How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign

Abstract

What kind of mathematical knowledge do prospective teachers need for teaching and for understanding student thinking? And how can its construction be enhanced? This article contributes to the ongoing discussion on mathematics-for-teaching by investigating the case of understanding students’ perspectives on equations and equalities and on meanings of the equal sign. It is shown that diagnostic competence comprises didactically sensitive mathematical knowledge, especially about different meanings of mathematical objects. The theoretical claims are substantiated by a report on a teacher education course, which draws on the analysis of student thinking as an opportunity to construct didactically sensitive mathematical knowledge for teaching for pre-service middle-school mathematics teachers.

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Acknowledgments

The author would like to thank the reviewers for their constructive criticism and comments, and his Ph.D. student Katja Schreiber for the excerpt of her transcript of Episode 2.

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Correspondence to Susanne Prediger.

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Prediger, S. How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign. J Math Teacher Educ 13, 73–93 (2010). https://doi.org/10.1007/s10857-009-9119-y

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Keywords

  • Teacher education
  • Mathematics-for-teaching
  • Diagnostic competence
  • Meaning
  • Algebra
  • Equal sign
  • Variables