Abstract

This study presents the results of a series of design experiments that aimed to engage twelve fourth-grade students in mathematical activity exploring the volume of right prisms and cylinders as a dynamic sweep of a surface through a height, an approach that is referred to as Dynamic Measurement for Volume (DYME-V). This article describes this approach and discusses the qualitatively different forms of DYME-V reasoning that students exhibited through this mathematical activity. The analysis of students’ reasoning illustrates how students may reason about the quantities involved in DYME-V, their multiplicative relationship, and also their coordinated multiplicative change. The findings show the potential of the DYME-V approach for supporting a perception of right prisms and cylinders as spaces that are generated and thus defined by other objects as the approach emphasizes dynamic images of change in volume measurement.

摘要

本研究展示了一系列设计实验的结果，旨在让 12 名四年级学生参与数学活动，探索直棱柱和圆柱体的体积作为表面通过高度的动态扫描，这种方法被称为动态体积测量 (DYME-V)。本文描述了这种方法，并讨论了学生通过这种数学活动展示的 DYME-V 推理的不同形式。对学生推理的分析说明了学生如何推理 DYME-V 中涉及的数量、它们的乘法关系以及它们协调的乘法变化。