CAREER: An Interdisciplinary Study of Learning: Student Understanding of Linear Algebra in Physics

标题：职业：学习的跨学科研究：学生对物理中线性代数的理解与国家推进科学、技术、工程和数学(STEM)学科的责任一致，国家研究委员会(NRC)的报告(2012)“基于学科的教育研究：理解和改善本科科学和工程中的学习”描述了关于高年级STEM课程学生的学习和知识转移的跨学科研究的必要性。在这方面，该项目将为改善STEM学科的本科教育提供新的见解。这项研究的结果不仅将扩大已知的学生对数学和物理的跨学科理解的研究基础，而且还将通过利用数学和物理教育研究在教与学方面的协同作用，对本科水平的教学影响做出贡献。该项目还将有助于开发本科生数学学习的创新评估工具。该项目将结合研究和教育，在量子物理的框架内研究线性代数的本征理论和相关的关键思想。研究的重点将是：(1)描述学生对量子物理中与本征理论相关的概念进行推理和符号化的各种方式；(2)确定学生对与本征理论相关的概念的语言和符号是如何跨数学上下文和量子物理上下文进行比较和对比的；以及(3)探索教师对语言和数学符号的使用如何与学生对量子物理中本征理论的理解、符号化和解释有关。该项目还将制作和审查一个面向概念的本征理论多项选择扩展(MCE)评估工具。以上(1)-(3)项的研究将包括教科书分析、MCE本征理论工具的创建和实施、访谈方案的制定和实施、课堂观察和对参与教师的访谈，以及衔接序列的开发。

Title:CAREER: An Interdisciplinary Study Of Learning: Student Understanding Of Linear Algebra In PhysicsConsistent with the national charge for the advancement of Science, Technology, Engineering, and Mathematics (STEM) disciplines, the National Research Council's (NRC's) report (2012) "Discipline-Based Education Research: Understanding and Improving Learning in Undergraduate Science and Engineering" describes a need for interdisciplinary studies regarding learning and the transfer of knowledge for students in upper division STEM courses. This project will contribute towards this national need for basic research by investigating students' learning and understanding of key topics and ideas from linear algebra - a fundamental mathematics topic for STEM majors in multiple disciplines - as applied to undergraduate upper-division physics. In connection with this, the project will provide new insights in improving undergraduate education within the STEM disciplines. The results of this study will not only extend the research base of what is known about student understanding of mathematics and physics across disciplines, but it will also contribute to pedagogical implications at the undergraduate level by leveraging the synergy between mathematics and physics education research on teaching and learning. The project will also contribute to the development of innovative assessment instruments for undergraduate mathematics learning. The project will integrate research and education to investigate eigentheory and related key ideas from linear algebra within the framework of quantum physics. The research focal points will be to: (1) characterize the various ways in which students reason about and symbolize concepts related to eigentheory in quantum physics; (2) determine how students' language and symbols for concepts related to eigentheory compare and contrast across mathematics contexts and quantum physics contexts; and (3) explore how instructors' use of language and mathematical symbols relates to students' understanding, symbolization, and interpretation of eigentheory in quantum physics. To help foster and diversify the research investigations, data will be collected from the quantum physics courses at three academic institutions: Virginia Polytechnic Institute and State University; Oregon State University; and the University of Maine. The project will also produce and vet a conceptually oriented multiple-choice extension (MCE) assessment instrument for eigentheory. Included in the research to address items (1)-(3) listed above will be textbook analysis, the MCE eigentheory instrument creation and implementation, interview protocol development and implementation, classroom observations and interviews with participating instructors, and bridging sequences development. To enhance and expand the overall infrastructure and collaborations for research and education across disciplines, this instrument together with research results from the investigations will be disseminated widely through research and practitioner publications, presentations, and workshops in mathematics and physics education.