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
Description:
The mistake students made in constructing a counterexample was failing to form an abelian group. This mistake is due to a lack of accuracy so as not to re-check the terms of a group. Errors also caused by the lack of understanding of the concept of the group. This problem can be a basis for finding solutions in subsequent lessons by conducting interviews with subjects to dig deeper to find the causative factors. So that in the next lecture, it is hoped that found solutions to overcome student difficulties in building counterexamples.
