The Rationality Debate: Application of Cognitive Psychology to Mathematics Education
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Research in mathematics education usually attempts to look into students’ learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of cognitive psychology. Our aim in this paper is to show how some recent developments in cognitive psychology can help interpret empirical results from mathematics education. In particular, we will be looking into the heuristics-and-biases research by Kahneman and Tversky, the alternative views by Gigerenzer et al., and the more recent dual-process theory that has come to play a central role in interpreting this research. We first introduce the relevant background from cognitive psychology and survey its connections to previous work in mathematics education; then we apply this theoretical framework for re-interpreting previously-published empirical data from mathematics education research. We conclude with a discussion of potential theoretical and practical benefits of such synthesis.
- Arcavi, A.: 1994, ‘Symbol sense: Informal sense-making in formal mathematics’, For the Learning of Mathematics 14(3), 24–35.
- Clement, J., Lockhead, J. and Monk, G.: 1981, ‘Translation difficulties in Learning Mathematics’, American Mathematical Monthly 88, 286–290. CrossRef
- Dawkins, R.: 1976/1990, The Selfish Gene, Oxford University Press, Oxford.
- Fischbein, E.: 1987, Intuition in Science and Mathematics: An Educational Approach, Reidel.
- Gallian, J.A.: 1990, Contemporary Abstract Algebra, 2nd edn., Heath, Boston.
- Geary, D.: 2002, ‘Principles of evolutionary educational psychology’, Learning and Individual Differences 12, 317–345. CrossRef
- Gigerenzer, G. and Todd, P.M.: 1999, Simple Heuristics that Make us Smart, OxfordUniversity Press, New York.
- Gilovich, T., Griffin, D. and Kahneman, D. (Eds.): 2002, Heuristics and Biases: The Psychology of Intuitive Judgment, Cambridge University Press.
- Hazzan, O. and Leron, U.: 1996, ‘Students' use and misuse of mathematical theorems: The case of Lagrange's theorem’, For the Learning of Mathematics 16(1),23–26.
- Kahneman, D. (Nobel Prize Lecture, December 8): 2002, ‘Maps of bounded rationality: A perspective on intuitive judgment and choice’, in T. Frangsmyr (ed.), Les Prix Nobel, pp. 416–499. Also accessible at http://www.nobel.se/economics/laureates/2002/kahnemann-lecture.pdf.
- Kahneman, D., Slovic, T. and Tversky, A.: 1982, Judgment Under Uncertainty: Heuristics and Biases, Cambridge University Press.
- Leron, U. and Hazzan, O.: 1997, ‘The world according to Johnny: A coping perspective in mathematics education’, Educational Studies in Mathematics 32, 265–292. CrossRef
- Pinker, S.: 2002, The Blank Slate: The Modern Denial of Human Nature, Viking.
- Polya, G.: 1973, How to Solve It? Princeton University Press, Princeton, New-Jersey.
- Ridley, M.: 2003, Nature via Nurture: Genes, Experience, and What Makes Us Human, Harper Collins.
- Samuels, R., Stich, S. and Tremoulet, P.D.: 1999, ‘Rethinking rationality: From bleak implications to darwinian modules’, in E. LePore and Z. Pylyshyn (eds.), What Is Cognitive Science?, Blackwell.
- Schoenfeld, A.H.: 1985, Mathematical Problem Solving, New York: Academic Press.
- Schoenfeld, A.H.: 1987, ‘What is all the fuss about metacognition?’, in A.H. Schoenfeld (ed.), Cognitive Science and Mathematics Education, Lawrence Erlbaum Associates, pp. 189–215.
- Schön, D.A.: 1983, The Reflective Practitioner, Basic Books.
- Schön, D.A.: 1987, Educating the Reflective Practitioner: Towards a New Design for Teaching and Learning in The Profession, San Francisco, Jossey-Bass.
- Simon, H.A.: 1982, Models of Bounded Rationality, MIT Press.
- Soloway, E., Lochhead, J. and Clement, J.: 1982, ‘Does computer programming enhance problem solving ability? Some positive evidence on algebra word problems’, in R.J. Seidel, R.E. Anderson and B. Hunter (eds.), Computer Literacy, Academic Press, pp. 171–185.
- Stanovich, K.E. and West, R.F.: 2000, ‘Individual differences in reasoning: Implications for the rationality debate’, Behavioral and Brain Sciences 23, 645–726. CrossRef
- Stanovich, K.E. and West, R.F.: 2003, ‘Evolutionary versus instrumental goals: How evolutionary psychology misconceives human rationality’, in D.E. Over (ed.), Evolution and the Psychology of Thinking: The Debate, Psychology Press, pp. 171–230.
- Stavy, R. and Tirosh, D.: 2000, How Students (Mis-)Understand Science and Mathematics: Intuitive Rules, Teachers College Press.
- Todd, P.M. and Gigerenzer, G.: 2000, ‘Precis of simple heuristic that make us smart’, Behavioral and Brain Sciences 23, 727–780. CrossRef
- Vinner, S.: 1997, ‘The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning’, Educational Studies in Mathematics 34, 97–129. CrossRef
- The Rationality Debate: Application of Cognitive Psychology to Mathematics Education
Educational Studies in Mathematics
Volume 62, Issue 2 , pp 105-126
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