Many students have not mastered the concept of group theory well. Hence, the researcher intended to describe the conceptual understanding of group theory based on the student’s mathematical abilities. The implementation of this research begun with the students studied about Group Theory classically. Next, to examine the mathematical abilities of students, the researcher administered the questionnaire to obtain the data about the GPA (Grade Point Average) of students. Then, the researcher chose the participants of this study based on the high, middle, and low GPA. The selected research subjects were then given test questions that had been validated by the experts. Data was analyzed using the indicators of conceptual understanding, namely: (1) explaining or restate the group concept, (2) providing an example and a nonexample, (3) using group concept to solve the problem. The results showed that the students with high mathematical abilities reached three indicators of conceptual understanding perfectly. Students with medium mathematical abilities reached two indicators of conceptual understanding but it was not perfect, she did not write the answer completely. In addition, students with low mathematical abilities could not do the test at all, he could not write the group correctly. He did not reach any indicators of conceptual understanding, thus, it can be concluded that the students with low mathematical abilities did not understand the concept well.
The history of combinatorial group theory: A case study in the history of ideas
