Teaching Undergraduates to Think With Algebra

该项目旨在通过改善本科数学教育，特别是大学代数的开始，为国家利益服务。代数是进入更高水平的数学和科学课程的看门人。如果没有丰富的代数知识，学生就不会在STEM中取得成功。这个项目将强调代数的泛化和象征意义，帮助学生认识到代数不仅是需要思考的东西，也是需要思考的东西。为此，该项目将开发、试点和完善课程，以便在大学和社区学院开始代数课程时使用。为了支持这些单元的实施，该项目将为大学数学教师举办教师讲习班，包括关注代数的性质。该项目是基于研究人员先前的项目，每个人的概念代数准备，该项目的重点是为3-8年级的学生准备代数。这个新项目将帮助大学生建立对代数的概念性理解，以便更好地为他们在更高水平的数学和科学中取得成功做好准备。没有某种形式的符号化，概括就无法表达，而符号化对于发展代数推理至关重要(Kaput，Blanton，Moreno，2008)。符号化提供了一种简洁的方式来表达数学推理。扩展了Sfard(2000)关于话语和数学思想的思想，数学概念和符号化反射性地共同创造了彼此。概括的符号化通过使思维清晰而有助于推理过程。在这种情况下，代数不仅是需要思考的东西，而且是需要思考的东西，因此才有了这个项目的标题。该项目的目标是开发关于代数主题的大学水平的课程单元，并为大学教师举办研讨会。研究问题是：1)课程单元对学生的代数知识有何影响？2)专业发展对高校辅导员使用本科生单位的培养效果如何？将使用并行混合方法研究模型来评估该计划的影响。项目材料将开放获取，项目成果将通过会议报告和学术期刊上的出版物传播。最终，该项目有可能提高本科生在代数、高级数学课程和其他STEM课程中的成功。NSF IUSE：EHR方案支持研究和开发项目，以提高STEM教育对所有学生的有效性，包括代表性不足的学生。通过参与的学生学习路径，该计划支持有前景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优势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.