Teachers’ knowledge of the nature of definitions: The case of the zero exponent

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 interviews it was shown that some teachers are not aware that definitions and domains are intrinsically connected and some teachers believe that definitions may be proved. Findings also indicate that knowledge of the nature of definitions may be dependent on the context.

► Some junior high school teachers are not aware that a0 = 1 is a definition. Instead, they believe that they may prove this equality. ► Some junior high school teachers are not sensitive to the issue of the domain of a definition. ► Some junior high school teachers believe that some definitions may be proved. ► Junior high school teachers’ knowledge of definitions and proofs is more stable within the context of geometry than it is within the context of exponentiation.