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Definitions of mathematical knowledge for teaching: using these constructs in research on secondary and college mathematics teachers

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Abstract

The construct “mathematical knowledge for teaching” (MKT) has received considerable attention in the mathematics education community in recent years. The development and refinement of the MKT construct, including the components of common content knowledge (CCK) and specialized content knowledge (SCK), came from research into elementary teachers’ practices. In this article, we argue that various issues arise as these constructs are used in research on secondary and post-secondary teachers. For example, elementary teachers typically differ from teachers of higher grades in their content preparation. What then is the relationship of CCK to SCK for those holding a bachelors degree or higher in mathematics? The MKT construct is based on CCK being knowledge held or used by an average mathematically literate citizen and that SCK is different. However, among those teaching in secondary and post-secondary contexts, what should be considered CCK? Is conceptual understanding of the CCK among those with bachelor’s degrees or higher level mathematics the same as SCK? We examine these questions as well as others that arose from our examination of definitions of CCK and SCK as we attempted to utilize those definitions to characterize the nature of MKT at secondary and undergraduate levels. We illustrate these issues with data from two instructional settings.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grants Nos. DRL-0629266 and DUE-0536231. This material is based upon work supported while serving at the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Author notes

  1. Heather Howell

    Present address: Educational Testing Service, 660 Rosedale Road, Princeton, NJ, 08541, USA

Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Maine, 234 Neville Hall, Orono, ME, 04469, USA

    Natasha M. Speer

  2. Division of Research on Learning in Formal and Informal Environments, National Science Foundation, 4201 Wilson Blvd, Suite 885N, Arlington, VA, 22230, USA

    Karen D. King

  3. New York University, 82 Washington Square East 7th floor, New York, NY, 10003, USA

    Heather Howell

Authors
  1. Natasha M. Speer
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  2. Karen D. King
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  3. Heather Howell
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Correspondence to Natasha M. Speer.

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Speer, N.M., King, K.D. & Howell, H. Definitions of mathematical knowledge for teaching: using these constructs in research on secondary and college mathematics teachers. J Math Teacher Educ 18, 105–122 (2015). https://doi.org/10.1007/s10857-014-9277-4

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