-factor analysis of their responses to the atomic structure related content
knowledge assessment items?
188
Responses to 34 multiple-choice items from the course exams for which the
content was related to atomic structure were used through q methodology to identify
clusters of Group 2 students in terms of their responses to these items. Student clusters
were further examined in terms of characteristics common to the students within each
cluster to characterize the three components (CP1, CP2, and CP3) which resulted.
Individual characteristics such as gender and course grades were also considered.
5. 4. Discussion and educational implications
The nature and structure of an atom is a principal concept in science and an
important issue in science education. To this end, the analysis of mental models in this
study has provided information describing student understanding and alternative
concepts of the nature and structure of an atom. In addition to an assessment of student
cognition, information produced from this study can serve as an important resource for
curriculum development, teacher education, and instruction. The valuable assessments of
this study can be used as an opportunity to gather the attention of scientists and educators
and to build the communication necessary to develop meaningful scientific models.
5. 4. 1. Understanding and learning atomic structure in college chemistry
This study has resulted in five recommendations for instructional practice and
curriculum development.
1) As can be seen in various assessments used in this study, there were
differences in the degree of changes detected by different types of assessments. However,
189
based on findings from those assessments, this study concludes that conceptual
development in student mental models can be achieved, either by elevating models
toward the higher levels of understanding (in-depth understanding of each concept) or by
combining models to make a single mental model for atomic structure (through interrelational thinking).
The mental model analysis in this study provides a glimpse of student conceptual
models of atomic structure that can make a difference in the inter-relational thinking for
constructing the concept of atomic structure. There were students who employed a mixed
model of two different models to explain their atomic structure. For example, although
one student developed the Quantum model (Q) of atomic structure at the 4/3 level of
understanding, he utilized Bohr’s model (B) to describe orbitals for atomic structure.
This study reinforces the importance of higher-order thinking skills for students to relate
concepts in order to construct a target model of atomic structure and provides examples
showing the relationship between conceptual understanding and higher-order thinking for
conceptual development.
In this respect, this study suggests instruction for atomic structure needs to be
designed by considering the inter-relationships between concepts such as orbitals,
quantum theory, and atomic theory for building a mental model of atomic structure.
2) According to the analysis and identification of alternative models, this study
revealed that many students had alternative models for atomic structure as revealed in the
pre-assessments. This observation indicates that many students had already developed a
190
preconception with alternative models in their previous learning. Most of all, Bohr’s
orbiting electrons and orbital structure seems to have had a strong influence on student
perceptions of atomic structure. Data from questionnaires revealed a reliance on Bohr’s
orbiting electrons in the majority of the pre-responses and this number increased in the
post-questionnaire responses. This indicates that many students have models of atomic
structure influenced by Bohr’s orbital structure at the 3/1 level of understanding. The
influence is represented as a single Bohr’s model or a mixture of two separate models
such as the Quantum model (Q) for an atom and Bohr’s model (B) for orbitals.
In addition, most students who had Bohr’s model as a preconception did not
make progress toward the Quantum model; however, students who had the Quantum
model as a preconception showed improvement toward the target model. This indicates
that changes for the students who had Bohr’s alternative models did not occur by the end
of this course but the students who already had the Quantum model did increase in their
level of understanding. This can be thought of as (a) the strong influence of Bohr’s
model, (b) ineffective instruction or curriculum for student development of the Quantum
model, or (c) non-readiness of students to learn the Quantum model in terms of levels of
understanding.
In this respect, this study suggests the instructional importance to teach the
concept “orbitals” related to “quantum theory” to build correct mental models for atomic
structure. In addition, the need of curriculum development to teach orbitals by relating
quantum theory to atomic structure is also suggested.
191
3) Although the data from this study provides evidence of student conceptual
development in understanding atomic structure, there are relatively few students who
developed understanding at the level of the target model, the Quantum model at levels
4/3 - 4/5. The target model requires student understanding of the basic ideas of quantum
theory related to atomic structure such as probability for finding electrons, different
geometrical shapes of orbitals, energy quantization, wave function, and quantum
numbers. In this respect, the understanding of quantum theory may serve as a hindrance
or threshold for moving toward the target model for understanding atomic structure. This
study supports the difficulty and importance of understanding and building mental
models of atomic structure based on the idea of quantum theory.
