The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties.

“, Chiappe, Hasher, & Siegel, 2000), as well as to speed of processing (Salthouse, 1996) and knowledge (see, e.”

“By kindergarten, WM capacity is predictive of Gf (Engel de Abreu et al., 2010), and individual differences in WM capacity predict children's verbal and mathematical aptitude (Cowan et al., 2005; Gathercole & Pickering, 2000; Swanson & Beebe-Frankenberger, 2004).”

“…IQb Readingb DS backward WRAT-3 Arithmetic Siegel and Ryan (1989) Child, ID IQb Readingb Listening span comp., Counting span WRAT Arithmetic Swanson and Beebe-Frankenberger (2004) Child, ID, and Predictor of word problem solving ability Nonverbal IQa,c Algorithm knowledgec Math…”

“Several other researchers have also found that problems with numerical digit span have been identified with MD (Geary & Brown, 1991; Siegel & Ryan, 1988; Swanson & Beebe-Frankenberger, 2004 ).”

“The independence of the working memory association with severity of learning diYculties from phonological awareness skills is also consistent with other Wndings from studies of children with learning diYculties (e.g., Swanson & Beebe-Frankenberger, 2004).”

“…Lee et al., 2010; Männamaa, Kikas, Peets, & Palu, 2012; Navarro et al., 2011; Simmons, Willis, & Adams, 2012; van der Sluis, de Jong, & van der Leij, 2007; St Clair-Thompson & Gathercole, 2006; Swanson & Beebe-Frankenberger, 2004; Swanson, 2004; Thorell, 2007; Zheng, Swanson, & Marcoulides, 2011).”

“…1994; Lee et al., 2004; Lemaire, Abdi, & Fayol, 1996; Logie, Gilhooly, & Wynn, 1994; Passolunghi & Siegel, 2004; Passolunghi et al., 2007; Rammelaere, Stuyven, & Vandierendonck, 2001; Swanson, 2006; Swanson & Beebe-Frankenberger, 2004; Thomas, Zoelch, Seitz-Stein, & Schumann-Hengsteler, 2006).”

“…Brown, & Pickering, 2003) and of substantial working memory problems for the majority of children identified on the basis of learning disabilities (e.g., Gathercole, Alloway et al., 2006; Swanson & Beebe-Frankenberger, 2004), including language impairments (Archibald & Gathercole, 2006b).”

“Moreover, weaknesses in working memory capacity are a characteristic of young children with math difficulties (Geary, Brown, & Samaranayake, 1991; Koontz & Berch, 1996; Wilson & Swanson, 2001; Swanson & Beebe-Frankenberger, 2004).”

“No clear patterns can be discerned from the results; some studies found a strong and statistically significant association between response inhibition and math (e.g., Espy et al., 2004), but others did not (Swanson & Beebe-Frankenberger, 2004).”

“…genetic, cognitive, and environmental links (Farrington-Flint, Vanuxem-Cotterill, & Stiller, 2009; Gathercole, Pickering, Knight, & Stegmann, 2004; Hart, Petrill, Thompson, & Plomin, 2009; Rohde & Thompson, 2007; Spinath, Spinath, Harlaar, & Plomin, 2006; Swanson & Beebe-Frankenberger, 2004).”

“Indeed, a relationship between math performance and math-related skills has been documented in the areas of reading (Mazzocco & Myers, 2003; Rasanen & Ahonen, 1995), visual‐spatial skills (Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999; Fias & Fischer, 2005), and working memory (Bull & Scerif, 2001; Epsy et al., 20…”

“ry performance (Andersson and Lyxell, 2007; Fuchs et al., 006; Swanson and Beebe-Frankenberger, 2004; Swanson nd Jerman, 2006).”

“Kover, 2007; Passolunghi & Pazzaglia, 2004, 2005; Swanson & Beebe-Frankenberger, 2004).”

