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Developing mathematical practices through reflection cycles

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Abstract

This paper focuses on reflection in learning mathematical practices. While there is a long history of research on reflection in mathematics, it has focused primarily on the development of conceptual understanding. Building on notion of learning as participation in social practices, this paper broadens the theory of reflection in mathematics learning. To do so, it introduces the concept of reflection cycles. Each cycle begins with prospective reflection, which guides one’s actions during an experience, and ends with retrospective reflection, which consolidates the experience and informs the next reflection cycle. Using reflection cycles as an organizing framework, this paper synthesizes the literature on reflective practices at a variety of levels: (1) metacognition, (2) self-assessment, (3) noticing, and (4) lifelong learning. These practices represent a spectrum of reflection, ranging from the micro level (1) to macro level (4).

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  1. Department of Mathematics, San Diego State University, 5500 Campanile Drive, San Diego, CA, 92182-7720, USA

    Daniel L. Reinholz

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  1. Daniel L. Reinholz
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Correspondence to Daniel L. Reinholz.

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Reinholz, D.L. Developing mathematical practices through reflection cycles. Math Ed Res J 28, 441–455 (2016). https://doi.org/10.1007/s13394-016-0175-1

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  • DOI: https://doi.org/10.1007/s13394-016-0175-1

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