The Power of Natural Thinking: Applications of Cognitive Psychology to Mathematics Education
Concurring with Uri Leron’s cross-disciplinary approach to distinct modes of mathematical thinking, intuitive and analytic, I discuss his elaboration and adaptation to our field of the cognitive psychology dual-processing theory (DPT). I reflect on (a) the problem significance, (b) aspects of the theory he adapts, and (c) elegance of presentation. Then, I further discuss DPT in light of a constructivist stance on the inseparability of thinking and learning. I link DPT to accounts of (i) brain-based conceptual learning and (ii) how mathematics teaching may promote such learning—and discuss advantages of those accounts.
Tzur, R. (2010). How may conceptual learning in mathematics benefit from dual processing theories of thinking? In P. Brosnan, D. B. Erchick, and L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (vol. 6, pp. 21-32). Columbus, OH: The Ohio State University.