MIND, BRAIN, AND EDUCATION Volume 2—Number 2 © 2008 the Authors Journal Compilation © 2008 International Mind, Brain, and Education Society and Wiley Periodicals, Inc. 80 ABSTRACT —This article examines the role of working memo- ry, attention shifting, and inhibitory control executive cogni- tive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based approaches to understanding the ways in which children become proficient in mathematics. Task analysis indicates that executive cognitive functions likely operate in concert with procedural and conceptual knowledge and in some instances might act as a unique influence on mathematics problem-solving ability. It is concluded that consideration of the executive cognitive demand of mathematics can contribute to research on best practices in mathematics education. In the study of developing proficiency in mathematics, a pri- mary focus of research has been on knowledge acquisition and on determining at what age and in what manner children come to acquire knowledge of number and of relations among quantities. A complementary line of research that has received less attention in the study of developing ability in mathemat- ics, however, concerns the cognitive processes that support reasoning about quantity, referred to as executive functions (EFs) or cognitive control processes. Certain of these control processes play a well-defined role in reasoning about rela- tions among quantities, but their nature, development, and relation to knowledge growth and achievement in mathemat- ics are not well known. Accordingly, this article describes a cognitive control framework for thinking about elementary mathematics achievement that complements knowledge- based approaches. DEVELOPMENT AND KNOWLEDGE-BASED APPROACHES The study of the development of numerical and mathematical competency in young children has advanced rapidly over the past two decades. Advances have come both in the area of core knowledge (Feigenson, Dehaene, & Spelke, 2004) and in research on strategy acquisition (Siegler, 1999). Core knowl- edge concerns the hypothesis that there is a foundational neural basis for representing quantity, localized primarily to the horizontal segment of the bilateral intraparietal sulcus (IPS; Dehaene, Molko, Cohen, & Wilson, 2004). This neural substrate is thought to provide for elementary abilities such as discriminating quantities and tracking small numbers of objects. Building on the idea that the mammalian brain is phylogenetically configured to represent quantity, research on core knowledge has sought to determine at what point in development, competence in enumeration, ordinality, and cardinality can be established. Findings provide some evi- dence of the representation of cardinality in early infancy but present a more protracted developmental timetable for the development of knowledge of relations among quantities (Mix, Huttenlocher, & Levine, 2002). In contrast to work in core knowledge, which attempts to link brain to behavior and focuses primarily on early develop- ment, research on strategy acquisition in the study of simple addition in young children has led to a renewed focus on learn- ing as a primary mechanism of development (Siegler, 2005). The emphasis in this research is on how and when strate- gies emerge that facilitate working with number (Siegler & Jenkins, 1989). This research has established an expected developmental progression for the types of strategies that 1 Department of Human Development and Family Studies, Penn State University 2 Department of Educational Policy Studies, Penn State University Address correspondence to Clancy Blair, Department of Human Development and Family Studies, Pennsylvania State University, 110 Henderson South, University Park, PA 16802-6504; e-mail: cbb11@psu.edu Is There a Role for Executive Functions in the Development of Mathematics Ability? Clancy Blair 1 , Hilary Knipe 2 , and David Gamson 2