Mental structure construction of field independent students based on initial proof ability in APOS-based learning

Abstract

Mathematics proof plays an important role in learning the abstract algebra included group theory. The aim of this study was to describe the mental structures that might take place when FI students were learning the concept of group theory through APOS-based learning. This study was a descriptive qualitative. The participants of this study were eight (8) undergraduate students who were taking Introduction to Algebraic Structure 1, included group theory, at Universitas Negeri Semarang. Each of low and medium level of initial proof ability consisted of 3 participants, while high level of initial proof ability consisted of 2 participants. There were two instruments used to gather data: written examination in the course and a set of interview. The participants with low level of initial proof ability tended to construct the mental structure of Object for a set, did not construct the mental stucture of Object for the binary operation and the axioms of group. The participants with medium level of initial proof ability constructed the mental structure of object for a set, tended to construct Object for the binary operation, the axioms of group, and tended to construct the scheme of group. The participants with high level of initial proof ability constructed mental structure of Object for a set, has not fully constructed the mental structure of Object for the binary operation and for the axioms of group yet, as well as has not fully constructed the scheme of group.