PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Paradoxes of Infinity - The Case of Ken
Page: 2-684
Previous studies have shown that the normative solutions of the Pin-Pong Ball Conundrum and the Pin-Pong Ball Variation are difficult to understand even for learners with advanced mathematical background such as doctoral students in mathematics. This study examines whether this difficulty is due to the way they are set in everyday life experiences. Some variations of the Pin-Pong Ball Conundrum and the Pin-Pong Ball Variation and their abstract versions set in the set theoretic language without any reference to everyday life experiences were given to a doctoral student in mathematics. Data collected suggest that the abstract versions can help learners see beyond the metaphorical language of the paradoxes. The main contribution of this study is revealing the possible negative effect of the metaphorical language of the paradoxes of infinity on the understanding of the learner.