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Toward a framework for the development of mathematical knowledge for teaching

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Abstract

Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics. One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has started to gain attention as an important concept in the mathematics teacher education research community, there is limited understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article, we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in both mathematics education and the learning sciences.

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Notes

  1. We borrow this idea from Thompson and Saldanha (2000, October), who developed the notion of epistemic subject as a way to explain how a teacher can attend to the intellectual needs of an entire classroom without having to attend to the needs of every student in it. An epistemic subject is an idealized person who happens to think in a particular way. Our use of “categories of ways of thinking” is equivalent to Thompson and Saldanha’s use of “epistemic subject.”.

  2. Piaget defined the word broadly as any change to the perceptual input (Piaget, 1967).

  3. Thus there is a transformation in the development of further refined and developed mathematical knowledge. It is, however, new mathematical knowledge, not pedagogical knowledge.

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Authors and Affiliations

  1. Drexel University, Philadelphia, PA, USA

    Jason Silverman

  2. Arizona State University, Phoenix, AZ, USA

    Patrick W. Thompson

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  1. Jason Silverman
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  2. Patrick W. Thompson
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Correspondence to Jason Silverman.

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Silverman, J., Thompson, P.W. Toward a framework for the development of mathematical knowledge for teaching. J Math Teacher Educ 11, 499–511 (2008). https://doi.org/10.1007/s10857-008-9089-5

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