Levels of Students' Understanding of Counterexample

From a logical point of view, finding a counterexample can disprove a mathematical proposition, but from students' point of view, this is not necessarily the case. Recognizing and understanding a counterexample requires skill and mastery. This study aimed to investigate the levels of students' understanding of counterexample. The research was conducted by phenomenology method and analyzing problem-based interviews of 26 eighth grade students. This report details the results of students’ encounter to a counterexample and suggests a taxonomy of student performances and reactions whose levels are not necessarily hierarchical. This categorization sheds light on a more detailed process of how students can progress from understanding the nature and role of the counterexample. It also provides instances of students' work on the convincing power of the counterexample for them to the degree of explanation of the examples.