How Reading Research Can Inform Mathematics Difficulties The Search for the Core Deficit

ersten, Jordan, and Flojo's (inthis issue) article is importantkand provocative in severalways. First, they have done an excel-lent job in discussing some of the char-acteristics of young children withmathematics difficulties (MD). Second,they have presented some practicalimplications of their findings. Morespecifically, they have identified somepromising measures for the early iden-tification of children at risk for MD, aswell as instructional strategies thatshow potential as approaches for inter-vention. These are important contribu-tions, and they point the field inpromising directions for both under-standing and meeting the needs ofchildren with MD. However, they ac-knowledge that the study of MD is inits infancy, whereas reading researchhas matured and shown tremendousprogress in the last 25 years. In thiscommentary, I will discuss how the as-sumptions, models, and methodolo-gies developed by reading researcherscan guide MD research. By heedinglessons learned from the field of read-ing disabilities (RD), investigators canavoid many of the challenges thatreading researchers had to overcome.Gersten et al. (in this issue) haveoutlined the wide array of deficitsshown by children with MD. This in-cludes low mastery of and fluency inthe retrieval of arithmetic combina-tions, slow digit naming speeds, ineffi-cient and immature counting strate-gies, low number sense, and impairednonverbal working memory. Readingresearchers were also faced with abroad range of tasks that differentiatedchildren with RD. For example, chil-dren with RD showed impaired per-formance on tasks that assessed phono-logical processing, vocabulary, syntacticprocessing, and verbal working mem-ory. However, reading researchers tookthe important step of distinguishingbetween those factors that play acausal role in reading failure and thosethat are consequences of these fac-tors. There is considerable consensusthat the causal deficit in RD is im-paired phonological processing, whichis most evident as impaired phonolog-ical awareness-the ability to identifyand manipulate phonemes (Adams,1990; Cunningham & Stanovich, 1997;Stanovich & Siegel, 1994). Deficits inphonological awareness directly inter-fere with the acquisition and masteryof the spelling-sound correspondencesthat underlie fluent reading (Goswami& Bryant, 1990; Tunmer & Hoover,1992). However, because children withRD tend to avoid reading, their expo-sure to print is limited. This providesthem with fewer opportunities to ac-quire the breadth of vocabulary andsyntactic structures that skilled readersacquire (Stanovich, 1986). In short,deficits in phonological awareness havea direct relationship with decodingability and an indirect relationship withother correlates of RD.By exploiting the variables thatplay a direct causal role in reading fail-ure, researchers have been able to de-velop reading readiness tests that havepredictive validities in the range of.6 to .7, and an array of interventionsthat prevent reading difficulties beforethe onset of formal reading instruction,thereby avoiding the cognitive and lin-guistic consequences associated withreading failure. The field of MD willmake similar progress once investiga-tors can distinguish between thosevariables that cause MD and thosethat are consequences of MD. Becausemathematics is a broad domain withmany subdisciplines, more than onevariable may play a causal role in MD.However, it may be possible to identifyone that is relevant to the developmentof arithmetic skills.The task for the field of MD istherefore to identify a core deficit ordeficits. Furthermore, this deficit mustsatisfy the assumption of specificity(Stanovich, 1993; Stanovich & Siegel,1994). This is the assumption that chil-dren with learning disabilities have acognitive deficit that involves a domain-specific process, rather than a domain-general one, such as processingspeed, general auditory processing, orautomaticity. The concept of learningdisabilities requires that the deficitsnot extend too far into other domainsof cognitive abilities. Otherwise, thedeficits would depress cognitive func-tioning in all domains, and not just,say, reading or mathematics. In short,if the cause of MD fails to satisfy the as-sumption of specificity, significant dif-ficulties in mathematics would befound only in individuals with low in-telligence, which research suggests isnot the case (Siegel, 1988; Stanovich,1999). The underlying deficit of MDmust therefore be assumed to be a