1- Ph.D. student, Department of Education, Ar.C., Islamic Azad University, Arak, Iran
2- Associate Professor, Department of Mathematics, Ar.C., Islamic Azad University, Arak, Iran ,majid.haghverdi@iau.ac.ir
3- Assistant Professor, Department of Education, Ar.C., Islamic Azad University, Arak, Iran
2- Associate Professor, Department of Mathematics, Ar.C., Islamic Azad University, Arak, Iran ,
3- Assistant Professor, Department of Education, Ar.C., Islamic Azad University, Arak, Iran
Abstract: (282 Views)
Objective: This study addresses this gap by employing a think-aloud protocol to investigate the cognitive strategies and processes characteristic of CMR in eighth-grade students. Understanding these mechanisms is vital for developing effective pedagogical approaches that foster deeper mathematical understanding and innovation.
Methods: This research utilized a qualitative approach, implementing a think-aloud protocol with six eighth-grade students as they solved number-pattern problems. Participants verbalized their thought processes in real-time, providing rich data for analysis.
Results: The analysis identified five key cognitive strategies students engaged in: visual-spatial analysis, combined deductive-inductive reasoning, flexible use of multiple representations, metacognitive self-monitoring, and iterative reconstruction. Furthermore, the study delineated three primary phases of CMR: exploration and pattern recognition, abstraction and formulation, and verification and generalization. Distinct differences emerged between students who successfully exhibited CMR and those who struggled. Successful problem-solvers demonstrated more systematic visualization, robust self-monitoring, and greater flexibility in switching between strategies. Conversely, less successful students often exhibited limitations in these areas, resorting to less adaptive approaches.
Conclusions: The findings indicate that CMR is not an innate talent but a set of teachable cognitive skills. The study highlights the efficacy of explicit strategy instruction, scaffolding metacognitive awareness, and encouraging reflective practices in cultivating CMR. These insights have significant implications for educational reform, suggesting that curricula and teaching methods should be adapted to prioritize the development of these strategic and metacognitive components. By fostering CMR, educators can equip students with the creative problem-solving abilities necessary for success in increasingly complex mathematical domains and future academic pursuits.
Methods: This research utilized a qualitative approach, implementing a think-aloud protocol with six eighth-grade students as they solved number-pattern problems. Participants verbalized their thought processes in real-time, providing rich data for analysis.
Results: The analysis identified five key cognitive strategies students engaged in: visual-spatial analysis, combined deductive-inductive reasoning, flexible use of multiple representations, metacognitive self-monitoring, and iterative reconstruction. Furthermore, the study delineated three primary phases of CMR: exploration and pattern recognition, abstraction and formulation, and verification and generalization. Distinct differences emerged between students who successfully exhibited CMR and those who struggled. Successful problem-solvers demonstrated more systematic visualization, robust self-monitoring, and greater flexibility in switching between strategies. Conversely, less successful students often exhibited limitations in these areas, resorting to less adaptive approaches.
Conclusions: The findings indicate that CMR is not an innate talent but a set of teachable cognitive skills. The study highlights the efficacy of explicit strategy instruction, scaffolding metacognitive awareness, and encouraging reflective practices in cultivating CMR. These insights have significant implications for educational reform, suggesting that curricula and teaching methods should be adapted to prioritize the development of these strategic and metacognitive components. By fostering CMR, educators can equip students with the creative problem-solving abilities necessary for success in increasingly complex mathematical domains and future academic pursuits.
Keywords: Creative reasoning, Think-aloud protocol, Cognitive strategies, Metacognition, Problem-solving
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