Collaborative Research: Extending Inquiry-Oriented Linear Algebra

合作研究：扩展探究导向的线性代数

基本信息

批准号：
1915156
负责人：
Megan Wawro
金额：
$ 30.39万
依托单位：
Virginia Polytechnic Institute and State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-10-01 至 2024-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915156&HistoricalAwards=false
关键词：
Collaborative Research Extending Inquiry Oriented

项目摘要

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.

在 NSF 改善本科生 STEM 教育计划：教育和人力资源（IUSE：EHR）的支持下，该项目旨在通过改善学生对线性代数的学习来服务于国家利益。为了实现这一目标，该项目将为线性代数创建基于研究的教学和教师支持材料。该项目是弗吉尼亚理工学院与州立大学、佛罗里达州立大学、亚利桑那州立大学和克莱顿州立大学之间的合作项目。它符合国家号召让学生通过探究进行学习。为此，它旨在帮助学生通过数学讨论、发展和测试猜想、解释和证明他们的想法来学习数学。该项目有四个主要目标：（i）创建四个新单元，与现有的面向探究的线性代数材料集成并补充；㈡为四个新单元制作教学辅助材料； (iii) 通过对学生推理的实证研究和线性代数中有效的探究型教学实践贡献新知识； (iv) 促进本科数学中以探究为导向的教学实践。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哪些数学概念？ (ii) 在这种环境下，哪些教学举措可以促进学生的学习？该项目有潜力提高使用探究型方法的知识和能力，以改善本科数学教学，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、配对教学等阶段组成的设计研究周期实验 (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。该项目将扩展当前的面向探究的线性代数材料，以包括完整的线性代数入门课程，提供一套全面的支持，帮助教师采用面向探究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探究式教学的影响扩展到更多的学生和机构。解决研究问题的数据将从至少十二个机构收集，这些机构的地理位置、机构类型、规模和学生人口统计数据各不相同，从而丰富了研究人群的多样性。该项目开发的资源及其研究成果将通过网站、研讨会以及数学和数学教育领域的研究和实践期刊上的出版物进行传播。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以探究为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大探究式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 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。