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一个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)，旨在通过改善学生在本科生线性代数课程中的数学体验来服务于国家利益。线性代数主题提供了与几个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、改进和传播一套虚拟现实(VR)工具和资源，旨在支持具有21世纪数学技能和能力的学生成长。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，并将提供完全身临其境的表示，使学生能够平等地体验构建、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，结果才会扩展到包括更高维度的环境。该项目的头两年涉及开发、测试和改进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21世纪的数学技能，批判性和分析性思维，以及高水平的概念理解，以满足未来社会的要求。这个项目将追求几个与改善学生在数学，特别是线性代数方面的体验和成功有关的目标。目标1是开发工具和资源来实施创新的虚拟现实中介学习环境，以激发学生的兴趣并提高他们的参与度。第二个目标是研究这一背景，以增加关于如何更好地支持学生发展技能和对线性代数概念、计算、应用和理论基础的深入理解的知识库。太多时候，学生只意识到与这些功能相关的外围理解。第三个相关的目标是提高关于如何利用图像和视觉表现在数学，特别是线性代数的交流和推理中的中心作用的现有知识状态。目标4是就VR对深入学习数学概念和过程的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，同时向STEM教育界提供项目工具和资源。最初的动机将是研究诸如向量、矩阵、线性变换和二维和三维笛卡尔坐标系中的线性代数模拟等主题。然后，通过建立VR工具的使用与例如投影、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。该项目将由以下两个研究问题(RQ1)指导：(RQ1)视觉几何和面向行动的VR中介干预在多大程度上支持和增强对线性代数概念的深入学习和在这种背景下的操纵能力？(RQ2)在以VR为媒介的学习线性代数的环境中，学生推理的本质是什么？本项目将在建立和完善虚拟现实工具以及实施和调查课堂教学实验方面利用基于设计的混合方法研究实施。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，学生在录制的临床访谈、评估和调查中的反应将被编码和分析。项目成果将通过在影响较大的同行评议的教育期刊上发表的出版物、在会议和年度会议上的介绍、网络研讨会、座谈会、专业发展讲习班、与同事的沟通会议、公共项目网站的维护以及在科技馆的公众示范等方式主动传播。与这一传播计划相一致，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，以提高所有学生的STEM教育的有效性。通过参与的学生学习路径，该计划支持有前景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优势和更广泛的影响审查标准进行评估，被认为值得支持。