Exploring the Gap: Creative Mathematical Reasoning of Pre-service Teachers in Solving Multiple Solution Analytical Geometry Tasks
), Wardono Wardono(2), Adi Nur Cahyono(3), Riyan Hidayat(4), Zaenuri Zaenuri(5), Yohanes Leonardus Sukestiyarno(6), Stevanus Budi Waluya(7)
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Country:
(1) Department of Mathematics Education, Universitas Negeri Semarang, Indonesia
(2) Department of Mathematics Education, Universitas Negeri Semarang, Indonesia
(3) Department of Mathematics Education, Universitas Negeri Semarang, Indonesia
(4) Department of Mathematical Research, Universiti Putra Malaysia, Malaysia
(5) Department of Mathematics Education, Universitas Negeri Semarang, Indonesia
(6) Department of Mathematics Education, Universitas Negeri Semarang, Indonesia
(7) Department of Mathematics Education, Universitas Negeri Semarang, Indonesia
Corresponding Author
With the rapid changes in the times, the emphasis in education has also shifted, from equipping students with highly codified knowledge to developing routine skills to empower them to face and overcome complex and non-routine cognitive challenges. Students must be able to think flexibly and creatively when asked to solve problems for which they do not yet have strategies. The purpose of this study was to describe the creative mathematical reasoning (CMR) abilities of students in solving multiple solution tasks (MSTs) in analytical geometry problems. The CMR indicators in this study were novelty, plausibility, and mathematical foundation. The research used a qualitative descriptive design, describing how students' CMR abilities and their own abilities in solving MSTs questions. The subjects of this study were second-semester students in the mathematics education program at a university in Subang in the 2024/2025 academic year. The subjects were given MSTs questions, grouped into high, medium, and low groups based on their scores. Then, two participants were selected from each group. The criteria for selecting research subjects were: fulfilling the CMR ability aspect; being able to solve several MSTs questions to assess novelty, plausibility, and mathematical foundation, including the stages of initiating reasoning, developing reasoning (incubation, illumination), verifying reasoning, and justifying reasoning; and being able to communicate well. The research subjects were divided into three groups based on the MSTs' question scores: high, medium, and low. The results of the study illustrate that students' mathematical creative reasoning abilities in solving MSTs questions are not optimal, as reflected in the solutions they provide. Therefore, to optimize students' CMR abilities, assignments should combine question types and use interactive, practical, relevant, comfortable, and connected learning models. For example, project-based or technology-based learning models.
Keywords: analytical geometry, creative reasoning, multiple solution tasks.
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