Exploration Mathematical Aesthetics through Logical and Critical Thinking Based on High Mathematical Ability

Abstract

This study aims to explore the logical and critical thinking process of junior high school students in solving ill-structured problems based on mathematics ability. The research subject consisted of one student with high mathematics ability. The supporting instruments for data collection were: 1) Test of Mathematical Ability (TKM) consisting of 10 items in the form of descriptions to select subjects with high mathematical ability, 2) Ill-structured Problem Task (TMI), 3) Interviewing the subject based on the task (TMI). The data analysed in this study are interview transcript data, document data and field notes. This study used three stages in data analysis, namely data condensation, data display and conclusion drawing and verification. To validate the findings, the author applied method triangulation until consistent data was obtained, i.e. the data was structured and the content was relatively the same. Furthermore, consistent data in this study is categorised as research data. The results showed that the logical and critical thinking process of high mathematics ability students in solving ill-structured problems consisted of: (1) problem representation; (2) Generating Solution; (3) Justification; and (4) Monitoring and Evaluation. Based on the results of research related to the exploration of mathematical aesthetics through logical and critical thinking, it is recommended as material for further research development in terms of other aspects