By Julie M. Clark, David J. DeVries, George H. Litman, Maria Meletiou,
Steve Morics, Keith E. Schwingendorf, and Draga Vidakovic
The authors believe that when a group of researchers adheres to a particular framework and theoretical perspective over a period of time considerable progress can be made both in understanding how students learn mathematics and in building pedagogy on that understanding. In order to make this point, the authors report on the collective works of a group of researchers who have adopted a framework for research and the associated Action-Process-Object-Schema (APOS) theoretical perspective as the basis for research studies of college students' cognitive development and understandings of mathematical concepts. This paper first provides a brief overview of the APOS theoretical perspective followed by a sample discrete mathematics lesson on learning (single-level) quantification. This lesson is offered as an example of how research rooted in the APOS perspective has led to pedagogical strategies. The paper then summarizes some of the research, the instructional materials, and the methods which have been developed over the past decade using this framework and theoretical perspective. The research described is in the areas of student understandings of concepts in pre-calculus, calculus, abstract algebra, statistics, and discrete mathematics.