Collaborative Research: Extending Inquiry-Oriented Linear Algebra

本项目由美国国家科学基金会改善本科STEM教育计划：教育与人力资源（IUSE: EHR）资助，旨在通过提高学生线性代数的学习来服务于国家利益。为了实现这一目标，该项目将创建基于研究的线性代数教学和讲师支持材料。该项目由弗吉尼亚理工学院和州立大学、佛罗里达州立大学、亚利桑那州立大学和克莱顿州立大学合作完成。它与通过探究让学生参与学习的国家号召相一致。为此，它打算通过参与数学讨论、发展和检验猜想、解释和证明他们的想法来帮助学生学习数学。该项目有四个主要目标：(i)创建四个新单元，整合和补充现有的面向查询的线性代数材料；（ii）为四个新单元制作教学辅助材料；（iii）通过对线性代数中学生推理和有效的探究性教学实践的实证研究贡献新知识；（四）培养本科数学探究性教学实践。该项目的两个广泛的研究问题是：(i)学生通过参与任务发展了什么样的数学概念？（ii）在这种情况下，哪些教学动作有助于学生的学习？该项目有潜力提高知识和能力，使用探究导向的方法来改善本科数学教学，特别是线性代数。为了实现其目标，该项目将使用由任务设计、配对教学实验（Steffe & Thompson, 2000）、课堂教学实验（Cobb, 2000）、在线工作组（Fortune, Keene, & Hall, 2017）和网站开发阶段组成的设计研究周期。该项目将扩展现有的以探究为导向的线性代数教材，包括整个线性代数入门课程，提供一套全面的支持，帮助教师采用以探究为导向的方法来教授线性代数。通过关注新的教师和环境，该项目有可能将主动学习和以探究为导向的教学的影响扩大到更多的学生和机构。解决研究问题的数据将从至少12个机构收集，这些机构在地理位置、机构类型、规模和学生人口统计方面各不相同，从而丰富了研究人口的多样性。项目开发的资源及其研究成果将通过数学和数学教育领域的网站、研讨会以及研究和从业者期刊的出版物进行传播。此外，该项目考虑并遵守有关公平和机会的研究建议，将促进和推进探究导向的公平教学实践。这项工作有可能通过改善本科数学教学和扩展研究性教学的使用来造福社会。NSF IUSE: EHR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。

With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR), this project aims to serve the national interest by improving student learning in linear algebra. To accomplish this goal, the project will create research-based teaching and instructor support materials for linear algebra. This project is a collaboration between Virginia Polytechnic Institute and State University, Florida State University, Arizona State University, and Clayton State University. It aligns with national calls to engage students in learning through inquiry. To this end, it intends to help students learn mathematics by engaging in mathematical discussions, developing and testing conjectures, and explaining and justifying their thinking. The project has four main goals: (i) create four new units that integrate with and complement existing Inquiry-Oriented Linear Algebra materials; (ii) create instructional support materials for the four new units; (iii) contribute new knowledge through empirical research about student reasoning and effective inquiry-oriented instructional practices in linear algebra; and (iv) foster inquiry-oriented instructional practices in undergraduate mathematics. The two broad research questions for the project are: (i) What mathematical conceptions do students develop through their engagement with the tasks? (ii) What instructional moves facilitate student learning in this setting? The project has the potential to advance knowledge about and capacity for using inquiry-oriented approaches to improve undergraduate instruction in mathematics, particularly linear algebra.To accomplish its goals, the project will use a Design Research Cycle comprised of phases of Task Design, Paired Teaching Experiments (Steffe & Thompson, 2000), Classroom Teaching Experiments (Cobb, 2000), Online Working Groups (Fortune, Keene, & Hall, 2017), and Website Development. The project will extend the current Inquiry-Oriented Linear Algebra materials to include an entire introductory linear algebra course, providing a comprehensive set of supports to help instructors adopt an inquiry-oriented approach to teaching linear algebra. By focusing on new instructors and settings, the project has the potential to extend the impact of active learning and inquiry-oriented teaching to a larger number of students and institutions. Data to address the research questions will be collected from at least twelve institutions that vary in geographic location, institution type, size, and student demographics, thus enriching the diversity of the research population. Resources developed by the project and its research results will be disseminated through websites, workshops, and publications in both research and practitioner journals within mathematics and mathematics education. In addition, the project's consideration of and adherence to research recommendations regarding equity and access will promote and advance inquiry-oriented, equitable teaching practices. This work has the potential to benefit society by improving undergraduate mathematics instruction and extending the use of inquiry-oriented teaching. The NSF IUSE: EHR 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.