Making connections among representations of eigenvector: what sort of a beast is it?
Making connections among representations of eigenvector: what sort of a beast is it?
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在特征向量的表示之间建立联系：它是什么样的野兽？
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Gulden Karakok
中科院分区：
文献类型：
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作者：
Gulden Karakok
许多研究提供了学生对各种线性代数主题的概念以及他们在概念化所需的多种思维模式方面所面临的困难的见解。虽然理解学生的初始概念很重要，但学生将这些概念迁移到后续课程中可以为构建有意义的课程材料提供额外的信息。本研究探讨了物理专业学生学习本征值和特征向量的先决经验向量子力学迁移的情况。数据分析的重点是对本科生的三次任务型访谈、对物理课程的观察和学生的课程人工制品。已有的关于学生对线性代数主题概念的研究表明，为了掌握线性代数，有必要在不同的思维模式之间进行灵活的转换。这项研究的参与者最初有线性代数的学习经验，在量子课程之前，他们也被观察到在这种转变中挣扎。似乎量子课程中的各种背景和明确的教学方法为学生提供了加强特征值和特征向量的初始学习的机会。特别是，量子课程的一位讲师对课堂解题时某些表征的选择进行了明确的推理，似乎有助于学生构建相似性，从而为以行动者为导向的迁移提供了证据。这项研究的结果与最近开发的教材和干预措施的目标一致，这些教材和干预措施强调让学生有机会询问和联系多种思维模式。
Many studies provide insights into students’ conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed for conceptualization. While it is important to understand students’ initial conceptions, students’ transfer of learning of these conceptions to subsequent courses can provide additional information to structure meaningful curricular materials. This study explores physics students’ transfer of learning of eigenvalues and eigenvectors from prerequisite experiences to quantum mechanics. Data analysis focused on three task-based interviews with undergraduate students, observations of physics courses, and students’ course artifacts. Existing studies on students’ conceptions of linear algebra topics indicate the necessity of developing flexible shifts between different modes of thinking in order to grasp linear algebra. This study’s participants, who had initial learning experiences of linear algebra, were also observed to struggle with such shifts prior to quantum courses. It seems that various contexts in quantum courses, and explicit instructional methods, provided opportunities for students to enhance this initial learning of eigenvalues and eigenvectors. In particular, the explicit reasoning of one of the quantum courses’ instructors concerning the choice of certain representations during problem solving in class, seemed to facilitate students’ construction of similarities, thus providing evidence for actor-oriented transfer. Results of this study align with goals for recently developed instructional materials and interventions that emphasize opportunities for students to inquire and connect multiple modes of thinking.