Promoting Conceptual
Change through
Cognitive Conflict
Beverly L. Wood
Department of Mathematics, University of Virginia
Wendi E. Dass
Department of Mathematics, Piedmont Virginia Community College
Introduction
APPLE
Longfield, J. (2009). “Discrepant Teaching Events: Using An Inquiry Stance To Address Students’
Misconceptions,” International Journal of Teaching and Learning in Higher Education, 21(2), 266-271.
Cognitive conflict and conceptual change refer to situations in which
new knowledge (learned by a child, a student, or discovered by a
research scientist) is incompatible with prior knowledge, and hence
might affect understanding of the material…. Faced with having to
absorb material that is in some way incompatible with prior
knowledge…an individual will try to assimilate new information into
their existing framework, thus creating a so-called synthetic model. As
mixtures of beliefs and scientific facts, these synthetic models represent
misconceptions about the subject. (emphasis added)
Clark, M., & Lovric, M. (2009). Understanding Secondary-Tertiary Transition in Mathematics,
International Journal of Mathematical Education in Science and Technology, 40(6), 755-776.
Conceptual Change Through Cognitive Conflict
1) There must be dissatisfaction with existing conceptions.
2) A new conception must be intelligible.
3) A new conception must appear initially plausible.
Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). “Accommodation of a
Scientific Conception: Toward a Theory of Conceptual Change,” Science Education, 66, 211227. doi:10.1002/sce.3730660207
Examples from Science Education
Bridging Analogies - Physics
Simulation - Mathematics
Clement, J. (1987). “Overcoming Students’ Misconceptions in Physics:
The Role of Anchoring Intuitions and Analogical Validity,” in
Proceedings of the International Seminar Misconceptions And
Educational Strategies in Science and Mathematics (Vol. 3), pp. 84-97.
A Short Quiz
Please take a moment to answer the
questions on the handout.
• If you teach mathematics or statistics, answer how you
think your students would.
Definitions
The representativeness heuristic is the cognitive shortcut for assessing the
likeness of objects or events to a prototype for the category (Gilovich &
Savitsky, 2002).
 believing that the gender sequence of children in a large family BGGBGB is
more likely than BBBBBG because it represents a closer fit to the theoretical
50/50 distribution of gender in the human population
Kahneman and Tversky (1973) describe the availability heuristic as assigning
likelihood based on the cognitive ease of imagining the uncertain outcome.
 estimating an event’s occurrence based on personal experience with the
event, believing the frequency they have witnessed indicates probability
Gilovich, T., Griffin, D., & Kahneman, D. (2002). Heuristics and Biases: The Psychology of
Intuitive Judgment. Cambridge, UK: Cambridge University Press.
Kahneman, D., & Tversky, A. (1973). “Availability: A heuristic for judging frequency and
probability,” Cognitive Psychology, 5, 207-232.
Examples from Statistics Education
Bridging Analogies
Simulation
TARGET: A fair coin is tossed 5 times
and the result is HHHHH . On the next
toss, which outcome, if either, do you
think has a better chance of occurring, H
(heads) or T (tails) ?
ANCHOR: A fair coin is tossed once
and the result is H. On the next toss,
which outcome, if either, do you think
has a better chance of occurring, H
(heads) or T (tails) ?
a) H has a better chance of occurring
b) T has a better chance of occurring
c) They both have the same chance of
occurring.
Fast, G.R. (1999). “Analogies and Reconstruction of Probability
Knowledge,” School Science and Mathematics, 99(5), 230-240.
Liu, Tzu-Chien (2010). “Developing Simulation-Based
Computer Assisted Learning To Correct Students'
Statistical Misconceptions Based On Cognitive Conflict
Theory, Using ‘Correlation’ as an Example,” Journal of
Educational Technology & Society, 13(2), 180-192.
More Simulations
 National Library of Virtual Manipulatives (nlvm.usa.edu)
Spinners, Monty Hall simulation, rare events
 Center for Technology and Teacher Education
(www.teacherlink.org)
Plinko simulation, Excel projects
 Rice Virtual Lab in Statistics (onlinestatbook.com)
Statistics Simulations
Discussion
How will you use cognitive conflict in your
classroom?