Promoting Mathematical Reasoning and Transforming Instruction in College Algebra

促进数学推理并转变大学代数教学

• 批准号: 2013186
• 负责人: Heather Johnson
• 金额: $ 159.98万
• 依托单位: University of Colorado at Denver
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2013186&HistoricalAwards=false
• 关键词: Promoting; Mathematical; Reasoning; Transforming; Instruction

This project aims to serve the national interest by transforming instructional practices in college algebra to improve students’ mathematical reasoning. This project will establish a partnership between the University of Colorado Denver and three Hispanic serving institutions: Metropolitan State University of Denver, Santa Fe Community College, and Texas State University. The project's institutional partners have a range of size and focus, and serve large populations of students of color and first-generation-in-college students. The project aims to address a significant problem in U.S. undergraduate mathematics education: the overemphasis on finding the right answer. Specifically, it intends to decrease the emphasis on answer finding, and increase the emphasis on mathematical reasoning in high enrollment lower division mathematics courses. The project will accomplish these goals by developing and refining “Techtivities” for college algebra students. Techtivities are free, interactive, online problems based on video scenarios, such as the movement of a Ferris wheel. They engage students in creating multiple graphs to represent numerical relationships between objects in the scenario. In addition to creating more Techtivities and embedding them in more courses, the project intends help instructors use them effectively. It will do so by developing an instructor professional development program and instructor Communities of Transformation. The project will complete a research study on the effectiveness of these activities in increasing mathematical reasoning in college algebra courses. By transforming instructional practices in gatekeeper introductory college math courses, the project may increase student persistence in STEM majors and help the U.S. prepare an increasingly diverse population for STEM professions. This project will develop and implement a new, potentially transformative approach to institutional change called DEEP, which includes four interconnected elements: Develop innovative digital tasks (Techtivities) that foster covariational reasoning; Embed tasks within existing courses, connecting to key content; Extend opportunities to instructors to examine how they determine which student voices get counted or marginalized; and Provide support for instructors to implement tasks that promote students’ reasoning. At the institutional level, the project will provide support for instructors to implement tasks to promote students’ reasoning and create Communities of Transformation to sustain evidence-based practices across institutions. The project includes a research project designed to draw connections between instructional practices, instructor beliefs, and students’ covariational reasoning, math attitudes, and course success. It will include graduate research assistants in all aspects of the project to contribute to the societal need of developing novice STEM researchers. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Institutional and Community Transformation track, the program supports efforts to transform and improve STEM education across institutions of higher education and disciplinary communities.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.

该项目旨在通过改变大学代数的教学实践来改善学生的数学推理来服务国家利益。该项目将在科罗拉多大学丹佛大学和三个西班牙裔服务机构之间建立合作伙伴关系：丹佛大都会州立大学，圣塔菲社区学院和德克萨斯州立大学。该项目的机构合作伙伴具有各种规模和专注的范围，并为大量有色人种和大学生的学生提供服务。该项目旨在解决美国本科数学教育中的一个重大问题：对找到正确答案的过分强调。具体而言，它打算减少对答案发现的重点，并增加对高入学率下层数学课程中数学推理的重视。该项目将通过为大学代数学生开发和完善“技术意义”来实现这些目标。基于视频场景（例如摩天轮的运动），技术的技术是免费的，互动的在线问题。他们让学生创建多个图表，以表示场景中对象之间的数值关系。除了创建更多的技术特征并将其嵌入更多课程外，该项目还打算帮助教师有效地使用它们。它将通过制定讲师专业发展计划和转型教师社区来做到这一点。该项目将完成一项研究这些活动在增加大学代数课程中数学推理方面的有效性的研究。通过改变守门员介绍大学数学课程的教学实践，该项目可能会增加STEM专业的学生持久性，并帮助美国为STEM专业人员准备越来越多样化的人群。该项目将开发并实施一种新的，潜在的变革性的方法来解决DEEP，其中包括四个相互联系的要素：开发创新的数字任务（技术），以促进协方差推理；在现有课程中嵌入任务，连接到关键内容；向讲师提供机会，以检查他们如何确定哪些学生的声音被计数或边缘化；并为讲师提供支持，以实施促进学生推理的任务。在机构层面，该项目将为教师提供支持，以实施任务以促进学生的推理，并建立转型社区，以维持跨机构的循证实践。该项目包括一个研究项目，旨在在教学实践，讲师信念和学生的协变性推理，数学参与者和课程成功之间建立联系。它将包括项目的各个方面的研究生研究助理，以促进发展新颖STEM研究人员的社会需求。 NSF IUSE：EHR计划支持研发项目，以提高所有学生STEM教育的有效性。通过机构和社区转型的轨道，该计划支持努力在高等教育和学科社区的机构中转变和改善STEM教育的努力。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影响的评估来进行评估的审查标准。

项目成果

Validating an assessment of students’ covariational reasoning

验证学生协变推理的评估

• 发表时间: 2021
• 期刊: Proceedings of the 43rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
• 作者: Johnson, H. L.;Olson, G.;Smith, A.;Gardner, A.;Wang, X.;& Donovan, C.
• 通讯作者: & Donovan, C.

Linear or nonlinear? Relating college algebra students’ covariational reasoning and graph selection

线性还是非线性？

• 发表时间: 2022
• 期刊: Proceedings of the 44th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
• 作者: Knurek, Robert;Johnson, Heather Lynn
• 通讯作者: Johnson, Heather Lynn

Promote Students’ Function Reasoning with Techtivities

利用 Techtivities 促进学生的函数推理

• DOI: 10.1080/10511970.2021.1872751
• 发表时间: 2022
• 期刊: PRIMUS
• 作者: Olson, Gary A.;Johnson, Heather Lynn
• 通讯作者: Johnson, Heather Lynn

College algebra students’ attitudes toward math and graphs: An exploratory factor analysis

大学代数学生对数学和图表的态度：探索性因素分析

• 发表时间: 2022
• 期刊: Proceedings of the 44th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
• 作者: Bechtold, Livvia;Donovan, Courtney;Johnson, Heather Lynn
• 通讯作者: Johnson, Heather Lynn

Boundary Transitions Within, Across, and Beyond a Set of Digital Resources: Brokering in College Algebra

一组数字资源之内、之间和之外的边界转换：大学代数中的经纪

• DOI: 10.1007/s40751-022-00113-2
• 发表时间: 2022
• 期刊: Digital Experiences in Mathematics Education
• 作者: Johnson, Heather Lynn;Olson, Gary;Tsinnajinnie, Belin;Bechtold, Livvia
• 通讯作者: Bechtold, Livvia