Chapter 5: Relationships Among Basic Computational Automaticity, Working Memory, and Complex Mathematical Problem Solving: What We Know and What We Need to Know

In this chapter we present a review of the literature that supports the relationship between the development of basic computational automaticity and the development of complex mathematical problem solving skills. More specifically, we take the position that automaticity of lower level skills such as basic arithmetic results in the freeing up of cognitive resources (working memory) that can be used in complex problem solving contexts. The chapter begins with a review of arithmetic research that shows that fewer working memory resources are needed to solve arithmetic problems as automaticity develops. Section two is a review of studies showing that there is a strong relationship between computational fluency and complex problem solving ability, even when IQ and other important variables are taken into consideration. In our conclusion we outline future research that will help to further specify the aforementioned relationship.