“Although Swanson and Beebe-Frankenberger (2004) found that digit span forward and digit span backward loaded on a short-term memory factor rather than a working memory factor (that included a task that required subjects to remember numerical information embedded in sentences), there nevertheless…”

“…in listening comprehension has been demonstrated for whole-number word problems but not calculations (e.g., Fuchs et al., 2008; Fuchs, Geary, Compton, Fuchs, Hamlett, & Bryant, 2010; Fuchs, Geary, Compton, Fuchs, Hamlett, Seethaler, et al., 2010; H. L. Swanson & Beebe-Frankenberger, 2004).”

“Our findings are consistent with several previous studies which have implicated the central executive in mathematical problemsolving in 7-to 12-year-old children (Adams & Hitch, 1997; Geary et al., 2004; Swanson, 2006; Swanson & Beebe-Frankenberger, 2004; Swanson, Cooney & Brock, 1993).”

“This is understandable because correlations between computational and problem-solving skill, as demonstrated elsewhere (e.g., Fuchs et al., 2006; Swanson & Beebe-Frankenberger, 2004), were only moderate, ranging from .30 to .49.”

“This appears to require working memory (e.g., Kintsch & Greeno, 1985), which is supported by much of the relevant literature (e.g., L. S. Fuchs et al., 2005; Swanson & Beebe-Frankenberger, 2004; Swanson & Sachse-Lee, 2001), including present results.”

“Studies by Swanson and colleagues (Swanson, 2004; Swanson & Beebe-Frankenberger, 2004; Swanson & Sachse-Lee, 2001) have shown that children with mathematical problem solving difficulties across different age groups perform poorly relative to controls on measures of WM.”

“Children with low WM capacity have relatively poor verbal and mathematical abilities (Cowan et al., 2005; Gathercole & Pickering, 2000; Swanson & Beebe-Frankenberger, 2004) and have difficulty following directions (Engle, Carullo, & Collins, 1991; Gathercole, Durling, Evans, Jeffcock, & Stone,…”

“…disabled children (e.g., Bull, Johnston, & Roy, 1999; Geary, Hoard, & Hamson, 1999; McLean & Hitch, 1999; Passolunghi, Cornoldi, & De Liberto, 1999; Passolunghi & Siegel, 2004; Swanson & Beebe-Frankenberger, 2004; Swanson & Sachse-Lee, 2001; van der Sluis, de Jong, & van der Leij, 2004).”

“These include reading difficulties (e.g., Gathercole, Alloway, Willis, & Adams, 2006), mathematics difficulties (e.g., Geary, Hoard, ByrdCraven, Nugent, & Numtee, 2007), and a combination of reading and mathematics difficulties (e.g., Swanson & Beebe-Frankenberger, 2004).”

“…abilities in children involve multiple cognitive processes, most notably visuospatial processing and working memory (Adams and Hitch, 1998; Swanson and Beebe-Frankenberger, 2004), and the relative contribution of these processes changes with instruction and development (Meyer et al.,…”

“…composite and mathematical outcomes could reflect a relation between mathematical outcomes and phonological skills and/or domain-specific skills, consistent with previous research (e.g., Fuchs et al., 2005; Jordan & Levine, 2009; Locuniak & Jordan, 2008; Swanson & Beebe-Frankenberger, 2004).”

“For example, behavioral inhibition and sustained attention are at least theoretically related to variability in mathematical performance (see e.g., Passolunghi & Pazzagliab, 2004; Passolunghi & Siegel, 2000; Swanson and Beebe-Frankenberger, 2004; Zentall, 1993).”

“WMC is implicated in processes such as reasoning ability, mathematical problem solving, language, and reading comprehension, and many other aspects of learning [21,22].”

