Combinatorial Methods for Undergraduate Mathematics Curriculum Analysis & Design

Abstract

Student retention is a significant issue in Research in Undergraduate Mathematics Education (RUME), and freshman calculus is notorious for “weeding out” students from STEM majors. Since the late 1980s, various attempts have been made to remedy Calculus courses around the United States. However, the percentage of students earning grades of D, F, W, or I (the DFWI rate) remains relatively high compared to freshman courses in other disciplines. Through a collection of research projects, this dissertation explores the theme of misalignment in various aspects of the university Calculus I curriculum by employing novel applications of combinatorics to mathematics education research. This is an example of Mathematics Discipline-Based Education Research (Math DBER), which is an emerging field that leverages mathematics methodologies in RUME.