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

开发虚拟现实介导的表示工具来支持和增强对线性代数关系的深入数学理解

• 批准号: 2315756
• 负责人: Ferdinand Rivera
• 金额: $ 40万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-15 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2315756&HistoricalAwards=false
• 关键词: Developing; Virtual; Reality; Mediated; Representational

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.

圣何塞州立大学的这个项目是美洲原住民太平洋岛民服务机构 (AANAPISI) 和西班牙裔服务机构 (HSI) 的项目，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国家利益。线性代数主题提供与多个 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，旨在支持学生培养 21 世纪的数学技能和能力。这些工具和资源将是实用的，并且将侧重于促进深入的思考和理解。 VR 工具将由计算机生成，并提供完全身临其境的呈现，使学生能够公平地体验构建、操作、模拟和理解对象和概念，主要是在二维和三维框架中。正是通过这些努力，结果将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。基本成果将是提高学生的 21 世纪数学技能、批判性和分析性思维以及高水平概念理解，以满足未来社会的需求。该项目将追求与改善学生在以下领域的体验和成功相关的几个目标：一般而言，数学，特别是线性代数。目标 1 是开发工具和资源来实施创新的 VR 介导的学习环境，以吸引学生的兴趣并提高学生的参与度。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，学生只能对这些功能有粗浅的了解。第三个相关目标是推进当前的知识水平，了解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 是提供基于研究的发现，说明 VR 对数学概念和过程的深度学习的潜在变革力量。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。最初的动力是研究二维和三维笛卡尔坐标系中的向量、矩阵、线性变换和线性代数模拟等主题。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，该设置将扩展到更一般的 n 维系统。该项目将遵循以下两个研究问题 (RQ)： (RQ1) 视觉几何和面向行动的 VR 介导的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其中进行操作的能力这个上下文？ (RQ2) 在 VR 介导的环境中学习线性代数的学生推理的本质是什么？该项目将利用基于设计的混合方法研究实施来建立和完善 VR 工具以及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治疗组的测试后表现。此外，学生在视频录制的临床访谈、评估和调查中的回答也将被编码和分析。项目成果将通过高影响力的同行评审教育期刊上的出版物、在会议和年会上的演讲、网络研讨会、座谈会、专业发展研讨会、与同事的阐述会议、公共项目网站的维护以及科学和技术方面的公开演示来积极传播。科技博物馆。根据该传播计划，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。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 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。