Students’ perception of infinity : Perception, obstacles, conception

Abstract

Several studies in mathematics education have shown that students face significant difficulties for understanding the concept of infinity. The purpose of this study is to suggest an explanation of how students understand the concept of infinity and identify the difficulties for understanding it. Explanation will be given through an investigation on the following aspects of understanding and the implementation of the corresponding theoretical background: i) primary perception in terms of Singer and Voica’s(2008) categories and secondary perception in the context of comparison of infinite sets ii) obstacles in coming to understand the concept in terms of the Theory of Epistemological Obstacles and iii) the construction of understanding in terms of APOS theory. The empirical part of this study was conducted in Norway. The subjects are five 12th graders and data for this study were collected by means of a questionnaire and an interview. A precise overview of the aim and contents of the thesis is given in the introductory part. The thesis begins with a historical analysis of the concept of infinity, aiming to reveal its paradoxical and contradictory nature. Next, the theoretical background is presented along with the basis of each theory. There has been a qualitative analysis on the collected data, by methods found in the literature. The results have shown that most of the students perceived infinity as a process while specific difficulties related to the notion of actual infinity were noticed. The analysis of the structure of understanding, raised the importance of “encapsulation” as a way to understand its actual form. The thesis hopes to shed light on students’ understanding and thus make a small contribution to mathematics education research