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Universal Screening for Prevention of Reading, Writing, and Math Disabilities in Spanish
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Some tests of an identical elements model of basic arithmetic skills

T C Rickard1, L E Bourne

  • 1Cognitive Neuroscience Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland 20892-1440, USA.

Journal of Experimental Psychology. Learning, Memory, and Cognition
|September 1, 1996
PubMed
Summary

The identical elements model suggests arithmetic skills are organized by unique problem components. Practice effects demonstrate that exact element matches lead to complete skill transfer, while mismatches show no transfer.

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Area of Science:

  • Cognitive Psychology
  • Cognitive Neuroscience
  • Educational Psychology

Background:

  • Basic arithmetic skills are fundamental to mathematical cognition.
  • Understanding how these skills are organized and acquired is crucial for effective learning.
  • Previous models proposed different organizational structures for arithmetic knowledge.

Purpose of the Study:

  • To test the identical elements model of basic arithmetic skill organization.
  • To investigate the role of abstract representations in arithmetic problem-solving.
  • To examine transfer of learning in multiplication and division tasks.

Main Methods:

  • Two experiments were conducted using multiplication and division problems.
  • Participants practiced specific arithmetic problems and were subsequently tested on altered versions.
  • Performance was analyzed to assess transfer of learning and practice-related speed-up.

Main Results:

  • Experiment 1 showed no positive transfer when practice and test problem elements did not exactly match.
  • Experiment 2 demonstrated complete transfer when practice and test problem elements were identical.
  • Experiment 2 also revealed both perceptually specific and nonspecific speed-up with practice.

Conclusions:

  • The findings support the identical elements model of arithmetic skill organization.
  • Abstract representations are key to understanding how arithmetic skills are learned and applied.
  • The study has implications for theories of number processing and arithmetic acquisition.