Mathematics Difficulty With and Without Reading Difficulty: Findings and Implications From a Four-Year Longitudinal Study
نویسنده
چکیده
An overarching question guided this study: What is mathematics difficulty (MD) independent of reading difficulty (RD)? The sample included 203 children whom the researchers followed from kindergarten to third grade. The researchers used latent growth modeling to investigate the relationship between MD and measures of working memory, short-term memory, cognitive processing speed, early numerical skills, and phonological processing, independent of reading. Two main findings emerged: (a) deficits in early numerical skills were a defining feature of MD with or without RD, and (b) early numerical skills and phonological processing influenced growth in mathematics from kindergarten to third grade. These results indicate that future MD research should focus on numerical and language-based skills, including whether the mathematics disorder in MD—specific or otherwise—reflects underlying language and/or numerical deficits. Exceptional Children MD refers to deficits in one primary domain of mathematics or deficits in many domains (e.g., computation, arithmetic fact fluency, algebra, geometry) or how deficits in one domain affect performance in other domains and across grade levels. Adding to the complexity is that many children with MD also have reading difficulty (RD); in fact, MD and RD co-occur more frequently than either RD or MD occurs alone (Dirks, Spyer, van Lieshout, & de Sonneville, 2008; Fletcher, 2005; Rubinsten, 2009). The research does not clarify whether the mathematics disorder in MD with RD (MD+RD) is the same as the mathematics disorder in MD without RD (MD-only). For instance, both MD-only and MD+RD groups commit more procedural errors than typically developing children (Geary, Hoard, & Hamson, 1999); do not have the same mastery of number facts as typically developing children (e.g., Jordan, Hanich, & Kaplan, 2003; Powell, Fuchs, Fuchs, Cirino, & Fletcher, 2009); and perform story problems more poorly than peers (Hanich, Jordan, Kaplan, & Dick, 2001; Jordan & Hanich, 2000). Furthermore, the groups do not differ in their rate of development in these skills, although children with MD+RD tend to start and end lower on procedural arithmetic and story problems (Jordan et al., 2003). Other than the presence of RD and the finding that children with MD+RD tend to have more severe deficits (Cirino, Fletcher, EwingCobbs, Barnes, & Fuchs, 2007; Jordan et al., 2003), it is not clear how these subtypes differ and indeed whether researchers need to consider MD subtypes. Some researchers have even suggested that the predictors of RD might be sufficient to identify children at risk for MD (Fletcher, 2005), effectively eliminating the need to consider MD separately from RD. The following overarching question guided the current study: What is MD independent of RD?
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