As addressed in the literature by Coll & Taylor, 2002; Coll & Treagust, 2003a;
Taber, 2002, the concept of quantum theory as a means of explaining atomic structure
can be difficult for students. Coll and Treagust showed students’ preferences for simple
models regardless of their grade level and education. The level of abstractness of the
concept can make the subject more difficult to learn (Lonning, 1998; Markow & Nakhleh,
Lowery, & Mitchell, 1996; Pestel, 1993). In addition, a ten-week course covering the
first nine chapters of an introductory chemistry textbook may not provide adequate
resource information for instructors to cover the concept in detail or for students to learn
the concept at the level desired.
The concept of atomic structure has been included in the secondary science
curriculum for many years. Due to the importance of the topic in the study of science,
192
curriculum development about quantum theory in terms of atomic structure needs to be
undertaken for each grade level of science education. Lessons for quantum theory need to
be developed with consideration for the appropriate cognitive developmental levels of
students.
4) This study included three different student assessments comprised of course
examinations, questionnaires, and interviews. As can be seen in this study, these various
assessments provided information that indicated the nature of student mental models of
atomic structure. Each assessment can be used to gather information to map out and
describe student mental models. The comparative analysis between these assessments has
provided detailed information related to the nature of student understanding. Among
these assessments, the interview provides in-depth analysis of student mental models at
levels of understanding. Particularly, interviews were a more precise and accurate
assessment for mixed models for atomic structure and higher levels of understanding.
Based on these findings, although there is some variation as was revealed in the
comparative study of qualitative interview analysis and responses to course exams
related to atomic structure by q-methodology, data from this study showed the coherent
existence of mental models as represented in different aspects of assessments.
5) Through the comparison between academic achievement and conceptual
understanding as represented by the interview responses, this study revealed that
academic achievement in the course assessments was related to conceptual development
of atomic structure. There were no clear differences between level of understanding and
193
course grades in the pre-responses; however, this study provided a glimpse of the
relationship between academic achievement and conceptual understanding of atomic
structure. In the comparison of the pre- and post-interview responses, this study showed
high achieving students moved toward more improved models or to the advanced levels
of understanding. In addition, q methodology revealed the distinctive characteristics of
CP2 as a group of students who are high achieving with advanced levels of
understanding.
5. 4. 2. A proposed model for learning and teaching atomic structure by mental model
development
Model-based learning is defined by Gobert and Buckley (2000) as a process of
building mental models of phenomena. Clement (2000) proposed a theoretical
framework of model-based learning and explained learning as a process that can be
achieved through the iterative and continuous construction of models. Figure 5.1 shows
Clement’s framework and the framework explains that modeling (building intermediate
models) leads students to develop a pathway toward the target model and to achieve
desired knowledge through instruction. The framework provides an overview of the
model-based learning for instruction; however, the framework is limited in explaining
student learning. From that perspective, it can be more appropriate to consider the
framework as a strategy/process model for teaching by modeling.
194
Preconceptions
1. Alternative
conceptions and
models
2. Useful
conceptions and
models
Intermediate
Model (M1)
Intermediate
Model (M2)
Target
Model
(Mn)
Expert
Consensus
Model
Learning processes
Natural
reasoning skills
Figure 5.1: Theoretical framework for model based learning (Clement, 2000)
Based on the observation and analysis of student learning processes, the results of this
study leads to a modified framework for the model-based learning, especially targeting
atomic structure. Figure 6.2 displays the modified framework from this study.
195
Figure 5.2: Theoretical framework for model-based learning of atomic structure
This framework extended the concept of learning in Figure 5.1. In addition, this
framework explains not only the learning process based on mental-model development
but also considers instructional methods together with the learning process. The
occurrence of alternative models and the developmental process through higher order
thinking are also considered.
As can be seen in the findings of this study, students have preconceptions before
learning the topic “atomic structure.” As it is addressed in Figure 5.1, the preconceptions
196
include alternative models and useful models. Those conceptions stay in or float around
students’ minds in what is termed a “pooled zone.” The learning process of atomic
structure in Figure 6.2 is divided into three steps. The first step is initial
conceptualization or internalization of the instructed concept through natural reasoning
skills and instructional support. Through the introduction of each concept related to
atomic structure, students are able to internalize or construct the initial models of atomic
structure. In the second step, students need to build a meaningful understanding of each
concept during this second conceptualization, support is needed from systematic
reasoning skills and reinforced instructions, in order to facilitate the building of students’
depth of knowledge of the concept of atomic structure. The last step relates to student
abilities for inter-relational thinking as a tool that facilitates conceptual development
toward the target model.
