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).”

“Math For untimed math, we expected numerosity to be the strongest significant relation, followed by WM (Willcutt et al., 2013), PS (Bull & Johnston, 1997; Fuchs et al., 2006; Willcutt et al., 2013), and PA (Fuchs et al., 2006; Willcutt et al., 2013).”

“Children with AD have adequate word recognition skills but problems with eye–hand coordination, shortterm memory, and some visual–spatial tasks (e.g., Bull & Johnston, 1997; Hitch & McAuley, 1991; Hitch & Towse, 1995; Morrison & Siegel, 1991a; Passolunghi, Cornoldi, & De Liberto, 1999; Siegel &…”

“Because arithmetic performance seems to be strongly predicted by processing speed (e.g., Bull & Johnston, 1997; Fuchs et al., 2006), arithmetic difficulties persist, perhaps due to persistent processing speed deficit, hampering automatic basic arithmetic fact retrieval (e.g., Geary, Hoard,…”

“…the 1990s, a growing number of studies focussed on strategy development in children with MD in the domain of simple addition and subtraction (e.g., Bull & Johnston, 1997; Geary, 1990, 1993; Geary, Bow-Thomas, & Yao, 1992; Geary & Brown, 1991; Geary, Brown, & Samaranayake, 1991; Geary, Hamson, &…”

“Frontiers in Psychology | Cognition December 2011 | Volume 2 | Article 359 | 2 Processing speed is considered an index of IQ (Kail, 2007), and is related to math abilities in older students (Bull and Johnston, 1997; Floyd et al., 2003).”

“…facts as well as for reading (Geary, 1993); problems in inhibiting closely related math facts in memory (Geary, 2003); slow information processing across cognitive domains, including math (Bull & Johnston , 1997); and difficulties in manipulating nonverbal representations ( Jordan et al., 2003b).”

“Although results regarding MD are more limited, several studies have found significant relations between RAN and MD (see Bull & Johnston, 1997; Chard et al., 2005; Landerl, Bevan, & Butterworth, 2004; Van der Sluis, De Jong, & Van der Leij, 2004).”

“Bull and Johnston ( 1997 ) showed in seven year olds that processing speed was the best predictor of arithmetic competence (compared with short‐term or long‐term memory ability).”

“As predicted by the Dehaene et al. [2003] model, number comparison, which is thought to capture the quantity representation of number, was significantly related to the execution of procedural strategies, while number reading, which is assumed to measure the verbal representation of number, was associated with children…”

“Processing speed has been found to be an independent predictor of math performance in the epilepsy(23) and nonepilepsy pediatric population.(24) Auditory working memory has been found to be associated with performance in math in both children with epilepsy(25) and without epilepsy,(26) but this relationship was not fo…”

“For instance, researchers have implicated working memory (e.g., Siegel & Ryan, 1989), phonological processing (e.g., Hecht, Torgesen, Wagner, & Rashotte, 2001), and short-term memory (e.g., Bull & Johnston, 1997; Geary et al., 2000; Passolunghi & Siegel, 2001) in both MD subtypes.”

“When addressing the question of non-typically developing children, our results do not validate the ‘defective module hypothesis’ (Butterworth, 2005) nor the ‘access deficit hypothesis’ (Rousselle & Noël, 2007). Part of the results are in line with Butterworth (2005) because the MD children in our sample already had di…”

“This choice reflects the increasing interest for the cognitive mechanisms underlying arithmetic and problem-solving difficulties (Bull & Johnston, 1997; McLean & Hitch, 1999; Passolunghi & Pazzaglia, 2004; Passolunghi & Siegel, 2001, 2004; Swanson & Sachse-Lee, 2001).”

“However, most of the previous studies concerning the relationship between mathematics and reading skills have been carried out among learning-disabled students ( Bull & Johnston, 1997; Geary, 1990, 1993; Jordan, Kaplan, & Hanich, 2002; Jordan, Hanich, & Kaplan, 2003; Macaruso & Sokol, 1998; Share, Moffitt, & Silva, 19…”

“Studies on the characteristics of the strategies that first and second graders with MD use to solve simple additions and subtractions up to 20 (Bull & Johnston, 1997; Geary, 1990; Geary, BowThomas, & Yao, 1992; Geary et al., 1999; Hanich, Jordan, Kaplan, & Dick, 2001; Jordan & Hanich, 2000)…”

“Bull and Johnston (1997) found that processing speed in 7-year-old children accounted for unique variance in math achievement when controlling for reading skills and verbal working memory.”