“Researchers have also determined that cognitive characteristics—such as those related to working memory (Swanson & Beebe-Frankenberger, 2004), processing speed (Cirino, Fuchs, Elias, Powell, & Schumacher, 2015), and phonological processing (Fuchs et al., 2006)—are distinctive for students with math…”

“…dealing with the limited capacity and management of information in immediate memory (i.e., working memory) during mathematics performance in general, and especially during completion of mathematics word problems (Fuchs et al., 2005; Passolunghi & Seigel, 2001; Swanson & Beebe-Frankenberger, 2004).”

“…with WP skill is language (e.g., Fuchs et al., 2005; Fuchs, Fuchs, Compton, et al., 2006; Fuchs, Fuchs, Stuebing, et al., 2008; Swanson, 2006; Swanson & Beebe-Frankenberger, 2004), and the language profiles of students with concurrent difficulty with mathematics and reading are lower than…”

“third graders, Swanson and Beebe-Frankenberger (2004) identified working memory as Intensive Intervention - 7”

“These include working memory (e.g., Barrouillet, Fayol, & Lathuliére, 1997; Engle, Tuholski, Laughlin, & Conway, 1999; Geary et al., 2007; Swanson & Beebe-Frankenberger, 2004), processing speed (e.g., Bull & Johnston, l997; Fuchs et al., 2005; Hecht, Torgesen, Wagner, & Rashotte, 2001), and…”

“Much of the literature, including the present results, provides support for this theoretical framework (e.g., Fuchs et al., 2005; Swanson & Beebe-Frankenberger, 2004; Swanson & Sachse-Lee, 2001), although findings Child Dev.”

“…in the face of distraction (e.g., Blair, 2002; Gathercole et al., 2008) and are taxed by some academic tasks, particularly math, which involve holding information in working memory, shifting attention, and inhibiting prepotent responses (Blair & Razza, 2007; Swanson & Beebe-Frankenberger, 2004).”

“This raises the possibility that the high scores of the low working memory children simply reflect the well-documented findings that these individuals typically make poor academic progress (e.g. Gathercole et al., 2004; Swanson & Beebe-Frankenberger, 2004).”

“In children with and without significant mathematics difficulties, Swanson and Beebe-Frankenberger(2004) found that working memory predicted solution accuracy on word problems independent of several academic and cognitive variables, such as fluid reasoning, reading skills, and phonological…”

“More recently, Swanson and Beebe-Frankenberger (2004) and Simmons, Singleton and Horne (2008) reported similar results.”

“…2012). at value (p) is for Total Effect. bBootstrapped 95% confidence interval (CI) is for indirect effects. differences in WM account for variance in WPs, when controlling for other cognitive resources (Fuchs, Geary, Compton, Fuchs, Hamlett, & Bryant, 2010; Swanson & Beebe-Frankenberger, 2004).”

“…in groups of children with learning disabilities (for a review, see Alloway & Archibald, 2008), attention deficits (Alloway, Rajendran, & Archibald, 2009), reading disabilities (e.g., Kibby, Marks, Morgan, & Long, 2009; Swanson & Beebe-Frankenberger, 2004), and LI (Ellis Weismer et al., 2000).”

“…MD should demonstrate comprehensive executive function deficits, while older children and adults with MD may show selective executive function deficits depending on types of MD (L. S. Fuchs et al., 2005; L. S. Fuchs et al., 2006; Passolunghi & Siegel, 2001; Swanson & Beebe-Frankenberger, 2004).”

“…addition, because using text to construct a word-problem model involves language (e.g., Fuchs et al., 2005; Fuchs et al., 2006; Fuchs, Fuchs, Stuebing et al., 2008; Swanson & Beebe-Frankenberger, 2004; Swanson, 2006) and because the language of students with MDRD is depressed Learn Individ Differ.”

“…& Catherine DeSoto, 2004; Holmes & Adams, 2006; Imbo & Vandierendonck, 2007; Meyer, Salimpoor, Wu, Geary, & Menon, 2010; Raghubar et al., 2010; Swanson & Beebe-Frankenberger, 2004; Swanson, 2006; Toll, Van der Ven, Kroesbergen, & Van Luit, 2011; Van der Ven, Van der Maas, Straatemeier, &…”

“In typically developing children, scores on working memory tasks predict reading achievement independently of measures of phonological skills (Swanson & Beebe-Frankenberger, 2004).”

