This paper focuses on three junior high school mathematics teachers and their knowledge of the nature of definitions. The mathematical context of exponentiation is used as a springboard for discussing two aspects of definitions: their corresponding domains and the distinction and relationships between definitions, proofs, and theorems. Through…

This study proposes a framework for research which takes into account three aspects of sociomathematical norms: teachers' endorsed norms, teachers' and students' enacted norms, and students' perceived norms. We investigate these aspects of sociomathematical norms in two elementary school classrooms in relation to mathematically based and…

This study investigates two sixth grade students' dilemmas regarding the parity of zero. Both students originally claimed that zero was neither even nor odd. Interviews revealed a conflict between students' formal definitions of even numbers and their concept images of even numbers, zero, and division. These images were supported by practically…