Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base
Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base
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角度测量、定量推理和教学连贯性：对数学思维方式作为教师知识库组成部分的作用的检验
DOI：
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发表时间：
2018
影响因子：
2.1
通讯作者：
Kristin Frank
中科院分区：
文献类型：
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作者：
M. Tallman;Kristin Frank
本文报告了一项研究的结果，该研究为哈雷尔（Zentralblatt für Didaktik der Math 40:893–907 2008b）将数学思维方式纳入教师专业知识库的组成部分提供了实证支持。具体来说，我们研究了定量推理的作用（Smith 和 Thompson，见：Kaput、Carraher、Blanton（eds）低年级代数，Erlbaum，纽约，2007 年；Thompson，见：算术和代数中基于数量的推理的理论模型，数学与科学教育研究中心：圣地亚哥州立大学 1990 年；Thompson，见：Hatfield 等人） （编辑）数学教育合作研究的新视角和方向，怀俄明大学，拉勒米，2011 年）关于经验丰富的中学教师角度测量教学的质量和连贯性。我们分析了教师教学的 37 个视频，以表征他在多大程度上支持学生对角度测量进行定量推理，并检验这种关注对教师教学所支持的含义的质量和连贯性的影响。我们的分析表明，教师传达的不一致的含义是由于他缺乏对学生定量推理的概念可供性的认识而造成的，这些概念对学生构建连贯的、有意义的角度测量理解的能力有影响。因此，我们的研究结果支持哈雷尔的观点，即教师的数学思维方式构成了其专业内容知识的重要组成部分。
This paper reports findings from a study that establishes empirical support for Harel’s (Zentralblatt für Didaktik der Math 40:893–907 2008b) inclusion of mathematical ways of thinking as a component of teachers’ professional knowledge base. Specifically, we examined the role of quantitative reasoning (Smith and Thompson, in: Kaput, Carraher, Blanton (eds) Algebra in the early grades, Erlbaum, New York 2007; Thompson, in: A theoretical model of quantity-based reasoning in arithmetic and algebra, Center for Research in Mathematics & Science Education: San Diego State University 1990; Thompson, in: Hatfield et al (eds) New perspectives and directions for collaborative research in mathematics education, University of Wyoming, Laramie 2011) on the quality and coherence of an experienced secondary teacher’s instruction of angle measure. We analyzed 37 videos of the teacher’s instruction to characterize the extent to which he attended to supporting students in reasoning about angle measure quantitatively, and to examine the consequences of this attention on the quality and coherence of the meanings the teacher’s instruction supported. Our analysis revealed that the inconsistent meanings the teacher conveyed were occasioned by his lack of awareness of the conceptual affordances of students’ quantitative reasoning on their ability to construct coherent, meaningful understandings of angle measure. Our findings therefore support Harel’s notion that teachers’ mathematical ways of thinking constitute an essential component of their specialized content knowledge.