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.

摘要

本文为有关准小学教师数学思维和学习的研究文献做出了贡献，重点是灵活性。我们提供了一个案例研究，该案例研究了一名预期的小学教师在“数字与运算”课程中在智力加减方面的灵活性的发展。在构建策略范围的基础上，我们介绍了脚手架策略范围，它描述了人们使用的策略集，这些策略集赋予了人们以多种方式解决任务的机会。像许多未来的基础老师一样，白兰地最初在智力加减法上显得缺乏灵活性。事实上，她无支架的策略范围仅限于标准算法的思维类似物。但是，白兰地的脚手架策略范围显示出更大的灵活性潜力。此外，