Addressing Cognitive and Instructional Challenges in Introductory Proofs Courses: A Gateway to Advanced STEM Studies

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

This project aims to serve the national interest by improving students’ abilities to reason logically, think critically, and solve complex problems. It will identify instructional strategies for introductory proofs courses that empower students to analyze and solve important problems in advanced STEM settings. Poor performance in proofs courses often serves as a barrier for students’ successful course progression and can prevent them from becoming or remaining as STEM majors. This IUSE Engaged Student Learning Level 1 project at Virginia Polytechnic Institute and State University (Virginia Tech) is designed to increase and diversify the pool of students pursuing STEM careers. This will be a two-phase project for which phase 1 will include a cyclical approach to investigate student reasoning and to design and study research-based instructional tasks that evoke and address challenges in the teaching and learning of foundational ideas. Efforts from phase 1 will have an immediate impact on every Virginia Tech mathematics major, including pre-service teachers preparing to teach secondary mathematics. In phase 2, project outcomes will be disseminated and used to support introductory proofs instructors nation-wide as they optimize instruction for facilitating students’ development of robust logical reasoning, critical thinking, and overall success in the STEM arena. The project will pursue several underlying goals. The first goal is to provide students taking an introduction to proofs course with opportunities to develop reasoning skills and to incorporate the logical structures that are essential for flexibly solving problems in advanced STEM settings. The second goal is to contribute to the knowledge base and fill gaps in the literature through research findings by investigating: (1) how students experience epistemological obstacles in proofs courses; (2) how course instructors experience these student obstacles; and (3) how to enable these instructors to employ teaching and learning interactions surrounding the epistemological challenges that provide the students with opportunities to realize, explore, and overcome these difficulties. The third goal is to disseminate (through national workshops and other venues) research findings, resources, and a replicable and sustainable course model that promotes student success to instructors, departments, and institutions working to enhance student learning, problem solving abilities, and success in introductory proofs courses and beyond. The project team will take a cyclical approach by investigating student reasoning and designing and modifying research-based instructional tasks for evoking student experience of the cognitive challenges associated with foundational ideas such as logical implication, quantifiers, and proof techniques. Research and task design will draw on action-object theory, which derives from Piaget’s (1970) genetic epistemology and Dubinski’s (1991) extensions. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all 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.