by David
Mathews, Michael
A. McDonald, and Kevin Strobel
This paper is part of a continuing series of research studies of college students' cognitive development of mathematical concepts by members of a collaborative group of post-secondary mathematics education researchers called the Research in Undergraduate Mathematics Education Community, or RUMEC. Data was gathered in the form of extensive interviews with students who had completed two semesters of calculus in either a traditional lecture/recitation calculus course or the learning theory based Calculus, Concepts, Computers and Cooperative Learning (C4L) calculus reform program. The Action-Process-Object-Schema (APOS) theoretical perspective was used to infer students' cognitive construction of the concept of sequence. We show that students tend to construct two distinct cognitive objects which they refer to as sequences. One construction, SEQLIST, is what we might see as a listing representation of a sequence. The other, SEQFUNC, is what we see as a functional (expression with domain N) representation of a sequence. As the connections between these two entities becomes stronger, and the students reflect on these connections, they begin to view sequence as a single cognitive object and SEQLIST and SEQFUNC as merely mathematical representations of this object. In this paper we detail the construction of SEQLIST and SEQFUNC by the students, and characterize the connections between them through a model of schema development.