Abstract

This study investigates the long-term effects of instructing Cantor set theory using constructivist learning approach on student knowledge retention. The participants included 60 first-year secondary mathematics pre-service teachers. Students were divided into two classes one of which was taught via traditional lecture (n = 30) and the other was taught using active learning approach (n = 30). A pre-test named “Minimum Requirements Identification Test” developed by the researcher was used in the determination of the groups. This test involves the concepts such as “set, relation, and function” which were required to be able to learn Cantor set theory. Student retention of Cantor set theory was measured by using a questionnaire which consists of open-ended questions about the topic. The test was administered to all of the students approximately 14 months after the first instruction. In addition, five students from each group were interviewed. Analyses of the data revealed that the students in the constructivist learning environment showed better retention of almost all of the concepts related to Cantor set theory than the students in the traditional class.

Key words: Cantorian set theory, teacher education, infinity, retention, active learning.