Attending to Precision: Mathematical Definitions in Courses for Pre-Service and Practicing Teachers

Abstract

In this article we address the Common Core State Standard for Mathematical Practice: Attend to Precision. We describe work in mathematics content courses for pre-service and inservice teachers focused on developing teachers’ understanding of mathematical definitions. We discuss teachers’ work in developing definitions for students at various levels of mathematics, in generalizing a definition in order to extend the domain to which it may be applied, and in correcting teachers’ misconceptions. The work discussed in this article is consistent with the recommendations of the Conference Board of the Mathematical Sciences for the mathematics education of teachers. In explicit response to contemporary mathematics education research, the author presents constructive assessment prompts which lend themselves to formal study by mathematics education researchers.

KEYWORDS:

• Education and instruction in mathematics

ACKNOWLEDGEMENTS

The author thanks the anonymous referees for their corrections and useful suggestions.

Additional information

Notes on contributors

Lisa Berger

Lisa Berger is an experienced middle school and high school mathematics teacher. An associate professor of mathematics at Stony Brook University, she currently teaches content and methods courses for pre-service and in-service secondary mathematics teachers.