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Experimental study of learning support through examples in mathematical problem posing.

Kazuaki Kojima1, Kazuhisa Miwa2, Tatsunori Matsui3

  • 1Learning Technology Laboratory, Teikyo University, 1-1 Toyosatodai, Utsunomiya, 320-8551 Japan.

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Summary
This summary is machine-generated.

Fostering learner problem posing is crucial in education. Learning by reproducing examples, rather than just solving or evaluating them, most effectively supports students in creating mathematical solutions.

Keywords:
Learning from examplesMathematical learningProblem posingProduction task

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Area of Science:

  • Mathematics Education
  • Cognitive Science
  • Educational Psychology

Background:

  • Problem posing is essential for real-world mathematical application, requiring learners to formulate problems independently.
  • Novice learners struggle with constructing mathematical solutions during problem posing, necessitating targeted learning support.
  • Traditional example-based learning (solving examples) may not adequately develop problem-posing skills due to differing cognitive demands.

Purpose of the Study:

  • To investigate the impact of different example-based learning strategies on learners' ability to compose solutions for problem posing.
  • To compare the effectiveness of learning by solving, reproducing, and evaluating examples in fostering problem-posing skills.
  • To identify optimal learning approaches for enhancing solution composition in mathematical problem posing.

Main Methods:

  • An experiment involving undergraduates was conducted to assess learning strategies for problem posing.
  • Participants engaged in one of three learning activities: solving, reproducing, or evaluating a provided mathematical example.
  • Following the learning activity, students were tasked with posing novel problems based on an initial problem, utilizing ideas gained from the example to compose solutions.

Main Results:

  • Learning by reproducing an example significantly enhanced undergraduates' ability to compose solutions for problem posing.
  • Reproducing examples provided a more effective scaffold for generating novel solution structures compared to solving or evaluating examples.
  • The study identified specific learning activities that better support the cognitive processes involved in mathematical problem posing.

Conclusions:

  • Reproducing examples is a highly effective pedagogical strategy for improving solution composition in mathematical problem posing.
  • Educational interventions should consider incorporating example reproduction to better foster independent problem-posing skills in learners.
  • This research offers valuable insights for curriculum design aimed at developing advanced mathematical problem-solving and posing competencies.