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首页> 外文期刊>International Journal of Mathematical Education in Science and Technology >Synergies among students' thinking modes and representation types in linear algebra: employing statistical implicative analysis
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Synergies among students' thinking modes and representation types in linear algebra: employing statistical implicative analysis

机译：线性代数中学生思维方式和表现形式之间的协同作用：采用统计暗示分析

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In this work, students' thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students' thinking modes and representation types of linear algebra. The participants were 74 undergraduate linear algebra students enrolled in the department of mathematics education of a government university located in western Turkey. The data was collected using six paper-and-pencil tasks, relating to a context of linear equations, matrix algebra, linear combination, span, linear independency-dependency and basis. A document analysis technique was used to analyze the data within a theoretical lens of thinking modes and representation types. To delineate similarity diagrams, hierarchical trees, and implicative models (which will be detailed in the paper), an R version of Cohesion Hierarchical Implicative Classification software was used. According to the results, students' analytic structural thinking modes on linear combination and span and linear independency significantly imply the use of algebraic and abstract representations. The results also confirm that the notions of linear combination and span and linear dependency/independency are core elements for theoretical thinking and are needed for learning linear algebra.
机译：在这项工作中，通过统计暗示分析技术研究了学生在线性代数中的思维方式和表现形式。具体而言，我们的研究问题考虑了学生的思维方式与线性代数的表示类型之间的内在联系。参与者是74名本科线性代数学生，就读于土耳其西部一所公立大学的数学教育系。使用六个纸笔任务收集数据，这些任务涉及线性方程，矩阵代数，线性组合，跨度，线性独立性和基础的上下文。使用文档分析技术在思维方式和表示类型的理论视角内分析数据。为了描述相似性图，层次树和隐含模型（将在本文中进行详细介绍），使用了R版本的内聚层次隐含分类软件。根据结果​​，学生对线性组合，跨度和线性独立性的分析性结构思维模式显着暗示了代数和抽象表示的使用。结果还证实，线性组合和跨度以及线性相关性/独立性的概念是理论思考的核心要素，是学习线性代数所必需的。

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