Mental arithmetic: Effects of calculation procedure and problem difficulty on solution latency

Abstract

In this chronometric study of mental arithmetic, problems with sums > 20 and < 100 were presented to third-grade subjects (age 8–9). It is argued that such problems are calculated by using procedures in which the problem is broken down into subproblems for which solutions are retrieved from a declarative knowledge base. Important bottlenecks in this process are the processing capacity (since only one subproblem can be handled at a time) and the storage capacity of working memory (since the original problem and all outcomes of subproblems have to be retained). Therefore it can be hypothesized that arithmetic procedures and types of problems that necessitate more subproblems will lead to longer solution times. Both hypotheses were confirmed. Significant interactions between types of problems and arthmetic procedures show an increasing difference in solution time between the procedures with increasing problem difficulty. It can be concluded that for the type of problems studied, arithmetic procedures requiring a smaller number of subproblems lead to better performance.