Children's Arithmetical Difficulties: Contributions from Processing Speed, Item Identification, and Short-Term Memory

“…measure processing speed are consistently found to be related to performance of other cognitive skills, and to measures of higher-order cognitive processes, for example, short-term memory (Hale, 1990; Kail, 1991; Kail & Hall, 1994; Kail & Park, 1994; Kail & Salthouse, 1994; Rabbitt & Goward, 1994).”

“…of studies of children with poor mathematical skills have revealed no significant limitations in verbal shortterm memory, or limitations being due to a third factor such as processing speed or co-occurring reading difficulties (e.g., Bull & Johnston, 1997; Geary et al., 1999; Geary et al., 2000).”

“…that some components of working memory and speed of processing are contributing factors to MLD, there are disagreements regarding the relative importance of these factors (Bull & Johnston, 1997; Bull et al., 1999; Geary et al., 2004; McLean & Hitch, 1999; Swanson, 1993; Swanson & Sachse-Lee, 2001).”

“First, the set of cognitive antecedents of math performance included in the study was limited and did not include, for example, memory span (Geary, 1993) and processing time ( Bull & Johnston, 1997; Pellegrino & Goldman, 1987).”

“…studies have compared measures of working memory in normal children, children with arithmetic difficulties, and children with enhanced arithmetical ability (e.g., Bull & Johnston, 1997; Dark & Benbow, 1990, 1991; Geary et al., 1991; Hitch & McAuley, 1991; Siegel & Ryan, 1989; Swanson, 1993, 1994).”

“For example, Bull and Johnston (1997) found a correlation of ).54 between one measure of language ability (naming latencies) and maths achievement.”

“…has focused on how young children with MD solve simple problems (e.g., 4 + 5; Garnett & Fleischner, 1983; Geary, 1990; Jordan & Montani, 1997), and less commonly on the cognitive mechanisms that may underlie these performance characteristics (Bull & Johnston, 1997; Geary, Bow-Thomas, & Yao, 1992).”

“…overall intelligence, information-processing speed, working memory, or other cognitive abilities that have been found to correlate with math achievement (e.g. Bull & Johnston, 1997; Geary, 1993; Koontz & Berch, 1996), although many of these correlate with vocabulary size which we did control for.”

“It should be noted, however, that children with MD only used finger-counting strategies more accurately than did children with MD–RD, suggesting better facility with counting procedures in the MD only group than in the MD–RD group ( Bull & Johnston, 1997; Geary et al., 1999; Jordan & Hanich, 2000; Jordan & Montani, 19…”

“This is because in addition to deficits on measures of working memory, children with MLD process information more slowly than TA children ( Bull & Johnston, 1997 ; Swanson & Sachse-Lee, 2001 ).”

“While the core cognitive deficits associated with reading, spelling and arithmetic disorders appear to be specific, one proposal regarding comorbidity between learning disorders is that domain-general cognitive risk factors, such as memory or processing speed deficits [47–49] are shared between learning disorders.”

“Children with mathematical difficulties (MD) are less likely to use direct memory retrieval to solve arithmetic questions (Bull & Johnston, 1997; Geary, Brown, & Samaranayake, 1991), and count more slowly and inaccurately than children with normal abilities (Bull & Johnston, 1997; Geary,…”

“Bull and Johnston (1997) found that processing speed was the best predictor of computational competence among 7-year-olds, subsuming all of the variance accounted for by long- and short-term memory, even with reading performance controlled.”

“It explains the development of the verbal (Kail, 1992, 1997a) and visuospatial short-term memory (Kail, 1997b), the evolutions of both reading recognition and comprehension (Kail & Hall, 1994), and performance in simple additions (Bull & Johnston, 1997) and in problem solving (Kail & Hall, 1999).”

“Bull and Johnston (1997) found that processing speed was the best predictor of arithmetic competence among 7-year olds, subsuming all of the variance accounted for by long- and short-term memory, even when controlling for reading performance.”

