Undergraduate students’ levels of understanding in solving mathematical proof problem: The use of Pirie-Kieren theory

One of problem solving cases that is often encountered by undergraduate students of mathematics education study program in various courses is the mathematical proof problem. This problem is encountered starting from the first year to the last year. This research used a qualitative approach that aimed to describe the levels of students’ understanding in solving mathematical proof problem. The description used Pirie-Kieren’s theory. In Pirie-Kieren’s theory, there are 8 levels of understanding, namely primitive knowing, image making, image having, property noticing, formalizing, organizing, structuring, and inventing. The subjects in this research were students of Mathematics Education study program of Universitas Sulawesi Barat who were taking Abstract Algebra course in the academic year of 2019-2020. Subjects consisted of 6 students with three levels of abilities: high, medium, and low. Each category was represented by 2 students. Data were obtained using mathematical proof problem test and interview guidelines. The results of the research and discussion in this research indicate that the levels of understanding of the high category subjects in solving mathematical proof problem are primitive knowing, image having, property noticing, formalizing, organizing, and structuring. The levels of understanding of the medium category subjects in solving mathematical proof problem, namely primitive knowing, image having, property noticing, formalizing, and organizing. Meanwhile, the low category subjects are only at the primitive knowing, image making, and property noticing levels.