RUME 26
2024
Omaha, Nebraska
Multivariational Reasoning in Linear Algebra: How Mathematicians Reason About Linear Transformations
Page: 1044
Student difficulties in introductory linear algebra courses are often attributed to the novelty of the concepts in the course and the disconnectedness of these concepts to students’ prior mathematical experiences. However, researchers have stated that a strong prerequisite understanding of the function concept is essential to students’ understanding of linear transformations in linear algebra. In calculus and related courses, covariational and multivariational reasoning has been determined to be necessary for students to appropriately reason about functions in two or more variables. However, research on multivariational reasoning in linear algebra, especially with respect to linear transformations, is scarce. To contribute to the literature, we designed a study exploring a hypothetical model of how students might come to reason multivariationally about linear transformations. In this preliminary report, I discuss a part of the study – interviews with seven mathematicians who have either taught linear algebra or used linear algebra in their research.