Core Course Analysis for Undergraduate Students in Mathematics

TL;DR

This paper introduces statistical tools to objectively identify core mathematics courses by analyzing their correlation and impact on students' GPA, using UCLA data.

Contribution

It develops novel statistical methods to quantify core course attributes, moving beyond traditional subjective labeling.

Findings

Core courses show high correlation with overall GPA.

Sparse regression effectively identifies impactful courses.

Methods distinguish core from non-core courses based on data.

Abstract

In this work, we develop statistical tools to understand core courses at the university level. Traditionally, professors and administrators label courses as "core" when the courses contain foundational material. Such courses are often required to complete a major, and, in some cases, allocated additional educational resources. We identify two key attributes which we expect core courses to have. Namely, we expect core courses to be highly correlated with and highly impactful on a student's overall mathematics GPA. We use two statistical procedures to measure the strength of these attributes across courses. The first of these procedures fashions a metric out of standard correlation measures. The second utilizes sparse regression. We apply these methods on student data coming from the University of California, Los Angeles (UCLA) department of mathematics to compare core and non-core coursework.