Exploring university students' mental constructions of the limit concept in relation to sequences and series.

Abstract

The present thesis refers to some first semester calculus 1 university students’ mental constructions of the limit concept in relation to sequences and series. A plethora of research on the limit concept is available and suggests that the concept is on record of being difficult for students to learn and comprehend. However, in Zimbabwe, there is inadequate research on mental constructions made by students of the limit concept in relation to sequences and series. This research aims at filling this gap in the literature. This study utilized the Action-Process-Object-Schema (APOS) theory in exploring conceptual appreciative displayed by students when dealing with limits of sequences and series. The study proposes the genetic decompositions on how students might construct the mental constructions in learning the sequences and series through the use of Activities-Classroom discussions –Exercises (ACE). Collection of data was done by the use of a methodology that used practical teaching. All the thirty students who took calculus 1 accepted to participate in this study and answered the limit test questions. The students’ written responses were analyzed using APOS theory. Ten students were selected for interviews through purposive sampling. Two declined to take part leaving eight to take part in the process. The APOS theory was used to analyze the interview results. The revision of preliminary genetic decomposition was done basing on the analyzed data. The instructional method employed, facilitated the appreciation of the limit concept in relation to sequences and series by the students. Nearly all students showed that they operated at the Action level, a good number showed that they operated at least at the Process level and more than half of the students showed that they operated at the Object level. Three out eight interviewed students indicated that the managed to operate at the Schema level on some of the test questions. However, there is need for the establishment of a conceptual basis that promotes and allows the construction of the limit concept schema in relation to sequences and series. Furthermore, interviewed students’ responses paralleled the chronological improvement of the limit concept as reported in literature. Historical analysis of the development of concepts needs to be reflected upon when preparing and designing instruction. This would help the lecturer to foresee the challenges that lay ahead and address students’ difficulties during the learning process. The implementation of APOS Theory is recommended for the learning of other mathematical aspects, which cause difficulties in students’ learning. Moreover, other constructivist learning methods can be fused together with the APOS Theory to obtain improved results on students’ performance in mathematics.