5. 5. Limitations of this study
First, data from this study reports that the student preconceptions of atomic
structure included many alternative models and few students achieved the target model
that they were expected to acquire from this course. Because data for this study was
collected from students at a specific grade level, it has limited generalization for
understanding the relationships among student preconceptions of atomic structure,
alternative models, and achievement of the target model. A longitudinal study from lower
grade levels (where the preconception starts) to upper grade levels (where the target
197
model can be achieved) would provide more information and a wider vision for
comprehending student understanding of atomic structure from internalized mental
models to construction of the target model.
Second, because of the somewhat higher achievement characteristics of the 20
interviewed students who comprised the original sample for in-depth qualitative
exploration compared to the students enrolled in the course, the generalization of the
findings from the analyses may be somewhat limited.
Third, the researcher transcribed all the audio/video taped interview data as well
as generated categories about the interview results. Although the researcher went over
the audio tapes repeatedly and was careful to examine the transcribed data during the
coding process for the interview data, lack of a second person to repeat those procedures
is a limitation of this study.
5. 6 Further study
5. 6. 1 Short-term research proposal relating to this study
1) Laboratory activity conclusion writing analysis
The conclusions that students wrote for the ninth laboratory report were
additionally collected for this study. The ninth experiment, titled “emission spectra”
(Casey & Tatz, 2004), was designed for students to observe the emission spectra of
helium and hydrogen and to determine the transitions responsible for the lines in the
198
visible spectrum of hydrogen. This laboratory activity was scheduled for the week
following mid-term 2, and it was based upon Bohr’s experiment and postulation for line
spectra. The observation of line spectra was a key factor in the development of electronic
atomic theory related to Bohr’s model. Students were asked to include four categories in
writing their conclusions for the lab: (1) the purpose of the experiment, (2) a brief
summary of the methodology of the experiment supported by grounding theories, (3)
findings and data analysis, and (4) error analysis and discussion.
Future study to analyze these conclusions collected from the Total Group of this
study could be done to identify the relationships between this laboratory experience and
changes in student mental models of atomic structure. The analysis will provide
information to help better understand student perceptions about atomic structure. In
addition, this experiment will provide good criteria for determining changes in students’
interpretation of Bohr’s model in relation to this experiment.
2) Understanding student mental models by comparing two different
representations: the written and diagrammatic descriptions of atomic structure
Information acquired through various means can be internalized into mental
models by students. In regards to the conceptualization processes, Paivio’s dual coding
theory (1971) addresses the existence of two separate cognitive (coding) systems
specialized for verbal and imagery, or diagrammatic representation for this study. In this
study, written and diagrammatic descriptions of atomic structure were compared. Atomic
structure is a fundamental concept in science and is an example of imagery
199
representation used as scientific explanation. Atomic models have been used to help
student understanding of scientific theories by illustrating the theoretical structure of
atoms in a diagrammatic representation. Though atomic models are represented as
concrete images, the models can transfer the abstract nature of atoms into students’
minds.
To this end, the dual coding theory can be a useful tool for interpreting student
mental models from the two representations explored in this study. In order to explore
the cognitive processes used in understanding scientific models, a future study could
compare student mental models as represented in written and diagrammatic/graphic
responses on questionnaires and interviews. Mental models represent student learning
and understanding of such atomic structure. Moreover, in relation to representations of
atomic structure that students are exposed to, analyzing student mental models helps us
to understand the relationship of cognitive processes and the two different
representations.
3) Understanding the relationship between gender and conceptual understanding
Group 2 student responses to the question related to atomic structure in multiplechoice course assessments (a mid-term 1, mid-term 1, and the final exam) were further
analyzed by q methodology. Data clustered Group 2 students by three components (CP1,
CP2, and CP3). For the characterization of the components, students in each component
were further explored by comparing given information (gender, major, and academic
achievement) and mental models from interview analysis. Componential analysis showed
200
differences among components by gender. Concerning these differences, this study did
not undertake further investigation or discussion related to the differences within
components by gender. Further study with twenty randomly selected samples from the
Total Group would provide generalized patterns related to the findings in this study.
