A Rule-Based Computational Model of Cognitive Arithmetic

Abstract: Cognitive arithmetic studies the mental processes used in solving math problems. This area of research explores the retrieval mechanisms and strategies used by people during a common cognitive task. Past research has shown that human performance in arithmetic operations is correlated to the numerical size of the problem. Past research on cognitive arithmetic has pinpointed this trend to either retrieval strength, error checking, or strategy-based approaches when solving equations. This paper describes a rule-based computational model that performs the four major arithmetic operations (addition, subtraction, multiplication and division) on two operands. We then evaluated our model to probe its validity in representing the prevailing concepts observed in psychology experiments from the related works. The experiments specifically explore the problem size effect, an activation-based model for fact retrieval, backup strategies when retrieval fails, and finally optimization strategies when faced with large operands. From our experimental results, we concluded that our model's response times were comparable to results observed when people performed similar tasks during psychology experiments. The fit of our model in reproducing these results and incorporating accuracy into our model are discussed.