Abstract The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in mathematics majors’ treatment of similar matrices and matrix representations of linear transformations in a computer-assisted learning environment by drawing primarily on three aspects of the experimental mathematics methodology, made possible by using modern digital tools to enhance learning: testing conjectures, suggesting proofs, and, computing lengthy hand derivations (Borwein & Bailey, 2003). The analysis revealed a diversity of innovative ways by which research participants coordinated analytic and computational (MATLAB) methods for understanding matrix similarity and its connections to the rest of linear algebra. The paper concludes by offering pedagogical implications and recommendations for further research.

中文翻译：

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线性代数学生在MATLAB辅助学习环境中对相似矩阵和线性变换的矩阵表示的理解

摘要这项研究的目的是在技术辅助（MATLAB）学习中进行的一系列深度定性访谈中，了解数学专业如何理解相似的矩阵（一个线性的代数主题，内部和外部的联系都很丰富）环境。这项研究还试图通过主要利用实验数学方法学的三个方面来发展数学专业的认知理论，以处理计算机辅助学习环境中的相似矩阵和线性变换的矩阵表示的情况，这可以通过使用现代数字技术来实现增强学习的工具：测试猜想，提出证明以及计算冗长的手推导（Borwein＆Bailey，2003）。分析揭示了多种创新方式，研究参与者可通过这些方式协调分析和计算（MATLAB）方法来理解矩阵相似度及其与线性代数其余部分的联系。本文最后通过提供教学意义和进一步研究的建议。