Title: 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.