“Indeed, studies of typically developing children have documented significant associations between processing speed and academic outcomes (Berg, 2008; Bull & Johnston, 1997; Gathercole, Pickering, Knight, & Stegman, 2004; Schatschneider et al., 2004; St Clair-Thompson & Gathercole, 2006).”

“Problem size was defined as described in Campbell and Xue (2001) (see also Barrouillet et al.”

“First, the role of working memory has been studied predominantly by means of correlations between working memory measures (e.g., counting span, Trails task, Stroop task) and simple arithmetic performance (e.g., Bull & Johnston, 1997; Bull et al., 1999; Bull & Scerif, 2001; McLean & Hitch, 1999; Passolunghi & Siegel, 2…”

“The Gs-to-arithmetic skill link (Bull & Johnston, 1997; Fiorello & Primerano, 2005; Floyd et al., 2003; Fuchs et al., 2006) has been explained in terms of counting speed (Geary, 1993, 2007), numerical processing fluency (Swanson & Jerman, 2006), and efficiency and consistency of execution of simple…”

“Different reading and math skills tap WM skills differently (e.g., Bull & Johnston, 1997; Carretti, Cornoldi, De Beni, & Romanò, 2005; Gathercole & Pickering, 2000).”

“The previous studies concerning the relationship between WM and mathematics have focused mainly on the general processing component, the CE (e.g. Bull & Johnston, 1997; Bull et al., 1999), and on phonological WM (e.g. Healy & Nairne, 1985; Logie & Baddeley, ISSN 0144-3410 print; ISSN 1469-5820…”

“In the second step (see panel 2), both estimated full scale IQ and word level reading were entered to control for general (global) learning mechanisms that could also underlie the observed associations between the predictors and math-related outcomes (cf., Bull & Johnston, 1997;Kail, 2004).”

“…of studies focusing on CHC theory (e.g., Floyd et al., 2003; Keith, 1999; McGrew et al., 1997; McGrew & Hessler, 1995), as well as others studies (Bull & Johnston, 1997; Fuchs et al., 2006; Kirby & Becker, 1988) that suggest that the ability to process and make decisions quickly about visual…”

“Processing speed deficits have long been associated with language and learning disorders (e.g., Bull & Johnston, 1997; Catts, Gillispie, Leonard, Kail, & Miller, 2002).”

“Children with poor mathematical ability do not always show particular problems in phonological working memory tasks ( McLean & Hitch, 1999 ; Passolunghi & Siegel, 2004 ), although Bull and Johnston (1997) found a significant association between phonological memory and individual differences in mathematical computation…”

“One approach that can be used to circumvent this instructional confound involves is to apply the theories and methods used to study mathematical competencies in normal children to the study of children with MD ( Bull & Johnston, 1997; Garnett & Fleischner, 1983; Geary & Brown, 1991; Geary, Widaman, Little, & Cormier,…”

“…Of the domain-general mechanisms, working memory, classroom attention, and speed of processing have all been show to predict NC performance (e.g., Bull & Johnston, 1997; Fuchs et al., 2005; Hitch & McAuley, 1991), but none of the studies assessed these potential mechanisms simultaneously with…”

“Speed of processing, also a predictor of arithmetic (Bull & Johnston, 1997; Hecht, Torgesen, Wagner, & Rashotte, 2001), may help support efficient counting to produce correct associations between problems and answers.”

“It has also been identified as predictive of arithmetic performance (Bull & Johnston, 1997; Fuchs, Fuchs, Stuebing, et al., 2008; Hecht et al., 2001).”

“For instance, in a population of normal 7-year-old children, arithmetical performance has been shown to correlate with CE capacity (Bull & Johnston, 1997; Bull & Scerif, 2001; Bull, Johnston, & Roy, 1999; Gathercole & Pickering, 2000; Gathercole, Pickering, Knight, & Stegmann, 2004).”

