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Promoting fundamental change in mathematics teaching: a theoretical, methodological, and empirical approach to the problem

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Abstract

Mathematics education reform, as conceptualized in the United States and a number of other countries, represents a fundamental change in the teaching of mathematics and the results it would produce for students. Whereas there are data that suggest some progress is being made in the direction of reform, teacher education and professional development during the last two decades have been largely unsuccessful in preparing teachers to enact the reform vision. In this article, I present a theoretical construct, major assimilatory structures, that can contribute to explaining the difficulty of promoting change in mathematics teaching. I describe a methodology—accounts of practice—for identifying major assimilatory structures of teachers and present an example of a major assimilatory structure, perception-based perspective, that emerged from our empirical work.

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Notes

  1. All people can be analyzed in terms of their assimilatory structures. In some cases it may be useful to characterize individuals or groups of individuals as having major assimilatory structures. These could be in the areas of religion, profession, parenthood and others. The key to such a claim is that the structure has wide impact and is resistant to change.

  2. A parallel can be drawn with research on students’ mathematical conceptions. The mathematical understandings of the researchers contribute to what they can notice and the distinctions they can make. Researchers who do not understand the mathematics would not have the same abilities. In the case of pedagogical conceptions, how researchers understand learning and teaching is central to what they notice and distinctions they can make.

  3. This inquiry led to a second line of research focusing on theory of learning and teaching. See Simon, Tzur, Heinz, & Kinzel, (2004); Simon & Tzur (2004); Tzur, R., Simon, M.A. (2004); and Simon et al. (2010).

  4. This is a way of expressing the underlying idea behind the assumption that everyone sees the same mathematical relationships in a given mathematical representation or situation.

  5. As a teacher educator, I engage in and support these practices.

  6. I extend my appreciation to the reviewer who raised this question.

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Correspondence to Martin A. Simon.

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Simon, M.A. Promoting fundamental change in mathematics teaching: a theoretical, methodological, and empirical approach to the problem. ZDM Mathematics Education 45, 573–582 (2013). https://doi.org/10.1007/s11858-013-0486-6

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