Students’ Mathematical Creative Thinking and Learning Obstacles in Solving Ill-Structured Exponential Problems
Abstract
Mathematical creative thinking (MCT) is crucial for equipping students to solve complex, real-world problems. However, students frequently encounter difficulties with non-routine tasks that require divergent thinking. This study investigates students' MCT and identifies their learning obstacles when solving ill-structured exponential problems. A qualitative descriptive approach under the Didactical Design Research (DDR) framework was employed, involving seven high school students from high, medium, and low achievement levels. Data were gathered through tests and semi-structured interviews, analyzing four MCT indicators: fluency, flexibility, originality, and elaboration. Results showed that students predominantly struggled with fluency and flexibility, often depending on a single method and facing difficulty in generating diverse representations. Originality was restricted by reliance on routine classroom procedures, whereas elaboration, despite being relatively stronger, occasionally led to incorrect conclusions. Identified learning obstacles (didactical, ontogenetic, and epistemological) stemmed from an instructional emphasis on procedural tasks, foundational conceptual misunderstandings, and rigid mathematical perceptions. Ill-structured tasks proved effective in revealing hidden learning obstacles that are often overlooked in routine activities. The study highlights the significance of regularly integrating ill-structured problems into mathematics instruction to foster creativity and address underlying learning challenges.
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References
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DOI: 10.24815/jdm.v12i1.43834
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