Our research is to compare students’ ability of presenting counter examples between Korean students and Hong Kong students and prospective teachers’ ability of treating counter examples between Korean prospective teachers and Hong Kong prospective teachers. Our analysis suggests the methodological implication for mathematics education of two countries on how to improve teaching methodology dealing with counter examples in classrooms through investigating students’ and prospective teachers’ ability on applying counter-examples.[Copyright © 2010 Issic K. C. Leung, Hee-Chan Lew & Tae Soen Cheon.]