Elizabeth A. Burroughs

Prospective Teachers' Understanding of Decimals with Single Repeating Digits.

Abstract This article investigates prospective elementary teachers’ conceptions of the repeating decimal .999.... Five students from a first-semester undergraduate course “Mathematics for Elementary School Teachers” were interviewed to ascertain their conceptions about the mathematical statement .999… = 1. All of the students indicated they do not believe .999… and 1 are equivalent. When faced with a proof that demonstrates the equivalence, several responded by rejecting some aspect of prior-held knowledge about mathematics. This article presents evidence that these students formed their misconceptions about repeating decimals in early grades rather than in higher-level courses that cover limit notions and that higher-level courses can lead students to reason incorrectly about infinitely repeating decimals.

By Definition: An Examination of the Process of Defining in Mathematics

Our work as mathematics education researchers in a department of mathematical sciences rests upon a foundation of reflections on our own teaching practices and on the mathematical practices that our preservice mathematics teachers are expected to learn. In the nexus of these reflections sit issues relevant to the learning and teaching of mathematics, and the understanding of these issues requires sustained and systematic research that includes and goes beyond reflecting on practices. We present an example of a teaching episode focused on preparing secondary mathematics teachers to better understand mathematical definitions and the process of creating mathematical definitions. We then examine some historical developments in mathematical practice related to definitions and the defining process and relate these developments to challenges entailed in teaching practice. We conclude with examples of researchable areas embedded in these issues and comment on the impact of our work.