ABSTRACT

We analyzed item responses provided by a nationwide sample of 990 in-service U.S. middle grades mathematics teachers to a novel survey focused on fraction arithmetic. The survey targeted four components of reasoning in terms of measured quantities: Referent units, Reversibility, Partitioning and iterating, and Appropriateness. Using the mixture Rasch model, a psychometric model that combines unidimensional scaling with classification, we detected 3 latent classes. To understand what distinguished the performance of teachers in the three classes, we analyzed their responses to each item. One main result is that the performance of teachers across the three classes was more clearly distinguished on items targeting Reversibility and Partitioning and iterating than it was on items targeting Referent units and Appropriateness. A second main result is that the three classes formed a nested structure that aligned with good performance on more and more components of reasoning targeted by the survey items.

摘要

我们分析了由 990 名在职美国中学数学教师组成的全国样本对一项专注于分数算术的新颖调查提供的项目回答。该调查针对测量数量方面的推理的四个组成部分：参照单位、可逆性、分区和迭代以及适当性。使用混合 Rasch 模型（一种将一维缩放与分类相结合的心理测量模型），我们检测到 3 个潜在类别。为了了解教师在三个班级的表现有何不同，我们分析了他们对每个项目的回答。一个主要结果是三个班级的教师在针对可逆性和分区和迭代比针对参考单位和适当性的项目进行。第二个主要结果是，这三个类形成了一个嵌套结构，在越来越多的调查项目所针对的推理组件上具有良好的性能。