5. 6. 2. Long-term research proposals related to this study
1) Conceptual development based on hierarchical complexity
The concept “atomic structure” requires inter-relational understanding of abstract
concepts, models, mathematical representations, and empirical observations based on
quantum theory. This study discussed the importance of inter-relational thinking. In order
to grasp the meaning of atomic structure, students need to develop their mental models
for related theories such as the energy quantization, orbitals, and wave functions.
Although student levels of understanding were varied, there were few students at the 4/4
or 4/5 level of understanding as recommended by curriculum guides. Concerning the few
students in the advanced levels of understanding, an analysis of student ability for the
inter-relational thinking could reveal the relationships between conceptual understanding
and the higher order thinking skills necessary for the level of understanding.
In order to characterize the form of higher order thinking beyond Piaget’s formal
operation stage (1970), Commons, Richards, and Kuhn (1982) and Commons, Richards,
and Krause (1998) propose stages of post-formal operations to help to explain
hierarchical complexity; these stages include systematic and meta-systematic levels.
201
Commons and Richards (2002) explain that complexity of self-conscious operation on a
system as a whole requires extending developmental stages to post-formal levels. The
Therefore, it is very important for students to develop systematic thinking (meaningful
understanding of concepts) and meta-systematic thinking (inter-relational thinking
between concepts). To this end, future study could extend this study to involve a wider
span of grade levels. First, a longitudinal study would provide information about the
relationships between developmental levels and conceptual understanding. Second, in
order to evaluate the inter-relational thinking, the future study could use concept
mapping as an assessment tool. The methodology would help us to assess student interrelational thinking for the understanding of atomic structure. Data from this study could
provide information for assessing student conceptual understanding of atomic structure
and student ability for higher-order thinking related to their levels of developmental
complexity.
2) Instructional design related to theoretical framework of model-based learning
According to a research agenda related to understanding the mechanism for
model-based learning as illustrated in Figure 5.2, this study would focus on the three
steps of learning which are proposed as necessary for students to achieve the target
model of atomic structure: initial internalization, in-depth fortification, and interrelational thinking. Each step depends on appropriate reasoning skills. Instruction
designed to target these steps has potential for facilitating appropriate student thinking
needed for meaningful learning related to the target models. The acquired knowledge
202
about model-based learning would help in the preparation of appropriate instructional
curriculum focused upon the learning process and the influence on student conceptual
development. At the first stage of the curriculum, the main purpose of the lesson might
be to introduce the concept to facilitate internalization of student models. At the second
stage, the lesson could be reinforced in order for students to achieve the systematic
understanding needed for learning the concept in depth. The last stage of instruction
could then be to focus on the inter-relational connections. Not only conceptualization but
also understanding inter-relationships of concepts should help students construct the
target models for atomic structure.
203
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210
APPENDIX A
COURSE SYLLABUS
211
212
213
214
215
216
APPENDIX B
RECRUITMENT LETTER
217
Dear student
I would like to invite you to participate in a study, “The analysis of students’ models related to
atomic models in college chemistry”.
My name is Eun Jung Park and I am a Doctoral student of Science Education in the College of
Education at the Ohio State University. Dr. Arthur L. White is a professor in College of Education, The
Ohio State University, and he will advise me for this research. I will conduct this research for my
dissertation and I hope that I can learn more about students’ learning, effective teaching, and educational
research methods.
Your participation in this study is very important and your responses will help us better to
understand conceptual learning of atomic models and students’ mental models. The evidence from this
research will yield valuable information, which will help improve student understanding, curriculum
development, class achievement, and instruction.
This research is designed to get data from class observations, questionnaires, and interviews. First,
written inquiries (questionnaires) will be distributed in class. The responses of the inquiries will take about
10 minutes and the students can choose a waver of written consent. Second, I will conduct interviews with
student volunteers who have interest in this research. Interviewees will be asked to answer several
questions about atomic models and each interview will take approximately 20 -40 minutes. The interview
will be scheduled at times most convenient for the students.
