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Identical elements model of arithmetic memory: extension to addition and subtraction
Jamie I D Campbell1, Shannon Fuchs-Lacelle, Thomas L Phenix
1Department of Psychology, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK S7N 5A5, Canada. jamie.campbell@usask.ca
Memory & Cognition
|August 29, 2006
Summary
The identical elements (IE) model accurately predicts arithmetic fact retrieval for addition and subtraction. This model also extends to multiplication and division, explaining how procedural strategies influence performance.
Area of Science:
- Cognitive Psychology
- Mathematical Cognition
- Human Memory
Background:
- The identical elements (IE) model explains how arithmetic facts are represented and retrieved.
- Previous research validated the IE model for multiplication and division.
Purpose of the Study:
- To test the applicability of the IE model to addition and subtraction.
- To investigate transfer effects in arithmetic fact retrieval across different operations.
Main Methods:
- Experiment 1: Examined response time (RT) savings in addition and subtraction using identical repetition, order change, and operation change paradigms.
- Experiment 2: Investigated transfer in multiplication and division, analyzing RT savings with and without direct retrieval trials.
Main Results:
- The IE model accurately predicted RT savings in addition and subtraction, with specific patterns for identical repetition and order changes.
- Symmetrical transfer was observed between multiplication and division.
- Cross-operation RT savings disappeared when only direct retrieval trials were considered.
Conclusions:
- The IE model provides a robust framework for understanding arithmetic fact representation across basic operations.
- Extending the IE model to include procedural strategies accounts for observed facilitative transfer effects.
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