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Related Experiment Videos

Mental multiplication: nothing but the facts?

C F Manly1, K T Spoehr

  • 1Department of Cognitive and Linguistic Sciences, Brown University, Providence, RI 02912-1978, USA.

Memory & Cognition
|December 10, 1999
PubMed
Summary

This study shows that adults use more than just facts and procedures for multiplication. Different mental representations, like number scales, aid arithmetic performance and problem-solving.

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Area of Science:

  • Cognitive Psychology
  • Mathematics Education

Background:

  • Current models of adult arithmetic performance primarily focus on factual retrieval and procedural execution.
  • The role of alternative representational structures, such as analogical scales or number multiples, in multiplication tasks is underexplored.

Purpose of the Study:

  • To investigate whether distinct representational structures beyond facts and procedures are utilized in adult multiplication.
  • To examine if associations between different representational structures can be detected through cross-task transfer.

Main Methods:

  • Utilized the practice transfer paradigm to assess associations between distinct representational structures.
  • Ensured initial task performance was retrieval-based to facilitate the detection of representational associations.

Main Results:

  • Demonstrated that associations between distinct representational structures can be detected via cross-task transfer.
  • Findings support the integrated-structures model of multiplication knowledge, indicating a more complex representational system than previously assumed.

Conclusions:

  • Adult arithmetic performance involves a richer set of representations than just facts and procedures.
  • The integrated-structures model provides a framework for understanding how diverse representations are integrated in multiplication knowledge.

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