Teaching Undergraduates to Think With Algebra

该项目旨在通过改善本科数学教育，特别是大学代数教育，为国家利益服务。代数是高等数学和科学课程的看门人。如果没有对代数的丰富理解，学生将无法在STEM中取得成功。这个项目将强调代数的泛化和象征方面，帮助学生学习代数不仅仅是思考的东西，也是思考的东西。为此，该项目将开发、试点和改进课程，用于大学和社区学院的初级代数课程。为了支持这些单元的实施，该项目将为大学数学教师举办一个教师研讨会，重点是代数的本质。该项目是基于研究者之前的项目“面向所有人的概念代数准备”，该项目的重点是为3-8年级的学生准备代数。这个新项目将侧重于帮助大学生培养对代数的概念理解，以便更好地为他们在更高水平的数学和科学方面取得成功做好准备。代数的一种观点是代数的泛化和符号化。如果没有某种形式的符号化，泛化就无法表达，而符号化对于代数推理的发展至关重要（Kaput, Blanton, Moreno, 2008）。符号化提供了一种简洁的方式来表达数学推理。延伸sard（2000）关于话语与数学思想的观点，数学概念与符号化反思性地相互创造。概括的符号化通过使思维明确来帮助推理过程。通过这种方式，代数不仅是需要思考的东西，而且是需要思考的东西，因此这个项目的标题。该项目的目标是开发关于代数主题的大学水平课程单元，并为大学教师举办讲习班。研究的问题是：1)课程单元对学生代数知识的影响是什么？2)在准备大学教师与本科生一起使用这些单元方面，专业发展的效果如何？一个并行的混合方法研究模型将被用来评估这个项目的影响。项目材料将开放获取，项目结果将通过会议发言和学术期刊出版物传播。最终，该项目有可能提高本科生在代数、高等数学课程和其他STEM课程中的成功程度。NSF IUSE: EHR计划支持研究和开发项目，以提高所有学生（包括代表性不足的学生）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。

This project aims to serve the national interest by improving undergraduate mathematics education, specifically beginning college algebra. Algebra is the gatekeeper to higher level mathematics and science courses. Without a rich understanding of algebra, students will not be successful in STEM. This project will emphasize the generalization and symbolism aspects of algebra, to help students learn that algebra is not just something to think about, but also something to think with. To do so, the project will develop, pilot, and refine curriculum for use in beginning algebra courses at universities and community colleges. To support implementation of the units, the project will hold a faculty workshop for college mathematics instructors, including a focus on the nature of algebra. The project is based on the investigator’s prior project, Conceptual Algebra Readiness for Everyone, which focuses on preparing students in grades 3—8 for algebra. This new project will focus on helping college students develop a conceptual understanding of algebra to better prepare them for success in higher level mathematics and science.One view of algebra is algebra as generalization and symbolization. Generalization cannot be expressed without some form of symbolization and symbolization is vitally important to developing algebraic reasoning (Kaput, Blanton, Moreno, 2008). Symbolization provides a compact way to express mathematical reasoning. Extending the idea of Sfard (2000) on discourse and mathematical ideas, mathematical concepts and symbolization reflexively co-create each other. Symbolization of generalizations aids the reasoning process by making thinking explicit. In this way, algebra is not merely something to think about but something to think with, hence the title of the project. The goals of the project are to develop college-level curriculum units on algebraic topics and a workshop for college instructors. The research questions are: 1) What is the impact of the curriculum units on students’ knowledge of algebra? and 2) How effective is the professional development in preparing college instructors to use the units with undergraduate students? A concurrent mixed-methods research model will be used to assess the impacts of this program. Project materials will be open access and project results will be disseminated through conference presentations and publications in scholarly journals. Ultimately, the project has the potential to improve undergraduates’ success in algebra, in higher level mathematics courses, and in other STEM courses. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students including underrepresented 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.