ABSTRACT

The purpose of this study was to investigate how teachers understand one specific aspect of proportional reasoning. We were interested in understanding the extent to which practicing teachers were able to make sense of reasoning that involved the fixed number of variable-sized parts perspective. We used two items, drawn from a larger dataset, that encouraged teachers to reason about proportional situations using a variable parts perspective. We analyzed teachers’ responses to these items using the knowledge in pieces perspective to identify fine-grained understandings teachers were applying to the situations. Our findings suggest that reasoning about variable-sized parts is not something all of these teachers did. Further, we found certain proportional structures that seemed to support teachers who were able to reason from this perspective.

摘要

本研究的目的是调查教师如何理解比例推理的一个特定方面。我们有兴趣了解实习教师在多大程度上能够理解涉及固定数量的可变大小部分视角的推理。我们使用了两个项目，它们来自一个更大的数据集，鼓励教师使用可变部分的角度来推理比例情况。我们使用分块知识来分析教师对这些项目的反应，以确定教师在具体情况下应用的细粒度理解。我们的研究结果表明，并非所有这些教师都对可变尺寸零件进行推理。此外，我们发现某些比例结构似乎支持能够从这个角度进行推理的教师。