Promoting Conceptual Change through Cognitive ConflictBeverly L. Wood Department of Mathematics, University of Virginia Wendi E. Dass Department of Mathematics, Piedmont Virginia Community College

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.

Introduction

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, 211-227. doi:10.1002/sce.3730660207

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.

Examples from Science Education

Please take a moment to answer the questions on the handout.

• If you teach mathematics or statistics, answer how you think your students would.

A Short Quiz

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.

Definitions

Examples from Statistics Education

Fast, G.R. (1999). “Analogies and Reconstruction of Probability Knowledge,” School Science and Mathematics, 99(5), 230-240.

Bridging Analogies Simulation

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.

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.

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?