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Cognitive arithmetic: a review of data and theory
1Department of Psychology, Cleveland State University, OH 44115.
Cognition
|August 1, 1992
Summary
This review explores cognitive arithmetic, focusing on how people mentally represent numbers and perform calculations. It examines key empirical effects and current models of arithmetic processing, including problem difficulty.
Area of Science:
- Cognitive psychology
- Neuroscience of mathematics
Background:
- Cognitive arithmetic investigates the mental representation of numbers and arithmetic operations.
- Understanding these processes is crucial for explaining mathematical cognition.
Purpose of the Study:
- To provide a tutorial review of the field of cognitive arithmetic.
- To discuss empirical effects, current models, and the architecture of cognitive arithmetic.
Main Methods:
- Review of empirical effects: problem size/difficulty, errors, relatedness, and processing strategies.
- Analysis of three current models of simple arithmetic processing.
- Discussion of the relationship between fact retrieval and rule-based systems.
Main Results:
- Identifies four key empirical effects in cognitive arithmetic research.
- Evaluates supporting and challenging evidence for current arithmetic processing models.
- Explores the interplay between memory retrieval and rule-based computation.
Conclusions:
- The problem difficulty effect remains a central, unresolved puzzle in cognitive arithmetic.
- Proposes insights into the overall architecture of the cognitive arithmetic system.
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