“The frequent repetition of this process enables information consolidation in long-term memory; this can become an easily and quickly recoverable arithmetic fact [7,30,31], which can increase the automatization of the calculation process.”

“These profiles did not differ in terms of age, sex, socioeconomic status, or intellectual ability.”

“…would make sense that phonological processing should impact on at least some mathematical skills, since speech sounds are known to play an important role in tasks such asmathematical computation (Bull & Johnston, 1997; Geary, 1993; Hecht, Torgesen, Wagner, & Rashotte, 2001; Rourke & Conway, 1997).”

“We also included processing speed (i.e., a speeded cross out task), which refers to the efficiency with which cognitive tasks are performed (Bull & Johnston, 1997), as a control variable because of its demonstrated role in arithmetic, which is required to solve WPs.”

“Fourth-grade estimates of IQ and word reading were included to rule out general learning mechanisms as an underlying reason for correlations between our predictors and criterion (Bull & Johnston, 1997; Hecht, 1998).”

“Lack of automatized retrieval of basic facts inhibits the development of arithmetical competencies and has been implicated as one factor contributing to poor mathematics achievement (Ashcraft, Donley, Halas, & Vakali, 1992; Bull & Johnston, 1997; Geary, 1993).”

“There is also substantial evidence, however, that children with poorer mathematics achievement generally are slower to process information (Bull and Johnston, 1997; Geary et al., 2012).”

“Studies have shown a close relation between processing speed and mathematical performance for children in Western counties (e.g., Hitch and McAuley, 1991; Bull and Johnston, 1997; Fuchs et al., 2005).”

“The data are also consistent with the hypothesis that verbal arithmetic difficulties might be related to problems in verbal working memory (Hitch & McAuley, 1991) and speed of processing (Bull & Johnston, 1997) rather than with conceptual aspects of number.”

“…with poor arithmetic skills show a lack of automaticity in retrieving numbers and number combinations from long-term memory, evidenced through slow item identification and through the use of slow, inefficient counting strategies rather than direct memory retrieval” (Bull & Johnston, 1997, p. 6).”

“…memory (e.g., Bull, Johnston, & Roy, 1999; Geary, 2011; McLean & Hitch, 1999; Siegel & Ryan, 1989; Swanson & Sachse-Lee, 2001); speed of processing (Bull & Johnston, 1997; Bull et al., 1999; Case, Kurland, & Goldberg, 1982); and reading and general cognitive factors (e.g., Dirks, Spyer, van…”

“In general, the role of phonological WM, which temporarily stores and rehearses linguistic material, is probably not major (e.g., Bull & Johnston, 1997; McLean & Hitch, 1999; Reuhkala, 2001), but it has been observed as necessary to certain specific maths skills such as counting (Healy & Nairne,…”

“…that have been the focus of most investigations of math skills are information retrieval (Geary, 1990, 1994; Geary, Brown, & Samaranayake, 1991), working memory (Geary, 1994; Hitch & McAuley, 1991; Shafir & Siegel, 1994; Swanson, 1994), and speed of processing (Bull & Johnston, 1997; Geary, 1994).”

“Indeed, younger students with mathematics difficulties have a more limited processing speed (Bull & Johnston, 1997).”

“In one other study on the relationship between math and reading achievement, Bull and Johnston (1997) found a significant correlation between these two factors with a group of seven year old children.”

“For example, processing speed (L. S. Fuchs, Fuchs, Stuebing, et al.) and working memory (Bull & Johnston, 1997) seem to contribute to CA development, whereas WP skill appears to be uniquely predicted by concept formation, nonverbal reasoning, sight-word proficiency, language, and reading (L. S.…”

“Among the general cognitive abilities that influence mathematical performance are fluid reasoning skills (e.g., Floyd, Evans and McGrew 2003), working memory capacity (e.g., Hayes 1973; LeFevre, DeStefano, Coleman and Shanahan 2005) and focused attention (e.g., Bull and Johnston 1997; Floyd et al. 2003; Kail and Hall…”

“Bull and Johnston (1997) also found that children with low mathematics abilities performed significantly worse than children with high ability in mathematics on short-term memory tasks before reading ability was controlled.”

