Promoting Mathematical Reasoning and Transforming Instruction in College Algebra

该项目旨在通过改变大学代数教学实践来提高学生的数学推理能力，从而为国家利益服务。该项目将在科罗拉多大学丹佛分校和三家西班牙裔服务机构之间建立伙伴关系：丹佛大都会州立大学、圣达菲社区学院和德克萨斯州立大学。该项目的机构合作伙伴有不同的规模和重点，并为大量有色人种学生和第一代大学生提供服务。该项目旨在解决美国本科数学教育中的一个重大问题：过分强调寻找正确答案。具体来说，它打算在高招生低年级数学课程中减少对答案寻找的重视，增加对数学推理的重视。该项目将通过开发和完善大学代数学生的“技巧”来实现这些目标。技术活动是免费的、互动的、基于视频场景的在线问题，比如摩天轮的运动。他们让学生创建多个图形来表示场景中对象之间的数字关系。除了创建更多的技术活动并将其嵌入更多的课程之外，该项目还打算帮助教师有效地使用它们。它将通过制定教师专业发展计划和教师转型社区来实现这一目标。该项目将完成一项关于这些活动在大学代数课程中增加数学推理的有效性的研究。通过改变大学数学入门课程的教学实践，该项目可能会增加学生对STEM专业的坚持，并帮助美国为STEM专业培养越来越多样化的人口。该项目将开发和实施一种名为DEEP的新的、可能具有变革性的制度变革方法，其中包括四个相互关联的要素：开发促进协变推理的创新数字任务（Techtivities）；在现有课程中嵌入任务，连接到关键内容；为教师提供更多机会，让他们检查如何确定哪些学生的声音被重视或被边缘化；并为教师实施促进学生推理的任务提供支持。在机构层面，该项目将为教师提供支持，帮助他们执行任务，促进学生的推理能力，并创建转型社区，以维持机构间的循证实践。该项目包括一个研究项目，旨在找出教学实践、教师信念、学生协变推理、数学态度和课程成功之间的联系。它将包括项目各个方面的研究生研究助理，以满足发展STEM新手研究人员的社会需求。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。通过机构和社区转型轨道，该计划支持高等教育机构和学科社区的STEM教育转型和改善。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。

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.