ABSTRACT

Three iterative, 18-episode design experiments were conducted after school with groups of 6–9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students’ mathematical thinking while developing a cohesive classroom community. Analysis of 10 episodes across experiments yielded five teaching practices that facilitated DI: using research-based knowledge of students’ mathematical thinking, providing purposeful choices and different pathways, inquiring responsively during group work, attending to small group functioning, and conducting whole class discussions across different thinkers. The latter three practices, at times, impeded DI. This study is a case of using second-order models of students’ mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students’ thinking are at the heart of differentiating mathematics instruction.

摘要

放学后与6–9名中学生组成的小组进行了三个迭代的18集设计实验，以了解如何区分数学教学。关于区分式教学（DI）和假设学习轨迹的先前研究指导了教学。随着实验的进行，DI的定义应运而生：在建立凝聚力的课堂社区的同时，主动根据学生的数学思维量身定制教学。通过对实验中的10集进行分析，得出了五种促进DI的教学实践：使用基于研究的学生数学思维知识，提供有目的的选择和不同的途径，在小组工作中进行响应式查询，参加小组活动以及在整个小组中进行全班讨论不同的思想家。后三种做法 有时会阻止DI。这项研究是使用学生数学思维的二阶模型来区分教学的一个案例，它揭示了对基于研究的知识的探究和对学生思维的响应式探究是区分数学教学的核心。