“…being involved in the process 114 CHAPTER 5 Individual differences in children’s mathematics achievement of accurately memorizing arithmetic facts (Bull and Johnston, 1997) and related suggestions that an impaired phonological loop might prevent children from changing toward arithmetic fact…”

“Learners can retain and think about information better when they have the knowledge necessary for interpreting the information and can recall it effectively (Bull et.al., 1997; Ericsson & Kintsh, 1995).”

“In fact, Bull and Johnston (1997) found that processing speed was the best predictor of calculation competence among seven-year-olds, when they controlled for long- and shortterm memory and reading performance.”

“Individuals with higher mathematical ability are more likely to rid unnecessary information from their WM. Speed of processing was found to be related to arithmetic performance (Bull & Johnston, 1997; Durand, Holme Larkin, & Snowling, 2005; Taub, Keith, Floyd, & McGrew, 2008).”

“They use direct retrieval of math facts less often, have higher error rates when they do use retrieval, and have very irregular solution times when solving problems (Bull & Johnston, 1997; Geary, 1994; Geary et al., 1991; Geary & Brown, 1992; McLean & Hitch, 1999; Passolunghi & Siegel, 2001).”

“However, all calculation tasks require the use of arithmetical basic facts, and the relationships between level of performance in basic fact retrieval and higher levels of problem-solving are strong (Bull & Johnston, 1997; Hecht et al., 2001; Tronsky & Royer, 2003).”

“These results have been reported in second graders (e.g., Bull & Johnston, 1997; Hecht et al., 2001) and in third graders (Fuchs et al., 2006).”

“…math reasoning skills, although many investigations examine the prediction of composite math scores, which include both computation as well as math reasoning measures (Bull & Johnston, 1997; Bull & Scerif, 2001; Casey, Pezaris, & Nuttall, 1992; Gathercole & Pickering, 2000a; McLean & Hitch, 1999).”

“A similar link has been made by Bull and Johnston (1997), who suggested that the slowed speed of information processing of children with mathematical difficulties may be because they are at the low end of the mathematics continuum (again, with other abilities likely to be affected). It is important to remember that no…”

“Processing speed is an important measure, particularly for basic overlearned mathematical abilities, and has previously been found to predict mathematics performance in 7-year-old children (Bull & Johnston, 1997).”

“Several previous studies (Bull & Johnston, 1997; Dark & Benbow, 1991; Durand et al., 2005) showed that Visual-search speed for numbers is correlated with individual arithmetic abilities.”

“First, phonological processing abilities account for arithmetic attainment (Bull & Johnston, 1997; Geary, 1993; Hecht, Torgesen, Wagner, & Rashotte, 2001; Simmons et al., 2008).”

“To assess a potential general slowdown in DYS participants (Bull & Johnston, 1997), a spatial judgment task on numerically neutral trials, consisting in a block of 24 triplets composed by three identical numbers (e.g., 12__12__12 vs. 12_12___12), was also performed by all participants.”

“Children with Dyslexia tend to be characterized by deficits in the phonological loop and central executive, while those with Dyscalculia also show central executive difficulties, as well as poor visuospatial working memory (Bull and Johnston, 1997; McLean and Hitch, 1999, Passolunghi and Siegel, 2001, 2004; Swanson an…”

“Processing speed facilitates the fluency with which children compute solutions during simple arithmetic by minimizing decay in working memory and by creating stronger associations for these in long-term memory (Bull & Johnston, 1997; Cirino et al., 2015; Fuchs et al., 2006, 2008, 2010).”

“Impairments in the rapid automatized naming (RAN) of numbers (Bull and Johnston, 1997), a lack of the congruency effect in the number-size interference task (Rubinsten and Henik, 2005), and impairment in symbolic (with sparing of nonsymbolic) number comparisons (Rousselle and Noël, 2007) have been…”

“…were found in their auditory-verbal working memory (Chi-square = 5.7, p = 0.01), which we did not consider signi# cant, since research has shown that auditory-verbal working memory is weakly associated with mathematical development (Bull & Johnston, 1997) ! e participants comprised 51 boys (44”