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The Role of Definitions in Teaching, Learning, and Doing Mathematics: An Example of MKT Hyman Bass and Mark Thames (Click name for speaker's biography) Improved mathematics achievement requires changes in the instructional dynamics in classrooms and in the mathematical education of teachers. Unfortunately, while there is broad agreement on the need for better mathematical preparation of teachers, there is a lack of clarity about what mathematics teachers need to know. To address this problem, we examine actual practice. We define mathematical knowledge for teaching (MKT) as the mathematical knowledge, skills and habits of mind entailed in the work of teaching and we study it empirically. One result has been the identification of a set of mathematical practices also key to teaching and learning. Surprisingly prominent has been the use of definitions. In this presentation, we introduce the notion of MKT and investigate the role of definitions in teaching and learning. In particular, we illustrate where and how definitions arise in the work of teaching.
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