Mathematical learning difficulties: The influence of working memory limitations on simple addition performance

Although basic addition facts have been described as the "simplest aspects of mathematical knowledge" (Russell and Ginsburg, 1984, p.242), the acquisition of these facts presents a serious challenge for some children, creating problems that persist into the adolescent years (Ostad, 1997). The inability to develop, strengthen, and access associations in memory that allow for the rapid and accurate retrieval of answers to problems such as 3+2, 4+5 and 8+7 is, to date, the most distinguishing and persistent characteristic of a specific mathematical learning disability (Jordan and Montani, 1997; Geary, Hamson and Hoard, 2000; Robinson, Menchetti, and Torgesen, 2002; Geary 2004). This chapter considers why students with mathematical learning difficulties (Md) do not move on to develop a reliance on retrieval for simple addition problems. In the first section we describe the complex developmental process involved in developing a reliance on retrieval. We also synthesize findings from 30 years of comparative research examining the simple addition performance of students with and without mathematical learning difficulties (Md) to present a concise picture of performance differences. In the second section we examine the theory and empirical support for explanations associating a difficulty in simple addition with a processing delay or working memory deficit, and critically evaluate these perspectives in terms of their ability to account for performance differences. We then offer a more comprehensive explanation based on working memory limitations. In the third and final section we present a study investigating variability in retrieval times that provides further support for the notion that working memory limitations can account for previously unexplained performance differences in simple addition between students with and without mathematical learning difficulties.