Generating a Research-Informed Transition to a Mathematical Proof Curriculum

Texas State University - San Marcos, San Marcos TX

Investigators

Abstract

This project aims to serve the national interest by developing a research-informed curriculum for mathematics transition to proof courses. Proofs and logical reasoning are tools used in mathematics to solve advanced problems. Many STEM majors, especially those in the mathematical sciences, need support in learning how to read and produce mathematical proofs. This skill is a primary means of learning and doing mathematics in third- and fourth-year college mathematics courses. Unlike most existing curricula, the new curriculum will focus on guiding students to read, understand, and appreciate mathematical proofs through several intertwined project activities. Rooted in prior research, the project's curriculum will support students in learning mathematical logic through reading and comparing proof texts. In conjunction with this, the project team will partner with several mathematicians to produce rich mathematical proof texts for students to study. As it is the case that students most often learn literature by reading great works, the curriculum will help students to learn about mathematical proofs by reading rich, challenging, and engaging proofs. The curriculum will include biographical stories of the mathematician authors to humanize mathematics. Project team members will collaborate with mathematicians of color and women mathematicians. The curriculum will provide an opportunity for students to see broader representation in the mathematical sciences. The three underlying components - reading, understanding, and appreciating - are designed to empower students to learn about and from mathematical proofs. They will support students in experiencing mathematics as a human activity in which they can participate. This project will pursue several goals related to enhancing student experiences and successes in transition to proof (TTP) courses. Because there has been relatively little clarity about the specific learning goals for TTP courses, a primary project goal is to build on prior research to establish clearer learning goals for TTP courses. A second goal is to incorporate the learning goals in the process of designing, developing, implementing, and refining a research-based curriculum for TTP courses in mathematics. The project aims to generate new knowledge and fill gaps in the TPP literature through the project’s research findings. An additional goal is to disseminate project outcomes and curriculum resources nationwide, particularly to mathematical sciences departments working to enhance student learning and success in TTP courses as well as subsequent courses and scenarios that rely on problem solving, proofs, and proving. The researchers will employ a rigorous research design to pursue efforts for establishing a curriculum while developing a theory regarding how learning occurs in this teaching and learning space. The project hypotheses is that: comparing proofs will support students in learning abstract logical concepts and proof techniques; analyzing and discussing complex proofs of non-trivial claims will support students in learning from proof texts; and reading stories from a diverse set of professional mathematicians will help humanize proof-based mathematics while envisioning their participation in the discipline. The project will employ research-based measures of understanding of logic, proof comprehension, and belonging in mathematics to study implementation of these hypotheses in the curriculum. The researchers will compare these outcomes to TTP courses taught with standard curricula, and, in the process, will study the learning activity fostered in the classroom to gain insight into these learning processes. Curriculum materials will be freely available to faculty and students online. These resources will also be disseminated through workshops, journal publications, professional conferences, and professional communities of mathematics instructors. 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 project is also supported by the NSF IUSE:HSI program, which seeks to enhance undergraduate STEM education, broaden participation in STEM, and build capacity at HSIs. 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.