Modules As Learning Tools in Linear Algebra

This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and curriculum development. Beginning with an online reading seminar, faculty paired with at least one other STEM faculty member at each institution to develop modules collaboratively with each other and with the group as a whole through regular project meetings. Two representative modules from this collaboration are presented with student and faculty feedback. A link is provided to other modules. We consider this a proof-of-concept paper with broader applicability beyond linear algebra to other mathematics and even STEM courses. We focus on linear algebra because it is widely taught in undergraduate mathematics programs and lends itself easily to a variety of applications and geometric analyses. We intend to continue to apply this approach to other content domains. We chose a particular theoretical framework, Action-Process-Object-Schema (APOS), because the mathematics education faculty in this group had considerable experience in the development and use of the framework.