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

这个项目在圣何塞州立大学，美国土著太平洋岛民服务机构（AANAPISI）和西班牙裔服务机构（HSI），旨在通过提高学生的数学经验，在本科线性代数课程服务于国家利益。线性代数主题提供了与多个STEM学科的本科专业相关的重要内容和概念，包括但不限于数学，计算机科学，物理和大多数工程学科。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，旨在支持学生的成长与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。VR工具将由计算机生成，并将提供完全沉浸式的表示，使学生能够获得公平的体验，主要在二维和三维框架中构建，操纵，模拟和理解物体和概念。正是通过这些努力，结果将被扩展到包括更高维度的设置。该项目的前两年涉及开发，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VR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世纪的数学技能，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。该项目将追求与改善学生的经验和成功的数学，一般来说，线性代数，特别是几个目标。目标1是开发工具和资源，以实现创新的VR介导的学习环境，以吸引学生的兴趣和提高他们的参与度。第二个目标是研究这种设置，以增加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基础。很多时候，学生只意识到与这些功能相关的外围理解。第三个和相关的目标是推进当前的知识状态，如何利用图像和视觉表示在数学，特别是线性代数的交流和推理中的核心作用。目标4是提供基于研究的结果，说明VR在数学概念和过程的深度学习方面的潜在变革力量。第五个目标是传播成果和研究成果，同时向STEM教育界提供项目工具和资源。最初的动力将是检查主题，如向量，矩阵，线性变换，线性代数模拟在二维和三维笛卡尔坐标系。然后，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，将设置扩展到更一般的n维系统。该项目将由以下两个研究问题（RQ）指导：（RQ 1）视觉几何和行动导向的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操作的能力？(RQ2)在以虚拟现实为媒介的学习线性代数的环境中，学生推理的本质是什么？本计画将以设计为基础的混合方法研究实作，建立与改善虚拟实境工具，并实作与调查课堂教学实验。项目评估项目将用于比较对照组和给药组的试验后表现。此外，学生在视频记录的临床访谈，评估和调查的反应将被编码和分析。项目成果将通过以下方式积极传播：在影响力大的同行评审的教育期刊上发表文章、在大会和年度会议上发言、网络研讨会、学术讨论会、专业发展讲习班、与同事的衔接会议、维护公共项目网站以及在科技博物馆进行公开演示。根据这一传播计划，该项目产生的工具、材料和资源将在网上免费提供。NSF IUSE：EDU计划支持研究和开发项目，以提高所有学生STEM教育的有效性。该奖项反映了NSF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.