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Textbook representations of radian angle measure: The need to build on the quantitative view of angle

机译：弧度角度测量的教科书表示形式：需要建立在角度的定量视图上

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摘要

Empirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the representations of radian angle measure in eight widely used U.S. high school mathematics textbooks. The data for this study are the 20 figures and the 8 definitions of radian angle measure in the textbooks. Inductive content analysis was used to identify the frequency of observable characteristics in the representations. Textbook figures of radian angle measure most frequently focus on a one-radian angle. Textbook figures also demonstrated radian angle measures in terms of pi, in standard position, even when the Cartesian-coordinate plane was not in the figure. The frequently used characteristics of radian representations could inadvertently reinforce a qualitative concept of angle, instead of fostering the quantitative attributes of radian angle measure. Moving forward, analyzing conceptions that are evoked by the frequently used representations of radian angle measure could build a link between evidence from this study and studies of learning.
机译：角度，角度量度和弧度角度量度的实证研究主要集中于记录学生和教师的观念。角度测量的表示形式有可能为这些概念提供信息并以其为基础。为了从课程角度深入了解弧度角度测量的概念，我调查了八本广泛使用的美国高中数学教科书中弧度角度测量的表示形式。这项研究的数据是教科书中的20个数字和8个弧度角度定义。归纳内容分析用于确定表示形式中可观察特征的频率。教科书上的弧度角测量值通常集中在一个弧度角上。教科书中的图形还显示了在标准位置上以pi为单位的弧度角度量度，即使笛卡尔坐标平面不在图中也是如此。弧度表示的常用特征可能会无意中强化角度的定性概念，而不是促进弧度角度测量的定量属性。展望未来，分析由弧度角测量的常用表示引起的概念可以在本研究的证据与学习研究之间建立联系。

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