Mathematical creative thinking skills: Using APOS theory to identify student errors in solving contextual problems
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Individuals with strong creative thinking abilities are particularly adept at effectively addressing mathematical contextual problems. However, students often need more vital creative thinking skills in the classroom, frequently due to errors they make themselves. This study aims to identify students’ specific errors when solving contextual problems related to integer operations. This research adopts a qualitative approach, using an exploratory and descriptive technique, focusing on sixth-grade elementary school students. Participants were selected based on the teacher’s recommendations, specifically targeting students with strong communication skills to comprehensively examine their errors in dealing with contextual problems and their creative thinking skills. The research utilized tests and interviews as instruments for data collection, incorporating methodologies such as testing, interviewing, and triangulation. The results indicate a significant deficiency in students’ innovative thinking skills, rendering them unable to solve problems effectively, which leads to an inability to meet the four criteria of creative thinking. Based on the Action-Process-Objects-Scheme (APOS) theory, the identified errors in students’ approaches to contextual mathematical problems can be categorized into four types: (1) interpretive errors, (2) errors in conceptual understanding, (3) procedural errors, and (4) computational or technical errors. The insight gained from this study can inform the design of integer learning activities, helping minimize contextual problem-solving mistakes that require creative thinking skills. Consequently, further research is essential to develop a mathematical learning model that can enhance students’ mathematical creative thinking abilities.
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