To date, research on math disability (MD) is far less extensive than research on reading disability (RD). A search of articles published between 1974 and early 2003 yielded 14 to 33 times as many citations for “dyslexia” versus “dyscalculia” in Psychlnfo and Pubmed searches, respectively. “Reading disability” was listed as a Psychlnfo key word, whereas no key word category existed for math (or mathematics) disability. Indeed, there were more citations for reading disability (2,415) than there were for math ability (2,154). Yet, like RD, MD is a significant obstacle to academic achievement for many children. There is a need to better understand its causes and manifestation. In this paper, we address the manifestation of MD as a means by which to help define it.
In view of the widespread research attention devoted to RD, it is not surprising that RD is better understood relative to MD.1
Phonological decoding deficits have been identified as core symptoms of RD, through replication and extension of seminal studies, including longitudinal research (e.g., Torgesen, Wagner, & Rashotte, 1994
). These core deficits are evident across the various subtypes of RD that have been described (Morris, Stuebing, Fletcher, Shaywitz, Lyon, Shankweiler, Katz, Francis, & Shaywitz, 1998
), and that persist over time (Shaywitz, Fletcher, Holahan, Shneider, Marchione, Stuebing, Francis, Pugh, & Shaywitz, 1999
). Knowledge of these core deficits leads to an empirically based definition of RD, which, in turn, enhances the ability to identify RD and to provide effective remediation (e.g., Torgesen, Wagner, & Rashotte, 1997
). This knowledge also provides a validated framework from which to study the effects of intervention (e.g., Foorman, Francis, Fletcher, Schatschneider, & Mehta, 1998
Research on mathematics disability is less well developed than RD research. Despite the foundation of research demonstrating cognitive differences in young children with versus without MD (e.g., Geary, Bow-Thomas, & Yao, 1992
; Geary, Hoard, & Hamson, 1999
; Russell & Ginsburg, 1984
; Hanich, Jordan, Kaplan & Dick, 2001
), critical gaps in our knowledge of MD remain. So large is this gap that no universally accepted definition of MD exists, in contrast to the consensus definition for RD (Consensus Project, 2002
). No core deficit has been identified for MD. It is possible that MD subtypes will not share a unifying core deficit because several different domains of function have been linked to poor math achievement, primarily reading-related, memory, visuospatial skills, and/or executive skills. In the field of MD, work toward establishing a consensus definition is in its early stages.
One promising aspect of early and ongoing MD research is the consistency in reports of cognitive correlates of math difficulties. These consistencies are in both the domains
of function with which associations are evident and in the strength
of these associations. For example, specific reading skills, particularly those associated with phonological processing, have been associated with computational math skills in children from grades 2 to 5 (Hecht, Torgesen, Wagner, and Rashotte, 2001
), as suggested by earlier studies of children with poor math achievement (Russell & Ginsburg, 1984
). Yet not all children with RD also have MD, so additional mitigating factors influence MD outcome. These other factors may be related to the types of math tasks on which an MD definition is based; for example, Hanich and colleagues report language-specific difficulties in children with MD and RD, relative to children with MD only (Hanich, et al., 2001
). In their study, children with only MD outperformed their peers with both MD and RD on exact arithmetic tasks, whereas both groups demonstrated comparable difficulty on approximate arithmetic tasks. Bull, Johnston, and Roy (1999)
also reported a significant correlation between math and reading abilities, and also found that math performance level was linked to executive function skills, even when statistically controlling for the contributions of reading ability and I.Q. score. Moreover, different components of executive function, as proposed by Miyake and colleagues (Miyake, Friedman, Emerson, Witzki, Howerter, & Wagner 2000
), each appears to account for some of the variability in children's math performance level, with particularly strong contributions of poor inhibition and poor working memory (Bull & Scerif, 2001
). These findings are consistent with Swanson's (1993)
report of working memory deficits in children with learning disability, including children with reading or math difficulties. Thus, there is consistency across reports that both reading-related and executive skills are associated with math achievement level. Still to be explained is the extent to which these cognitive correlates underlie one or more specific MD subtypes.
Unlike the key basic processes that underlie reading achievement, mathematical achievement is cumulative throughout and beyond the elementary school years with quantitative and qualitative changes occurring within and across grade levels. The required changes concern performance demands and the necessary prerequisite skills. Thus, another question that remains concerns whether deficits occur, or at least are manifested, at different points along the trajectory of expected math skills development. In order to define MD, we need to understand its manifestation within developmental levels, within the same children over time, and within and across MD subtypes. Longitudinal studies can help narrow the current gap in our knowledge, but only a few such studies are currently underway (e.g., Geary, Hamson, & Hoard, 2001
; Jordan, Hanich, & Kaplan, 2003
; Mazzocco, 2001
; Shalev, Manor, Auerbach, & Gross-Tsur, 1998
). These longitudinal studies address different questions, depending on how MD is defined in each study, and whether the study is retrospective or prospective.
In this paper, data from a prospective longitudinal study of math learning disability are presented. This study was designed to address the incidence of MD during the primary school age years (Kindergarten to Grade 3), the utility of different definitions of MD, the developmental trajectory of MD or of poor math achievement in primary school years, and evidence for subtypes of MD. The incidence of poor math achievement is examined as a function of performance on standardized psychometric instruments and experimental measures. The usefulness of proposed MD definitions are examined by applying various MD criteria, all based on widely used standardized measures, to the same group of children within each of four grade levels. Evidence of math LD subtypes is examined, in part, through correlational data, and also through assessment of the stability of MD criteria over time. To examine the developmental trajectory and stability of MD, we examine within-subject consistency of poor math achievement across the primary school age years. The information to be derived from the present study may enhance our ability to define and recognize MD and its subtypes. At the very least, this information should provide us with cautions about ignoring the complexities and limitations of current MD definitions when seeking to identify children who need special educational services; it also serves to illustrate the need for more research in this area.