Publication Date

Winter 12-14-2019

Abstract

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") for students within their respective fields. The data gathered was in the form of numerical responses (ratings from 0 to 5), where the response value indicated level of perceived/desired mastery. The analysis involved a jointly significant correlation network between the topics/ideas, one-tailed t-testing of `Desired Mastery' vs `Student Mastery' responses, the development of an ordinal logistic regression model used to predict grade based on given responses to specific topics, and the analysis of success of this model. Overall, there is some evidence to suggest that students, as a whole, perceive that they are sufficiently mastering Gaussian Elimination/LU-factorization, Linear Combinations/Linear (In)dependence, Properties of R^n, and Eigenvalues and Eigenvectors. There is not, however, evidence to suggest students perceive that they are sufficiently mastering the ideas of Orthogonality, Singular Value Decomposition, Linear Transformations, or Vector/Matrix Norms, with respect to surveyed professors' expectations.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Michael Nakamaye

Second Committee Member

Maria Cristina Pereyra

Third Committee Member

Monika Nitsche

Language

English

Keywords

linear algebra, education, pedagogic analysis, applied, ordinal logistic regression model

Document Type

Thesis

Download

Share

COinS