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Related Experiment Videos

Failure to construct and transfer correct representations across probability problems.

Marie-Paule Lecoutre1, Evelyne Clement, Bruno Lecoutre

  • 1ERIS, Laboratoire Psy.Co, E.A 1780, Université de Rouen, UFR Psychologie, Sociologie, Sciences de l'Education, 76821 Mont-Saint-Aignan Cedex, France. marie-paule.lecoutre@univ-rouen.fr

Psychological Reports
|April 14, 2004
PubMed
Summary

People struggle with probability problems, even when they seem simple. Understanding implicit models is key, as transfer of learning only occurs when initial training problems are solved correctly.

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Area of Science:

  • Cognitive Psychology
  • Mathematics Education

Background:

  • Individuals often exhibit difficulties with probability problems, attributed to implicit models guiding erroneous representations.
  • Prior knowledge significantly influences spontaneous reasoning in seemingly random situations.

Purpose of the Study:

  • To investigate the transfer of learning in probability problems with varying representations.
  • To examine whether structural isomorphism facilitates understanding across different problem contexts.

Main Methods:

  • 42 statistically naïve undergraduates participated in a learning phase with geometric probability problems.
  • A transfer phase involved a structurally isomorphic poker chip problem, testing cross-contextual understanding.
  • Problems involved complementarity and equivalence relations to assess implicit model activation.

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Main Results:

  • Participants failed to recognize the relational structure between problems presented in different formats.
  • Successful transfer of learning was observed exclusively in participants who correctly solved the initial training problems.
  • Performance on training problems predicted the ability to generalize concepts in the transfer phase.

Conclusions:

  • Explicit understanding of training problems is crucial for successful knowledge transfer in mathematics.
  • Instructional strategies should focus on building foundational understanding to overcome implicit biases in probability.
  • Implications for teaching mathematical concepts highlight the importance of addressing underlying cognitive models.