6 papers analyzed
These studies suggest that solving mathematical problems and proofs involves stages of problem-solving, heuristic and creative approaches, use of digital technologies, and reflection, with methods like George Pólya's and dynamic geometry software aiding in understanding and skill development.
Mathematical problem solving and proof construction are fundamental aspects of mathematics education and research. Understanding how individuals approach and solve mathematical problems, as well as how they construct proofs, is crucial for developing effective teaching methods and enhancing mathematical competence.
Stages of Problem Solving:
Heuristics and Problem Solving:
Role of Metacognition:
Creative Problem Solving:
Technology in Problem Solving:
Continuum of Problem Difficulty:
Explanation and Understanding in Proofs:
Mathematical problem solving and proof construction are multifaceted processes involving distinct cognitive phases, the use of heuristics, metacognitive reflection, and sometimes technology. Encouraging creative problem solving and providing interactive learning tools can significantly enhance mathematical understanding and proof skills. Understanding these processes can lead to more effective teaching strategies and improved mathematical competence.
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