## 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

## Recommended Citation

Taylor, Andrew. "A Pedagogic Analysis of Linear Algebra Courses." (2019). https://digitalrepository.unm.edu/math_etds/166