PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Finding free variables as a conceptual tool in linear algebra
Page: 941
This preliminary report examines students’ interpretations of free variables in linear algebra. In linear algebra, students build understandings of concepts, such as a (in)consistent system of equations, a linearly independent set of vectors, and a subspace. All these concepts will be the foundation for students’ future learning in various fields. Therefore, it is crucial to investigate the notion of free variables as it is one of the constructs underlying work with each of these concepts. Here, I analyzed 110 linear algebra students’ written assessments from three different classes using grounded theory (Strauss & Corbin, 1994). The analysis shows that students use free variables as a conceptual tool to answer questions given in different problem settings. This paper reports categories of students’ interpretations of free variables and explores what the free variables mean to students in each category.