The Prevention, Identification, and Cognitive Determinants of Math Difficulty.

Abstract

This study examined the efficacy of preventive 1st-grade tutoring in mathematics, estimated the prevalence and severity of mathematics disability, and explored pretreatment cognitive characteristics associated with mathematics development. Participants were 564 first graders, 127 of whom were designated at risk (AR) for mathematics difficulty and randomly assigned to tutoring or control conditions. Before treatment, all participants were assessed on cognitive and academic measures. Tutoring occurred 3 times weekly for 16 weeks; treatment fidelity was documented; and math outcomes were assessed. Tutoring efficacy was supported on computation and concepts/applications, but not on fact fluency. Tutoring decreased the prevalence of math disability, with prevalence and severity varying as a function of identification method and math domain. Attention accounted for unique variance in predicting each aspect of end-of-year math performance. Other predictors, depending on the aspect of math performance, were nonverbal problem solving, working memory, and phonological processing.

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

“…As shown in Figure 2, we could confirm our isolated number-words hypothesis, indicating that differences in phonological awareness substantially predicted individual differences in QNC Level I skills (number words not linked with quantities). However, in contrast to findings in other relevant studies that did not differentiate among quantity-number competencies, phonological awareness did neither directly contribute to the prediction of higher-order quantity-number competencies (number words linked with quantity; QNC Level II and above), nor to the prediction of math competencies in school (see also Fuchs et al, 2005;Fuchs et al, 2006;Durand et al, 2005). This finding confirms the assumption that although phonological awareness facilitates the acquisition of QNC Level-I skills (e.g., learning the precise number-word sequence), it seems less relevant for the formation of higher-order mathematical competencies that require the conceptual understanding of linking quantity information with number words and their Arabic notations (Level II and III in Krajewski's model;cf.…”

“…In their study, phoneme deletion was a unique predictor of individual differences in reading, but did not predict subsequent arithmetic skills. Also, Fuchs, Compton, Fuchs, Paulsen, Bryant, and Hamlett (2005) reported that phonological processing (measured by rapid digit naming, first sound and last sound matching) was a unique determinant of fact fluency but did not predict other aspects of math performance (e.g. story problems).…”

Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

“…Research has, however, rarely studied the role of attention more broadly. An exception is Fuchs et al (2005), who found that a teacher rating scale of attentive behavior predicted the development of first-grade skill with word problems.Nonverbal problem solving, or the ability to complete patterns presented visually, has been identified as a unique predictor in the development of problem-solving skill across first grade (Fuchs et al, 2005), a finding corroborated by Agness and McLone (1987). This is not surprising, because word problems, in which the problem narrative poses a question entailing relationships between numbers, appear to require conceptual representations.…”

“…However, on numerical working memory (but not on verbal working memory), students with specific computational difficulty performed comparably to their peers without difficulty. In terms of working memory, or the capacity to maintain target memory items while processing an additional task (Daneman & Carpenter, 1980), a body of work has established links with computation (Fuchs et al, 2005;Geary et al, 1991; Hitch & McAuley, 1991;Siegel & Linder, 1984;Webster, 1979;Wilson & Swanson, 2001) and problem solving (e.g., Fuchs et al, 2005;LeBlanc & Weber-Russell, 1996;Passolunghi & Siegel, 2004; Swanson & BeebeFrankenberger, 2004;Swanson & Sachse-Lee, 2001). Although other studies have raised questions about the tenability of this association (e.g., Fuchs et al, 2006;Swanson et al, 1993), the univariate results of the present study corroborate a role for working memory, verbal as well as numerical, in both computational and problem-solving difficulty.…”

“…Teacher ratings of inattentive behavior were identified as a correlate common to both subdomains of math, but the remaining abilities differed: for computation, phonological decoding and processing speed; for word problems, nonverbal problem solving, concept formation, sight word efficiency, and language. The fourth study (Fuchs et al, 2005) used beginning-of-the-year cognitive abilities to predict the development of skill across the year among 272 first graders. Results again suggested some common and some unique patterns of cognitive abilities.…”