Download Taxonomy of Conceptions for Size and Scale

Taxonomy of Conceptions for Size and Scale
Alejandra Magana, Sean Brophy, and Scott Schaffer
Purdue University
Introduction:
Notions of size and scale have been identified as:
• one of the “Big Ideas of Nanoscience and Nanotechnology”
• one of the four powerful common themes transcending math, science, and engineering
Methods:
Goals: How can we express conceptions of size and scale in a way that helps us frame our research and understand students’ scale cognition?
What are middle school students’ conceptions of size and scale relative to this frame?
Are there appropriate instructional strategies that will scaffold students’ conceptions of size and sale?
Participants in this study included approximately 150 middle school students:
• 110 students participated in a two days instruction based on the cognitive information processing perspective (CIP)
• 44 students received no instruction related to size and scale but participated in an informal learning environment about nanotechnology
Results:
Qualitative categorical --- size
Example:
• Classifying the virus and the diameter of the DNA double
strand as corresponding to the nanoscale
• Classifying the bacteria, red blood cell and human egg cell as
part of the microscale
• Classifying the ant and the human as part of the macroscale
Qualitative categorical --size
Qualitative categorical --size
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
Performanc e
Performanc e
Supported by the Generalization cognitive process
Group I
Group I
Group 2
Group 2
Group 3
Group 3
Pre
Pre
Day 1
Day 1
Qualitative relational --- size
Group I
Group I
Group 2
Group 2
Group 3
Group 3
Day 1
Day 1
Qualitative proportional --- size
Example:
• The difference in size between the height of a human and
the length of an ant is approximately the same –
proportional as the difference in diameter between a
bacteria and a DNA double strand.
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Treatment
Treatment
Non-treatment
Non-treatment
90
90
80
80
Percentage
Percentage
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
Treatment
Treatment
The majority of students
exposed to instruction
understood the proportional
relationship between objects.
The quantitative proportional
conception of scale is a
challenging concept at a middle
school level.
Quantitative Proportional --scale
Quantitative Proportional --scale
100
100
0
After instruction, students
exposed to instruction based on
the CIP improved their
performance in classifying
objects and ordering objects.
Some of the students who were
not exposed to instruction were
able to identify the qualitative
proportional relationship
between objects.
Qualitative Proportional --size
Qualitative Proportional --size
90
90
Quantitative proportional --- scale
Supported by Numerical Proportional reasoning
Example:
• The difference in length of an ant compared to the height of
a human is that an ant is about a thousand times smaller
than the height of a human. Proportionally, this
difference is equivalent to the size between a bacteria and
the diameter of a DNA double strand. These analogical
pairs are 3 times a power of ten different.
Day 2
Day 2
100
100
Percentage
Percentage
Supported by Logical proportional reasoning
Before instruction students
performed well in the ordering
task.
Qualitative relational --size
Qualitative relational --size
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
Perform anc e
Perform anc e
Supported by the Discrimination cognitive process
Example:
• Ordering objects according to its relative size such as
atom < virus < bacteria < red blood cell < human
egg cell < ant < human
Day 2
Day 2
Group 1 are the 59% of students
who classified the objects by
size. Group 2 are students that
did not classified by size.
Group 3 are students who did
not receive the instruction
based on the CIP perspective,
but were exposed to an informal
learning environment.
Non-treatment
Non-treatment
Many of the students were able
to identify in numerical terms
the difference between the pairs
of objects by using the scale
metaphor.
Quantitative absolute --- scale
Supported by Mathematical cognition
Example:
• The size of a bacteria is one micrometer, also expressed as
-6
1µm or in scientific notation as 1 x 10 m
Conclusions and Implications:
Instruction based on Cognitive Information Processing perspective may convey concepts of size and scale at the micro and nano level
A scale metaphor can be used as a scaffold to students’ cognitive processes for attaining scale cognition
Future work: How do students conception of size and scale relative to this taxonomy progress from middle school, high school, undergraduate and
graduate schools ability to reason?