“Number estimation has been found to be impaired in children with number difficulties (Geary et al., 2008).”

“…system is thus responsible for processing information during the performance of cognitive tasks and consequently plays an important role in learning new knowledge and developing new skills such as mathematics (Bull & Scerif, 2001; Lehto, 1995; Swanson, 1999; Swanson & Beebe-Frankenberger, 2004).”

“Naturally, there can be other variables such as visuospatial working memory and inhibition that have an effect on the relationships between predictors and outcome variables (see, e.g., LeFevre et al., 2010; Swanson & Beebe-Frankenberger, 2004; Zhang et al., 2014).”

“…there are some indications that children with MLD have problems with controlled retrieval of semantic information from long-term memory and are slower with respect to general processing speed (Andersson, 2008; Andersson & Lyxell, 2007; Bull & Johnston, 1997; Swanson & Beebe-Frankenberger, 2004).”

“…across TC and WP solving (L. S. Fuchs et al., 2015), and (c) shared but some distinctive predictive patterns for WP solving versus calculations (L. S. Fuchs et al., 2008; Swanson & Beebe-Frankenberger, 2004), we hypothesized that TC’s effects are stronger on WP solving than on pure calculations.”

“…Mazzocco & Myers, 2003; Murphy, Mazzocco, Hanich, & Early, 2007), whether there are core deficits involved in MD (e.g., Fuchs et al., 2005, 2006; Swanson & Beebe-Frankenberger, 2004), and whether the mathematics skills in children with MD can Requests for reprints should be sent to Rose K.…”

“Numerous other studies have supported that WMC is related to word problem solving (Passolunghi & Siegel, 2004; Swanson, 2006; Swanson & Beebe-Frankenberger, 2004).”

“…(Duranovic et al., 2014; Gathercole, Woolgar, Keivit, Astle, Manly, the CALM Team & Holmes, 2016; Pointus, 1981; Winner et al., 2001) and maths problems (Gathercole, et al., 2016; Swanson & Beebe-Frankenberger, 2004; Fuchs et al., 2005, 2006, 2015), as well as those with ADHD (Holmes et al., 2013).”

“…WM is considered an active system that involves both storage and processing of information, while STM typically involves situations in which the individual passively holds small amounts of information, as required in span forward tasks (Cornoldi & Vecchi, 2003; Swanson & Beebe-Frankenberger, 2004).”

“The dyscalculia research that utilizes neuroimaging is not as extensive as the dyslexia research, but studies of neurocognitive processes clearly have documented specific types of brain dysfunction (Swanson & Beebe-Frankenberger, 2004; Wilson & Swanson, 2001).”

“This is problematic because research indicates that many students with MD have limitations in working memory (Passolunghi & Cornoldi, 2008; Swanson & Beebe-Frankenberger, 2004).”

“Comparable results were obtained by Swanson (2004; Swanson & Beebe-Frankenberger, 2004), who showed that working memory predicted solution accuracy of arithmetic word problems independent of other skill measures such as fluid intelligence, reading skill, math skill, and short-term memory.”

“…on the child’s level of fluid intelligence, reading and arithmetic achievement, phonological processing, shortterm memory, and inhibition (Swanson & Beebe-Frankenberger, 2004); reading, IQ, perseveration, and inhibition efficiency (Bull & Scerif, 2001); maternal education and child…”

“Previous studies have demonstrated that specific activities of the central executive related to suppression of irrelevant information are deficient in children with poor problem-solving abilities (Passolunghi, Cornoldi, & de Liberto, 2001; Passolunghi & Siegel, 2001 ), and that central executive measures contributed u…”