Linear algebra revisited: An attempt to understand students’ conceptual difficulties. Educational Studies in Mathematics, 68, 19–35.īritton, S., & Henderson, J. London: Sage.īingolbali, E., & Monaghan, J. Research methods in cultural anthropology. Washington, DC: The Mathematical Association of America.īernard, R. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp.

Cognitive difficulties and teaching practices. We conclude with a discussion of this and how it may be leveraged to inform teaching in a productive, student-centered manner.Īrtigue, M. Furthermore, we found that all students interviewed expressed, to some extent, the technically inaccurate “nested subspace” conception that R k is a subspace of R n for k < n.

We also present results regarding the coordination between students’ concept image and how they interpret the formal definition, situations in which students recognized a need for the formal definition, and qualities of subspace that students noted were consequences of the formal definition. Through grounded analysis, we identified recurring concept imagery that students provided for subspace, namely, geometric object, part of whole, and algebraic object. We used the analytical tools of concept image and concept definition of Tall and Vinner (Educational Studies in Mathematics, 12(2):151–169, 1981) in order to highlight this distinction in student responses. This is consistent with literature in other mathematical content domains that indicates that a learner’s primary understanding of a concept is not necessarily informed by that concept’s formal definition. In interviews conducted with eight undergraduates, we found students’ initial descriptions of subspace often varied substantially from the language of the concept’s formal definition, which is very algebraic in nature. This paper reports on a study investigating students’ ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace.

Subspace definition definition