Can Dual Processing Theories of Thinking Inform Conceptual Learning in Mathematics?

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Concurring with Uri Leron's (2010) cross-disciplinary approach to two distinct modes of mathematical thinking, intuitive and analytic, I discuss his elaboration and adaptation to mathematics education of the cognitive psychology dual-processing theory (DPT) in terms of (a) the problem significance and (b) features of the theory he adapts. Then, I discuss DPT in light of a constructivist stance on the inseparability between thinking and learning. In particular, I propose a brain-based account of conceptual learning -- the Reflection on Activity-Effect Relationship (Ref*AER) framework--as a plausible alternative to DPT. I discuss advantages of the Ref*AER framework over DPT for mathematics education.