Developing Virtual Reality-Mediated Representational Tools for Supporting and Enhancing Deep Mathematical Understanding of Linear Algebra Relationships

圣何塞州立大学是美国土著太平洋岛民服务机构（AANAPISI）和西班牙裔服务机构（HSI），该项目旨在通过提高学生在本科线性代数课程中的数学经验来服务于国家利益。线性代数主题提供了与多个STEM学科（包括但不限于数学、计算机科学、物理和大多数工程学科）的本科专业相关的重要内容和概念。该项目将开发、实施、调查、完善和传播一套虚拟现实（VR）工具和资源，旨在支持学生发展21世纪的数学技能和能力。这些工具和资源将是实用的，也将侧重于促进深入思考和理解。虚拟现实工具将由计算机生成，并将提供完全沉浸式的表示，使学生能够公平地获得构建、操纵、模拟和理解物体和概念的体验，主要是在二维和三维框架中。正是通过这些努力，结果将被扩展到包括更高维度的设置。项目的前两年包括开发、测试和完善VR工具和补充教学资源。该项目的第三年将涉及对虚拟现实工具和资源的影响进行概念验证研究。一个潜在的结果将是提高学生的21世纪数学技能，批判性和分析性思维，以及高层次的概念理解，以满足未来社会的需求。该项目将追求几个与提高学生在数学方面的经验和成功相关的目标，特别是线性代数。目标1是开发工具和资源，以实施创新的虚拟现实媒介学习环境，以吸引学生的兴趣并提高他们的参与度。第二个目标是研究这种设置，以增加关于如何更好地支持学生发展技能和深入理解线性代数概念、计算、应用和理论基础的知识库。很多时候，学生们对这些特征只了解一些皮毛。第三个相关的目标是推进关于如何利用图像和视觉表征在数学，特别是线性代数的交流和推理中的核心作用的知识现状。目标4是为深度学习数学概念和过程的VR潜在变革力量提供基于研究的发现。第五个目标是传播成果和研究成果，同时为STEM教育界提供项目工具和资源。最初的推动力将是在二维和三维笛卡尔坐标系中研究诸如向量、矩阵、线性变换和线性代数模拟等主题。通过建立VR工具的使用与投影、低维近似、降维和数据压缩之间的关系，该设置将扩展到更一般的n维系统。该项目将以以下两个研究问题（rq）为指导：（RQ1）视觉几何和面向行动的vr介导干预在多大程度上支持和增强线性代数概念的深度学习以及在此背景下的操作能力？（RQ2）在vr介导的线性代数学习环境中，学生推理的本质是什么？本项目将采用基于设计的混合方法研究实施，建立和完善虚拟现实工具，实施和调查课堂教学实验。项目评估项目将用于比较对照组和实验组的测试后表现。此外，学生在录制的临床访谈、评估和调查中的回答将被编码和分析。项目成果将通过在高影响力的同行评审教育期刊上发表文章、在会议和年会上发表演讲、网络研讨会、座谈会、专业发展研讨会、与同事的交流、维护公共项目网站以及在科技馆进行公开展示等方式积极传播。与此传播计划一致，项目产生的工具、材料和资源将在网上免费提供。NSF IUSE:EDU项目支持研究和开发项目，以提高所有学生STEM教育的有效性。通过参与学生学习轨道，该计划支持有前途的实践和工具的创建，探索和实施。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project at San Jose State University, a Native American Pacific Islander Serving Institution (AANAPISI) and Hispanic Serving Institution (HSI), aims to serve the national interest by improving student's mathematical experiences in undergraduate linear algebra courses. Linear algebra subject matter provides important content and concepts that are pertinent to undergraduate majors across several STEM disciplines, including, but not restricted to, mathematics, computer science, physics, and most engineering disciplines. The project will develop, implement, investigate, refine, and disseminate a suite of virtual reality (VR) tools and resources that will be designed to support student growth with 21st century mathematical skills and competencies. These tools and resources will be practical, and also will be focused on promoting deep thinking and understanding. The VR tools will be computer-generated and will provide fully immersive representations that enable students to gain equitable access to experience constructing, manipulating, simulating, and understanding objects and concepts, primarily in two-dimensional and three-dimensional frameworks. It is through these efforts that results will then be extended to include higher-dimensional settings. The first two years of the project involve developing, testing, and refining the VR tools and supplemental instructional resources. The third year of the project will involve implementing a proof-of-concept study of the impact of the VR tools and resources. An underlying outcome will be to enhance students' 21st century mathematical skills, critical and analytical thinking, and high-level conceptual understanding to meet the demands of the society of the future.This project will pursue several goals related to improving student experiences and successes in mathematics, in general, and linear algebra, in particular. Goal 1 is to develop tools and resources to implement an innovative VR-mediated learning environment to capture the interest and enhance the engagement of students. A second goal is to study this setting to increase the knowledge base on how to better support students in developing skills and a deep comprehension of linear algebra concepts, calculations, applications, and theoretical underpinnings. Too often, students only realize a peripheral understanding related to these features. A third and related goal is to advance the current state of knowledge on how to capitalize on the central role of imagery and visual representations in communicating about and reasoning in mathematics, particularly linear algebra. Goal 4 is to provide research-based findings on the potentially transformative power of VR for deep learning of mathematical concepts and processes. A fifth goal is to disseminate outcomes and research findings while making project tools and resources available to the STEM education community. An initial impetus will be to examine topics such as vectors, matrices, linear transformations, and linear algebra simulations in two- and three-dimensional Cartesian Coordinate systems. The setting will then be extended to more general n-dimensional systems by establishing a relationship between the use of VR tools and, for example, projections, lower dimensional approximations, dimensional reduction, and data compression. The project will be guided by the following two research questions (RQs): (RQ1) To what extent does a visual-geometric and action-oriented VR-mediated intervention support and enhance a deep learning of linear algebra concepts and the ability to manipulate within this context? (RQ2) What is the nature of student reasoning elicited in a VR-mediated environment for learning linear algebra? This project will utilize a design-based mixed-methods research implementation in establishing and refining the VR tools and in implementing and investigating classroom teaching experiments. Project assessment items will be used to compare the post-test performance across control and treatment groups. In addition, students' responses in video recorded clinical interviews, assessments, and surveys will be coded and analyzed. Project results will be proactively disseminated through publications in high-impact peer reviewed education journals, presentations at conferences and annual meetings, webinars, colloquia, professional development workshops, articulation sessions with colleagues, maintenance of a public project website, and public demonstrations in science and technology museums. In concert with this dissemination plan, tools, materials, and resources that emanate from the project will be made freely available online. The NSF IUSE:EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.