Reflective thinking in solving number theory problem: A case study of pre-service teacher in terms of cognitive style

• Published in: AIP conference proceedings Vol. 2577; no. 1
• Main Authors: Dwiyanti, Widya, Waluya, Stevanus Budi, Walid
• Format: Journal Article
• Language: English
• Published: 13.07.2022
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0096137

Number theory is a mathematical subject area that presents mathematical interactions with integers. The discussion of the topics involves a mathematical proof process. Hence, solving number theory problems requires a depth of mathematical reflective thinking. However, the individual's reflective thinking process is influenced by one's cognitive style. Therefore, this study aims to analyze the mathematical reflective thinking of pre-service teachers in solving number theory problems in terms of cognitive style. The depth of such thinking is viewed from the thinking process involving reviewing or interpreting experience/situation, problem exploration, elaboration and generalization, and clarifying and resolving. In this study, descriptive research with a qualitative approach was applied. Two pre-service mathematics teachers at STKIP Sebelas April Sumedang, who have field-dependent (FD) and field-independent (FI) cognitive styles, participated as research subjects in this study. The data were collected through a mathematical reflective thinking test, Group Embedded Figure Test, semi-structured interviews. This study indicates that FD tends to be successful in solving problems when they get guidance through sub-questions or pictures/diagrams. But they also tend to have difficulty in capturing mathematical concepts hidden in mathematical situations, relating mathematical ideas between mathematical topics and the context of everyday life.