Linear independence from a perspective of connections

Abstract

We investigated understanding of the linear independence concept based on the type and nature of connections displayed in seven non-mathematics majors’ interview responses to a set of open-ended questions. Through a qualitative analysis, we identified six categories of frequently displayed connections. There were also recognizable differences in the way the connections were applied by the participants. Overall, our findings pointed to an understanding in the form of two main clusters of connections. The two clusters were connected only by linear combination ideas. Each cluster, furthermore, was distinguishable via representation types. The first cluster contained arithmetic/algebraic modes and the second cluster included, mostly, geometric ideas. This paper discusses similarities and differences within and between clusters supported by participant responses. In light of the findings, we provide suggestions for the improvement of linear algebra education of non-mathematics student population.

KEYWORDS:

• Linear algebra
• linear independence
• connectional reasoning

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This material is based upon work supported by a grant from the University of Texas System and the Consejo Nacional de Ciencia y Tecnología de México (CONACYT). The opinions expressed are those of the authors and do not necessarily represent views of these funding agencies.