Abstract Two iterative, after school design experiments with small groups of middle school students were conducted to investigate how students constructed quantitative unknowns, conceived of as values of fixed quantities that are not known but can be determined. Students solved problems about an unknown height or length measured in two different units. Of 13 students who participated, 6 structured quantities into three levels of units. These students constructed an unknown as a height consisting of an indeterminate number of length units, each of which consisted of smaller length units, and they symbolized these relationships in their equations. The other 7 students structured quantities into two levels of units. Five of these students symbolized only the relationships between the measurement units, with two students demonstrating more basic and advanced solutions. The study shows that grappling with unknowns as measured and indeterminate is beneficial for students’ construction of variable.

中文翻译：

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中学生数量未知数的建构

摘要 对小组中学生进行了两次迭代的课后设计实验，以研究学生如何构建定量未知数，将其设想为未知但可以确定的固定量值。学生解决了关于以两个不同单位测量的未知高度或长度的问题。在参与的 13 名学生中，有 6 个结构化数量分为三个级别的单元。这些学生构造了一个未知数，作为由不确定数量的长度单位组成的高度，每个长度单位由较小的长度单位组成，并且他们在他们的方程中符号化了这些关系。其他 7 名学生将数量组织成两个级别的单位。其中五个学生仅象征测量单位之间的关系，两名学生展示了更基本和更高级的解决方案。研究表明，处理测量和不确定的未知数有利于学生构建变量。