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The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties.
Abstract
This study identified cognitive processes that underlie individual differences in working memory (WM) and mathematical problem-solution accuracy in elementary school children at risk and not at risk for serious math difficulties (SMD). A battery of tests was administered that assessed problem solving, achievement, and cognitive processing in children in first (N = 130), second (N = 92) and third grades (N = 131). The results were that (a) younger children and children at risk for SMD performed poorer on WM and problem-solving tasks, as well as measures of math calculation, reading, semantic processing, phonological processing, and inhibition, than older children and children not at risk for SMD and (b) WM predicted solution accuracy of word problems independent of measures of fluid intelligence, reading skill, math skill, knowledge of algorithms, phonological processing, semantic processing, speed, short-term memory, and inhibition. The results support the notion that the executive system is an important predictor of children's problem solving.
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“The independence of the working memory association with severity of learning difficulties from phonological processing skills is also consistent with other findings from studies of children with learning difficulties (e.g., Swanson & Beebe-Frankenberger, 2004).”
From Working memory in children with reading disabilities (2006) · cites this paper as Swanson & Beebe-Frankenberger, 2004
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“In many studies composite scores consisting of two or more of these measures are used to examine the relationship between mathematics and reading (for example Dirks et al., 2008; Swanson & Beebe-Frankenberger, 2004; Wise et al., 2008).”
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“Several studies have assumed that selective attention can be observed in this mathematical domain (McLean and Hitch 1999; Passolunghi and Siegel 2001; Swanson and Beebe-Frankenberger 2004).”
BackgroundPrediction and Stability of Mathematics Skill and Difficulty
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“…(measures of word problem solving components, estimation) as well as measures of executive processing (e.g., inhibition), have been implicated along with WM as predictors math performance (e.g., Cowan & Powell, 2014; Fuchs et al., 2006; 2012; Lee et al., 2004; Swanson & Beebe-Frankenberger, 2004).”
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Swanson, H. L., Arizmendi, G. D., & Li, J. (2020) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2020.104988 · Cited by 46
Self-citationEndophenotypes for intelligence in children and adolescents
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BackgroundInfluentialCognition and literacy in English language learners at risk for reading disabilities.
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“…solving (Fuchs et al., 2015), and (c) shared but some distinctive predictive patterns for word-problem solving versus calculations (Fuchs et al., 2008; Swanson & Beebe-Frankenberger, 2004), we hypothesized that the effects of Gates are stronger on word-problem solving than on pure calculations.”
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“Poor WM can lead to counting errors (Swanson & Beebe-Frankenberger, 2004), procedural errors due to problems with monitoring and updating information (e.g., adding instead of subtracting, not borrowing or carrying correctly), and difficulties with multistep problems (Geary, 2004).”
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“Working memory deficits are commonly found in students with MD (Swanson & Beebe-Frankenberger, 2004).”
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“WPS difficulty, in the face of intact computation skill, may reflect the fact that WPS, with its combined focus on text, mathematical ideas, and computational skill, engages more cognitive resources than computational skill does (Daroczy et al., 2015; Swanson & Beebe-Frankenberger, 2004).”
BackgroundThe Critical Role of Word Reading as a Predictor of Response to Intervention
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“Thus, performance on tasks that demand working memory such as math calculations may well predict other working memory-demanding tasks such as word reading (Geary et al., 2007; H. L. Swanson & Beebe-Frankenberger, 2004).”
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“Perhaps there are elements to solving algebraic problems, like visual and spatial reasoning, that contribute to difficulty with conceptualizing and understanding algebraic problems in the form of equations or functions (Fuchs et al., 2012; Swanson & Jerman, 2006).”
BackgroundEffect of fine motor skills training on arithmetical ability in children
Asakawa, A., Murakami, T., & Sugimura, S. (2017) · European Journal of Developmental Psychology · doi:10.1080/17405629.2017.1385454 · Cited by 35
“This task was standardized in Japan and has also been used in a previous study as part of a test battery measuring arithmetical abilities (Barnea-Goraly, Eliez, Menon, Bammer, & Reiss, 2005; Li, Hu, Wang, Weng, & Chen, 2013; Swanson & Beebe-Frankenberger, 2004).”
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“…the question, (b) identify important numbers, (c) explain what the question is trying to answer, (d) select the operation needed to solve, (e) create the picture or computational strategy used to solve, and (f) discern distractible or unimportant information (Swanson & Beebe-Frankenberger, 2004).”
