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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 Lecture content by chapters 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. 107 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. 108 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 113 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. 170 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 171 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. 172 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 173 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. 174 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. 175 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 176 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 177 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 178 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 179 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. 180 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.” 183 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 REFERENCES Anderson, B. (1990). Pupils’ conceptions of matter and its transformations (ages 12-16). Science Education, 18, 53-85. Asimov, I. (1991). Atom: Journey across the subatomic cosmos. New York: Truman Talley Books-Dutton. 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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 226