Abstract
We offer evidence that people can construe mathematical relations as causal. The studies show that people can select the causal versions of equations and that their selections predict both what they consider most understandable and how they expect variables to influence one another. When asked to write down equations, people have a strong preference for the version that matches their causal model. Causal models serve to structure equations by determining the preferred order of variables: Causes should be on one side of an equality, and a single effect should appear on the other.
Article PDF
References
Andersson, B. (1986). The experiential gestalt of causation: A common core to pupil’s preconceptions in science.European Journal of Science Education,8, 155–171.
Chi, M. T. H., Feltovich, P. J., &Glaser, R. (1981). Categorization and representation of physics problems by experts and novices.Cognitive Science,5, 121–152.
DiSessa, A. A. (1993). Towards an epistemology of physics.Cognition & Instruction,10, 105–225.
Driver, R., Guesne, E., &Tiberghien, A. (1993). Some features of children’s ideas and their implications for teaching. In R. Driver, E. Guesne, & A. Tiberghien (Eds.),Children’s ideas in science (pp. 193–201). Buckingham, U.K.: Open University.
Glymour, C. (2001).The mind’s arrows: Bayes nets and graphical causal models in psychology. Cambridge, MA: MIT Press.
Hall, R., Kibler, D., Wenger, E., &Truxaw, C. (1989). Exploring the episodic structure of algebra story problem solving.Cognition & Instruction,6, 223–283.
Hinsley, D. A., Hayes, J. R., &Simon, H. A. (1977). From words to equations: Meaning and representation in algebra word problems. In M. A. Just & P. A. Carpenter (Eds.),Cognitive processes in comprehension (pp. 89–105). Hillsdale, NJ: Erlbaum.
Hunt, E., &Minstrell, J. (1994). A cognitive approach to the teaching of physics. In K. McGilly (Ed.),Classroom lessons: Integrating cognitive theory and classroom practice (pp. 51–74). Cambridge, MA: MIT Press.
Larkin, J. (1983). The role of problem representation in physics. In D. Gentner & A. Stevens (Eds.),Mental models (pp. 75–98). Hillsdale, NJ: Erlbaum.
Nathan, M. J., Kintsch, W., &Young, E. (1992). A theory of algebra-word-problem comprehension and its implications for the design of learning environments.Cognition & Instruction,9, 329–389.
Paige, J. M., &Simon, H. A. (1966). Cognitive processes in solving word problems. In B. Kleinmuntz (Ed.),Problem solving: Research, method, and theory (pp. 51–119). New York: Wiley.
Pearl, J. (2000).Causality: Models, reasoning and inference. New York: Cambridge University Press.
Priest, A. G., &Lindsay, R. O. (1992). New light on novice-expert differences in physics problem solving.British Journal of Psychology,83, 389–405.
Reif, F., &Allen, S. (1992). Cognition for interpreting scientific concepts: A study of acceleration.Cognition & Instruction,9, 1–44.
Reiner, M., Slotta, J. D., Chi, M. T. H., &Resnick, L. B. (2000). Naive physics reasoning: A commitment to substance-based conceptions.Cognition & Instruction,18, 1–34.
Sherin, B. L. (2001). How students understand physics equations.Cognition & Instruction,19, 479–541.
Sloman, S. [A.], &Lagnado, D. [A.] (2004). Causal invariance in reasoning and learning. In B. Ross (Ed.),The psychology of learning and motivation (Vol. 44, pp. 287–325). San Diego: Academic Press.
Sloman, S. A., &Lagnado, D. A. (2005). Do we “do”?Cognitive Science,29, 5–39.
Spirtes, P., Glymour, C., &Scheines, R. (1993).Causation, prediction, and search. New York: Springer-Verlag.
Waldmann, M. R. (1996). Knowledge-based causal induction. In D. R. Shanks, K. J. Holyoak, & D. L. Medin (Eds.),The psychology of learning and motivation: Vol. 34. Causal learning (pp. 47–88). San Diego: Academic Press.
White, B. Y. (1993). ThinkerTools: Causal models, conceptual change, and science education.Cognition & Instruction,10, 1–100.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was funded by NASA Grant NCC2-1217.
Rights and permissions
About this article
Cite this article
Mochon, D., Sloman, S.A. Causal models frame interpretation of mathematical equations. Psychonomic Bulletin & Review 11, 1099–1104 (2004). https://doi.org/10.3758/BF03196743
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03196743