The ability of mathematics education students to build counterexamples in solving cyclic group problems

Abstract

This study examines the students' ability to build counterexamples in solving problems related to cyclic groups. This research is an instrumental type case study research involving 109 undergraduate students of Mathematics Education FKIP Lambung Mangkurat University. Students work on one question, which is part of the midterm exam questions in the form of a statement by providing a true or false answer along with the reasons. The results showed that 76 students (69.72%) answered the statement incorrectly and gave a counterexample, 24 students (22.01%) answered that the statement was true and provided proof. The remaining nine students (8.25%) did not provide a true or false answer. The ability to construct a sample can be grouped into four types, namely: (1) no answer; (2) provide correct examples; (3) provide a counterexample but fail to show the statement is false, and (4) provide proof (which is not true) for a false statement.