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.

该项目位于圣何塞州立大学，美国原住民太平洋岛民服务机构（AANAPISI）和西班牙裔服务机构（HSI），旨在通过改善学生在本科线性代数课程中的数学经验来服务国家利益。线性代数主题提供了重要的内容和概念，这些内容和概念与几个STEM学科的本科专业有关，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，这些工具和资源将旨在通过21世纪的数学技能和能力来支持学生成长。这些工具和资源将是实用的，也将专注于促进深思熟虑和理解。 VR工具将是计算机生成的，并将提供完全沉浸式的表示形式，使学生能够公平地访问经验，主要是在二维和三维框架中建造，操纵，模拟和理解对象和概念。正是通过这些努力，结果将扩展到包括较高维度的设置。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实施对VR工具和资源影响的概念验证研究。一个基本的结果将是增强学生的21世纪数学技能，批判性和分析性思维以及高级概念性理解，以满足未来社会的需求。该项目将追求几个与改善学生在数学方面的经验和成功的目标，总的来说，尤其是线性代数。目标1是开发工具和资源，以实施创新的VR介导的学习环境，以捕捉兴趣并增强学生的参与度。第二个目标是研究这种环境，以提高如何更好地支持学生发展技能的知识基础，并对线性代数概念，计算，应用和理论基础深入理解。通常，学生只会意识到与这些功能相关的周边理解。第三个且相关的目标是促进有关如何利用图像和视觉表示在数学（尤其是线性代数中的沟通和推理）中的核心作用的当前知识状态。目标4是提供基于研究的发现，以了解VR的潜在变革力，以深入学习数学概念和过程。第五个目标是在为STEM教育社区提供项目工具和资源的同时传播结果和研究结果。最初的动力将是检查二维和三维笛卡尔坐标系统中的向量，矩阵，线性变换和线性代数模拟等主题。然后，通过建立VR工具的使用与预测，较低维近似值，尺寸降低和数据压缩之间的关系，将设置扩展到更通用的N维系统。该项目将以以下两个研究问题（RQS）指导：（RQ1）在多大程度上，视觉几何和以动作为导向的VR介导的干预支持并增强了对线性代数概念的深入学习，以及在这种情况下操纵的能力？ （RQ2）在学习线性代数的VR介导的环境中引起的学生推理的性质是什么？该项目将利用基于设计的混合方法研究实现来建立和完善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控制和治疗组之间的测试后表现。此外，将对视频记录的临床访谈，评估和调查的回答进行编码和分析。项目结果将通过高影响同行审查的教育期刊的出版物，会议和年度会议的演讲，网络研讨会，座谈会，专业发展研讨会，与同事的表达会议，维护公共项目网站以及科学和科技博物馆的公共示范网站进行主动传播。与该项目散发出来的该传播计划，工具，材料和资源一致，将在线免费提供。 NSF IUSE：EDU计划支持研发项目，以提高所有学生STEM教育的有效性。通过参与的学生学习轨道，该计划支持有希望的实践和工具的创建，探索和实施。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估的评估来支持的。