Your participation in this study is entirely voluntary and your cooperation is greatly appreciated. In
order to insure the confidentiality of the data, all data will be identified by arbitrary pseudonyms. Any
information that is obtained in connection with this study will be strictly confidential.
If you decide to participate or you have any questions/concerns, please do not hesitate to contact me
or you can contact my research advisor, Dr. Arthur L. White, (Professor in the College of Education at The
Ohio State University).
Thank you very much for your time and interest.
Respectfully
Arthur L. White
Eun Jung Park
218
APPENDIX C
CONSENT FORM
219
Protocol # _________________
CONSENT FOR PARTICIPATION IN RESEARCH
I consent to participating in research entitled:
“The analysis of students’ models related to atomic models in college chemistry”
.
Arthur L. White, Principal Investigator, or his/her authorized representative Eun Jung
Park
has explained the purpose of the study, the procedures to be followed, and the
expected duration of my participation. Possible benefits of the study have been
described, as have alternative procedures, if such procedures are applicable and available.
I acknowledge that I have had the opportunity to obtain additional information regarding
the study and that any questions I have raised have been answered to my full satisfaction.
Furthermore, I understand that I am free to withdraw consent at any time and to
discontinue participation in the study without prejudice to me.
Finally, I acknowledge that I have read and fully understand the consent form. I sign it
freely and voluntarily. A copy has been given to me.
Date:
________________________________
Signed:
__________________________________
(Participant)
Signed:
________________________________
(Principal Investigator or his/her
authorized representative)
Signed:
__________________________________
(Person authorized to consent for
participant, if required)
HS-027E Consent for Participation in Exempt Research
220
APPENDIX D
QUESTIONNAIRES
221
Questionnaires 1
1. Name
Name:
. Section :
.TA :
Female
Male
.
.
2. Year in College?
a. 1st year
b. 2nd year
c. 3rd year
d. 4th year
.
d. recommended
.
e. other
.
3. Expected Major
Department
.
4. Why are you enrolled in this course?
a. requirement
b. elective
c. free-elective
e. other
.
5. a. Did you take a chemistry course in high school?
yes
no
other
.
b. Have you taken a previous chemistry course in university?
yes
no
other
.
c. How do you define atoms?
.
6. Atomic Structure
a. Describe or explain atomic structure.
b. Draw a picture of an atom. (you may use any atom as an example)
c. Identify and describe the parts in your drawing.
d. Does your drawing (representation) help you to understand the atom and its structure?
If so, explain why and if not, explain why not.
7. a. Explain what is meant by the term ‘orbital’.
b. Draw an orbital based on your understanding.
c. Can orbitals have different shapes?, explain.
d. How many electrons can an orbital hold?
e. What is a node?
222
223
Questionnaire 2
1. Name:
Section :
TA :
.
2. Define atoms.
3. Atomic Structure
a. Describe or explain atomic structure.
b. Draw a picture of an atom. (you may use any atom as an example)
c. Identify and describe the parts in your drawing.
d. Does your drawing (representation) help you to understand the atom and its structure?
If so, explain why and if not, explain why not.
4. Orbitals
a. Explain what is meant by the term ‘orbital’.
b. Draw an orbital based on your understanding.
c. Can orbitals have different shapes?, explain.
d. How many electrons can an orbital hold?
e. What is a node?
224
APPENDIX E
INTERVIEW PROTOCOL
225
Category
Question
Definition of atom
What is an atom?
Previous Knowledge
Have you studied the structure of atom before taking this course?
General Knowledge
Please explain or describe the structure of an atom.
Please draw an atom.(you may use any atom as an example)
Tell me about the parts of your drawing of the atom.
Please explain more about your drawing.
Does your drawing help you to understand the structure of an atom?
If yes, why?
If your answer is no, why not?
Do you know what is meant by a “model” in science?
When we name the models that are used in the field of science as
‘scientific models’, can you give me some examples of scientific
models?
How do you understand or use it? (you may answer by using
your examples)
Can you explain why it is useful or why not?
Can you give me a model of an atom?
Tell me about your understanding of the atomic model of an atom.
Do those models help you to understand the atomic structure?
If yes, why?
If your answer is no, why not?
Can you explain about
Table F.1 Interview questions
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