Teaching Undergraduates to Think With Algebra

Purdue University, West Lafayette IN

Investigators

Abstract

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.