The Refinement of The Preliminary Genetic Decomposition of Group

Mathematics proof is one of the characteristics of advanced mathematics thinking, and proof plays an important role in learning the abstract algebra included group theory. The depth and complexity of individual's understanding of a concept depend on his/her ability to establish connections among the mental structure that constitute it. One of the cognitive styles is field dependent/independent. Field independent (FI) and field dependent (FD) learners have different characteristics. Our research question is (1)How is the proposed refinement of preliminary genetic decomposition of group that is designed with a preliminary study of the learning with APOS works; (2) What understanding about group that is generated by student (Field Independent, Field Neutral, and Field Dependent) when learning through designed material. This study was a descriptive qualitative. The participants of this study were nine (9) undergraduate students who were taking Introduction of Algebraic Structure 1, which included group, in the even semester of academic year 2015/2016 at Universitas Negeri Semarang. Each of type of cognitive styles consisted of 3 participants. There were two instruments used to gather data: written examination in the course and a set of the interview. The FD and FN participants generated Action for a binary operation. The FI participant generated Action and Process for a binary operation. The FD, FN and FI participants generated Action, Process, Object, and Scheme for the set. The FD and FN participant did not generate mental structure for axiom. The FI participant generated Scheme for axiom. The FD, FN and FI participants tend to have no Coherence of Scheme of the group. Not all mental structure on the refinement of the preliminary genetic decomposition can be constructed by participants so well that there are still obstacles in the process of proving.