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Over the past several years, a community of researchers has been using and refining a particular framework for research and curriculum development in undergraduate mathematics education. The purpose of this paper is to share the results of this work with the mathematics education community at large by describing the current version of the framework and giving some examples of its application. Our framework utilizes qualitative methods for research and is based on a very specific theoretical perspective that is being developed through attempts to understand the ideas of Piaget concerning reflective abstraction and reconstruct them in the context of college level mathematics. Our approach has three components. It begins with an initial theoretical analysis of what it means to understand a concept and how that understanding can be constructed by the learner. This leads to the design of an instructional treatment that focuses directly on trying to get students to make the constructions cal...
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