An Applied Philosophical Analysis Of Understanding College Students' Application Of Limits To Infinite Series Convergence

This research involves an epistemological approach toward exploring college students’ knowledge and understanding of mathematical limits and their use of limits when dealing with convergence of infinite series. In this applied philosophical take on mathematics education, there are many “ways of knowing,” including Perception, Emotion, Reasoning, and Language (van de Lagemaat, 2005), through which students demonstrate their understanding for this “area of knowledge.” In order to deconstruct and denote common and overlapping ideas among students when explaining limits and infinite series, students were asked to explain infinite series in videotaped interviews, during which they often drew on their ideas of a limit.  Two students’ ideas are explored here, using the “theory of knowledge” framework, discussed by van de Lagemaat. Of the four “ways of knowing,” I claim that reasoning is the most important in understanding students’ ideas of limit, as it influences the other ways of knowing directly, but most immediately on the Language students are using (that which we call limit language) and the Perception of limits (the visual representations that students are producing). The impact of this research may provide a different outlook on lower-division math course pedagogy to go beyond the traditional algebraic representations and teaching styles when considering limits and convergence of infinite series.