ABSTRACT

Two-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11–12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented a balanced mix of students operating with each of three different multiplicative concepts that have been identified in prior research. This paper reports on the 11 students who were using the first or second multiplicative concept. Students operating with different multiplicative concepts all experienced similar perturbing elements in their solution of APs relative to their solution of CPPs, but they operated differently to resolve these perturbing elements. These differences are identified and their significance discussed in relation to other research findings on students’ combinatorial and multiplicative reasoning.

摘要

对14名11至12岁的14名六年级学生分别进行了为时两小时的发展性教学访谈。访谈的目的是调查学生如何解决布置问题（AP），以及他们对这些问题的解决方案与他们对笛卡尔乘积问题（CPP）的解决方案有何不同。这14名学生代表了在以前的研究中已经确定的三种不同乘法概念中的每一种的均衡操作。本文报告了使用第一个或第二个乘法概念的11名学生。使用不同乘法概念的学生相对于CPP解决方案，在AP解决方案中都经历了类似的干扰因素，但解决这些干扰因素的方法有所不同。