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Mathematical Knowledge for Teaching and its Specificity to High School Geometry Instruction

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Research Trends in Mathematics Teacher Education

Part of the book series: Research in Mathematics Education ((RME))

Abstract

This chapter documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on a piloted set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have statistically significant correlations with years of experience teaching high school geometry. Other interesting relationships regarding teachers’ MKT-G scores are also reported. We use these results to propose a way of conceptualizing how instruction-specific considerations might matter in the design of MKT items. In particular, we propose that the instructional situations that are customary to a course of studies can be seen as units that organize much of the mathematical knowledge for teaching such a course.

Author Note: Research reported had the support of the National Science Foundation through grant DRL-0918425 to P. Herbst. All opinions are those of the authors and do not necessarily reflect the views of the Foundation. We acknowledge helpful comments to earlier versions of this chapter by Deborah L. Ball and by members of the Geometry, Reasoning, and Instructional Practices (GRIP) lab at The University of Michigan School of Education.

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Notes

  1. 1.

    Daniel Chazan, a co-PI of this project, was also involved in design discussions. Individuals involved in the drafting of items, in addition to the authors, included Michael Weiss, Wendy Aaron, Justin Dimmel, Ander Erickson, and Annick Rougee.

  2. 2.

    The triangle inequality states that if a, b, and c are the lengths of the sides of a triangle, then a−c < b < a + c.

  3. 3.

    The number of diagonals in a polygon of n sides is n (n−3)/2.

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Author information

Authors and Affiliations

  1. School of Education, University of Michigan, Ann Arbor, MI, USA

    Patricio Herbst

  2. School of Teaching, Learning, and Curriculum Studies; College of Education, Health, and Human Services, Kent State University, Kent, OH, USA

    Karl Kosko

Authors
  1. Patricio Herbst
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  2. Karl Kosko
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Correspondence to Patricio Herbst .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, Michigan, USA

    Jane-Jane Lo

  2. Department of Mathematics Education, Brigham Young University, Provo, Utah, USA

    Keith R. Leatham

  3. Department of Mathematics, Western Michigan University, Kalamazoo, Michigan, USA

    Laura R. Van Zoest

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Herbst, P., Kosko, K. (2014). Mathematical Knowledge for Teaching and its Specificity to High School Geometry Instruction. In: Lo, JJ., Leatham, K., Van Zoest, L. (eds) Research Trends in Mathematics Teacher Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-02562-9_2

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