Learning Disabilities in Arithmetic: Problem-Solving Differences and Cognitive Deficits

The complexity of the field of mathematics makes the study of any associated learning disability daunting. In theory, a mathematical learning disability can result from deficits in the ability to represent or process information used in one or all of the many areas of mathematics (e.g., arithmetic and geometry), or in one or a set of individual domains (e.g., theorems vs. graphing) within each of these areas (Russell & Ginsburg, 1984). One approach that can be used to focus the search for any such learning disability (LD) is to apply the models and methods used to study mathematical development in academically normal children to the study of children with poor achievement in mathematics (e.g., Geary & Brown, 1991). Unfortunately, for most mathematical domains, such as geometry and algebra, not enough is known about the normal development of the associated competencies to provide a systematic framework for the study of LD. Theoretical models and experimental methods are, however, sufficiently well developed in the areas of number, counting, and simple arithmetic to provide such a framework {Briars & Siegler, 1984; Geary, 1994; Gelman & Meck, 1983; Siegler, 1996; Siegler & Shrager,1984). The use of these models and methods to guide the study of children with LD has revealed a consistent pattern of cognitive strengths and weaknesses. These studies suggest that most children with LD are normal (i.e., performance is similar to academically normal peers) or only slightly delayed in the development of number concepts (Geary, Hamson, & Hoard, 2000; GrossTsur, Manor, & Shalev, 1996). At the same time, several studies have shown that many children with LD do not understand certain counting concepts (Geary, Bow-Thomas, & Yao, 1992; Geary, Hoard, & Hamson, 1999), and many studies have revealed that these children have a variety of deficits in simple arithmetic (Ackerman & Dykman, 1995; Barrouillet, Fayol, & Lathuli (re, 1997; Bull & Johnston, 1997; Garnett, & Fleischner, 1983; Geary, Brown, & Samaranayake, 1991; Geary, Widaman, Little, & Cormier, 1987; Jordan & Hanich, 2000; Jordan, Levine, & Huttenlocher, 1995; Jordan & Montani, 1997; Ostad, 1997, 1998a; Rasanen & Ahonen, 1995; Rourke, 1993; Svenson & Broquist, 1975). The deficits in the basic arithmetical competencies of children with LD (hereafter, arithmetical disability, or AD) have been found