Cantorian Set Theory and Teaching Prospective Teachers

Infinity has contradictions arising from its nature. Since mind is actually adapted to finite realities attained
by behaviors in space and time, when one starts to deal with real infinity, contradictions will arise. In particular,
Cantorian Set Theory for it involves the notion of “equivalence of a set to one of its proper subsets,” causes
perceptual issues. Prospective mathematics teachers usually learn this concept via traditional lecture methods and
experience possible problems later. Since Cantorian Set Theory is used in courses like Topology, Algebra, etc. and
prospective teachers will teach it to students using appropriate methods, it is important that they comprehend it well.
The purpose of this study is to assess the effects of teaching Cantorian Set Theory via an Active Learning Based
Course on prospective students’ achievement. The results indicate that prospective teachers who were in
experimental group (taught by active learning based methods) were more successful than those who studied the
traditional lecture method and the difference between the groups was significant (p = 0.02).