“We assessed this by examining the relation between the three components of working memory and mathematics achievement in fifth grade, controlling for the relation between first grade working memory capacity and grade-related changes in mathematics achievement and controlling for other factors that are related to mathe…”

“In an attempt to find the underlying cause of children’s arithmetical difficulties, Bull and Johnston (1997) and Bull, Johnston, and Roy (1999) concluded that “specifically the functioning of the articulatory loop did not represent a fundamental deficit for children of low mathematical ability”…”

“Processing speed accounts for variation in mathematical skills independently of working memory in some studies (e.g., Andersson, 2010; Bull & Johnston, 1997; Chan & Ho, 2010; Fuchs et al., 2006; Hecht, Torgesen, Wagner, & Rashotte, 2001; but note Geary et al., 2008).”

“We found that processing speed deficits were one of the most salient cognitive deficits among MD, in line with most previous research (Bull & Johnston, 1997;”

“This task has consistently been used to examine working memory skills in children with MLD (Bull & Johnston, 1997; Passolunghi & Siegel, 2001, 2004; van der Sluis et al., 2005).”

“…one proposal regarding the comorbidity of RD and MD is that domain-general deficits, such as deficits in processing speed or working memory (Bull & Johnston, 1997; Geary & Hoard, 2005; Willcutt et al., 2013) are shared between RD and MD and this could explain why these disorders frequently…”

“Impaired executive functions appear to be associated with MLD in children as a few studies report problems with shifting ability and attention functions among these children (Bull & Johnston, 1997; Bull, Johnston, & Roy, 1999; McLean & Hitch, 1999; van der Sluis, de Jong, & van der Leij, 2004).”

“Working memory consistently correlates with performance on arithmetical computation and problem-solving tasks among children (Bull & Johnston, 1997; Bull, Johnston, & Roy, 1999; Bull & Scerif, 2001; Demetriou, Christou, Spanoudis, & Platsidou, 2002; Espy et al., 2004; Gathercole, Pickering, Knight,…”

“Similarly, theories that focus on the role of working memory capacity in math problem solving predict that performance should improve with age as executive processing capacity and phonological short-term memory mature (Adams & Hitch, 1997; Ashcraft, 1992; Barrouillet & Lepine, 2005; Bull & Johnston, 1997; Gathercole &…”

“…MD may have short-term memory deficits specifically for numerical information (Passolunghi & Siegel, 2001), and still other studies have not found differences on short-term memory between children with MD and typical developers (e.g., Bull & Johnston, 1997; Landerl, Bevan, & Butterworth, 2004).”

“However, the phonological loop did not represent a fundamental deficit for children of low mathematical ability when difference in reading is controlled for (Bull & Johnston, 1997 ; McLean & Hitch, 1999 ; Passolunghi, 2006 ; Passolunghi & Siegel, 2004 ).”

“Importantly, in addition to measures of WMC (complex span tasks requiring both storage and processing), participants also completed simple STM span measures (requiring only storage).”

“Copyright # 2002 John Wiley & Sons, Ltd. DYSLEXIA 8: 67–85 (2002) (iv) There may be fact-retrieval deficits in children attributed to general deficiencies in speed of processing (Ackerman and Dykman, 1995; Bull and Johnston, 1997).”

“…1993) or phonological processes (Fuchs et al., 2005; Hecht, Torgesen, Wagner, & Rashotte, 2001), as well as one or more aspects of working memory (Bull & Johnston,1997; Bull, Johnston, & Roy,1999; D'Amico&Guarnera, 2005; Geary, Hamson, & Hoard, 2000; Geary, Hoard, & Hamson, 1999; McLean & Hitch,…”

“…skill given prior work with whole-number calculations sometimes showing the unique contribution of processing speed but not working memory when both predictors compete for variance in the same model (e.g., Bull & Johnston, 1997; Fuchs, Fuchs, Stuebing, et al., 2008; Fuchs et al., 2010b).”