Issues in theorizing mathematics learning and teaching: A contrast between learning through activity and DNR research programs

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• 作者：Martin A. Simon
• 关键词：Learning theory ; Abstraction ; Mechanism of learning ; Task design ; Learning trajectory ; Instructional design
• 刊名：Journal of Mathematical Behavior
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：32
• 期：3
• 页码：281-294
• 全文大小：612 K

文摘

By continuing a contrast with the DNR research program, begun in , I discuss several important issues with respect to teaching and learning mathematics that have emerged from our research program which studies learning that occurs through students¡¯ mathematical activity and indicate issues of complementarity between DNR and our research program. I make distinctions about what we mean by inquiring into the mechanisms of conceptual learning and how it differs from work that elucidates steps in the development of a mathematical concept. I argue that the construct of disequilibrium is neither necessary nor sufficient to explain mathematics conceptual learning. I describe an emerging approach to instruction aimed at particular mathematical understandings that fosters reinvention of mathematical concepts without depending on students¡¯ success solving novel problems.