High school mathematics teachers' content knowledge of the logical structure of proof deriving from figural-concept interaction in geometry

Karpuz Yavuz; Atasoy Ercan

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High school mathematics teachers' content knowledge of the logical structure of proof deriving from figural-concept interaction in geometry

机译：高中数学教师的内容知识逻辑结构从几何信息概念相互作用导出

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摘要

The present study aims to examine high school mathematics teachers' content knowledge of the logical structure of proof in geometry. For this purpose, three scenarios were established based on errors in proof deriving from the figural-concept interactions. Based on these scenarios, clinical interviews were held with five mathematics teachers, who were working at different high schools, who used proof actively in their classrooms, and who had varying experiences. The obtained data from the interviews were analyzed descriptively under three categories. The results of the study revealed that the teachers did not have sufficient content knowledge to cope with proof errors deriving from figural-concept interactions in geometry. The teachers generally failed to base the information they obtained from figures on an axiom or theorem, to avoid sweeping generalizations based on geometric figures, and making accurate changes in figures when contradictions emerged as a result of valid reasoning processes. It is recommended that discussions be held on the justifications underlying the propositions constituting the proof and mistakes in geometric proof at the undergraduate level of education.

机译：本研究旨在审查高中数学教师的几何逻辑结构的内容知识。为此目的，基于从图形概念交互的证据错误建立了三种情况。根据这些情景，临床访谈与五个数学教师一起举行，他正在在不同的高中工作，他们在课堂上积极使用证据，并有不同的经历。来自面试的获得数据在三个类别下进行了分析。该研究的结果透露，教师没有足够的内容知识来应对从几何形状中的图解 - 概念相互作用导出的证据错误。教师通常未能基于在公理或定理上的图中获得的信息，以避免基于几何图形的扫描概括，并在由于有效推理过程的结果出现的矛盾时做出准确的图。建议讨论讨论基础的理由，该主题构成了在本科教育水平的几何证据中构成了对几何证明的证据和错误。

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来源
《International Journal of Mathematical Education in Science and Technology》 |2020年第4期|585-603|共19页
作者
Karpuz Yavuz; Atasoy Ercan;
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作者单位

Recep Tayyip Erdogan Univ Vocat Sch Tech Studies Rize Turkey;

Recep Tayyip Erdogan Univ Fac Educ Rize Turkey;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Content knowledge; geometry; proof; reasoning;

机译：内容知识;几何;证明;推理;

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High school mathematics teachers' content knowledge of the logical structure of proof deriving from figural-concept interaction in geometry

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