Documenting the Process of a Prospective Elementary Teacher’s Flexibility Development: Scaffolded Strategy Ranges and Sociomathematical Norms for Mental Computation

Abstract

This article contributes to the research literature concerning prospective elementary teachers’ mathematical thinking and learning with a focus on flexibility. We present a case study of a prospective elementary teachers’ development of flexibility in mental addition and subtraction during a Number and Operations course. Building upon the construct of strategy ranges, we introduce scaffolded strategy ranges, which describe the sets of strategies that people use given the opportunity to solve a task in multiple ways. Like many prospective elementary teachers, Brandy initially appeared inflexible in mental addition and subtraction. In fact, her unscaffolded strategy ranges were limited to just the mental analogs of the standard algorithms. However, Brandy’s scaffolded strategy ranges revealed greater potential for flexibility. Furthermore, the way of reasoning that appeared in Brandy’s scaffolded strategy ranges (a) influenced her interpretations of nonstandard strategies that she encountered in the Number and Operations course and (b) foreshadowed the direction in which her flexibility would develop.