## ABSTRACT

Mathematical cognition involves a variety of complex mental activities such as identification of relevant quantities, encoding or transcribing those quantities into an internal representation, mental comparisons, and calculations. Working memory encompasses “those mechanisms or processes that are involved in the control, regulation, and active maintenance of task-relevant information in the service of complex cognition” (Miyake & Shah, 1999, p. 450). Thus, it seems likely that mathematical cognition will involve working memory. In accord with this view, researchers have periodically emphasized the importance of working memory for understanding mathematical processing (Ashcraft, 1992, 1995; Ashcraft & Kirk, 2001; Hayes, 1973; Heathcote, 1994; Hitch, 1978). Despite the longevity and unanimity of the conclusion that mathematics and working memory should be closely connected, however, research on the role of working memory in mathematical cognition is sparse (Ashcraft, 1995; DeStefano & LeFevre, 2004) and none of the existing theories of mathematical cognition include an explicit role for working memory. This chapter is divided into three sections. First, we provide a brief overview of working memory and discuss models, methodologies, and tasks, using examples from the literature on mathematical cognition and working memory. Second, we review recent empirical research on mathematical cognition and working memory, focusing on four areas of particular interest. Third, we discuss directions for future research.