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“…Geary, Fuchs, Compton, & Hamlett, 2014; Fuchs, Gilbert, Powell, Cirino, Fuchs, Hamlett, Seethaler, & Tolar; 2016; Geary, Bailey, & Hoard, 2009; Swanson & Beebe-Frankenberger, 2004), factors for which increases in arithmetic fluency could plausibly compensate in children’s subsequent…”
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Self-citationAlgebra and problem‐solving in Down syndrome: a study with 15 teenagers
Martinez, E. M., & Pellegrini, K. (2010) · European Journal of Special Needs Education · doi:10.1080/08856250903450814 · Cited by 31
“In fact, the students’ performances might be related not only to an impairment of working memory (Swanson 2006 ; Swanson and Beebe‐Frankenberger 2004 ; Swanson, Cooney, and Brock 1993 ), but also to difficulties in the classification of problems, ie, to find the similarity between a particular problem with others that…”
BackgroundA review of mathematical learning disabilities in children with fragile X syndrome
Murphy, M. M. (2009) · Developmental Disabilities Research Reviews · doi:10.1002/ddrr.49 · Cited by 31
A naturalistic study of executive function and mathematical problem-solving
Kotsopoulos, D., & Lee, J. (2012) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2011.12.005 · Cited by 31
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“…capacity of the different components of working memory (e.g., Adams & Hitch, 1997; Geary, Brown, & Samaranayake, 1991; Passolunghi & Siegel, 2004; Swanson & Beebe-Frankenberger, 2004), although in recent years diverse investigations have appeared (e.g., Fuchs et al., 2006; Krajewski & Schneider,…”
BackgroundIrrelevant information in math problems need not be inhibited: Students might just need to spot them
Ng, J. J. H., Lee, K. L., & Khng, K. H. (2017) · Learning and Individual Differences · doi:10.1016/j.lindif.2017.09.008 · Cited by 29
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“…central executive plays a more general role in early learning as it supports the development of skills involved in reading (Gathercole et al. 2006; Swanson and Beebe-Frankenberger 2004), numeracy and mathematics (Geary et al. 2004; Swanson and Sachse-Lee 2001) and language comprehension (Cain,…”
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“WM performance accurately predicts other functions such as math skills, semantic processing, and inhibition (Swanson & Beebe-Frankenberger, 2004), and may be a better predictor of academic success than intelligence quotient (Alloway & Alloway, 2010).”
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“Several studies have shown that both domain-general factors, such as working memory (Adams and Hitch 1997; Passolunghi and Siegel 2001; Swanson 2004), reading comprehension (Swanson and Beebe-Frankenberger 2004), and processing speed (Kail and Hall 1994) as well as domainspecific factors, such as arithmetic computing…”
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Passolunghi, M., & Costa, H. M. (2019) · International Handbook of Mathematical Learning Difficulties · doi:10.1007/978-3-319-97148-3_25 · Cited by 22
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“…between mathematical ability and SIP have been undertaken mostly on children in elementary school (e.g. Berg, 2008; Geary & Brown, 1991; Swanson & Beebe-Frankenberger, 2004) or junior high school (e.g. Taub, Floyd, Keith, & Mcgrew, 2008), while very few studies have examined senior…”
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“This experimental test assesses the participant’s ability to identify (retrieve) propositional information within word problems (Swanson & Beebe-Frankenberger, 2004).”
BackgroundSelf-citationPeng, J., Mo, L., Huang, P., & Zhou, Y. (2017) · Cognitive Development · doi:10.1016/j.cogdev.2017.05.006 · Cited by 29
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“…Metcalfe, Swigart, & Menon, 2013; Caviola, Mammarella, Cornoldi & Lucangeli, 2012; Passolunghi & Cornoldi, 2008), word problem solving (Swanson & Beebe-Frankenberger, 2004; Swanson & Sachse-Lee, 2001; Zheng, Swanson, & Marcoulides, 2011) and geometry (Giofrè, Mammarella, & Cornoldi,…”
Are there advantages for additive bilinguals in working memory tasks?
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“More than this, Swanson and Beebe-Frankenberger (2004) argued that WM is a resource that enables the learner to integrate information retrieved from long-term memory with current inputs.”
BackgroundRest breaks aid directed attention and learning
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“…& Wynn, 1994; Alamolhodaei, 2009), mathematics problem solving (Cary & Carlson, 2001; DeStefano & LeFevre, 2004; Klein & Bisanz, 2000; Seitz & Schumann-Hengsteler, 2000; Swanson, 2004; Swanson & Beebe-Frankenberger, 2004; Alamolhodaei, 2009), and even mathematics anxiety (Ashcraft & Kirk, 2001).”
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“This finding is consistent with earlier research indicating that students with mathematics difficulties make more mistakes when executing direct retrieval strategies or algorithm strategies because of cognitive deficits in long term memory and working memory (Swanson and Beebe-Frankenberger 2004; Geary and Hoard 2005).”
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Self-citationWorking memory updating as a predictor of academic attainment
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“It has been shown that children with low mathematical skills perform worse in WMU tasks (e.g. Passolunghi & Pazzaglia, 2004, 2005; Swanson & Beebe-Frankenberger, 2004).”
BackgroundAllen, K., & Giofrè, D. (2021) · Educational Psychology · doi:10.1080/01443410.2020.1857702 · Cited by 24
“…components and working memory (e.g. arithmetic: Ashkenazi et al., 2013; Caviola et al., 2012; Passolunghi & Cornoldi, 2008, word problem solving: Swanson & Beebe-Frankenberger, 2004; Swanson & Sachse-Lee, 2001; Zheng et al., 2011, mathematical difficulties: Andersson & Lyxell, 2007; D’Amico &…”
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“Cognitively, working memory is important for mathematics given the need to keep in mind the components and order of multistep computational problems (Geary et al., 2015; Swanson & Beebe-Frankenberger, 2004).”
BackgroundFronto‐insular‐parietal network engagement underlying arithmetic word problem solving
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“Behavioral studies have suggested that cognitive control plays a crucial role in arithmetic word problem solutions (Passolunghi & Siegel, 2001; Swanson, 1993; Swanson & Beebe-Frankenberger, 2004; Swanson et al., 1993).”
BackgroundInfluentialThe relation between academic abilities and performance in realistic word problems
Fitzpatrick, C. L., Hallett, D., Morrissey, K., Yıldız, N. R., Wynes, R., & Ayesu, F. (2020) · Learning and Individual Differences · doi:10.1016/j.lindif.2020.101942 · Cited by 19
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“WM is considered an active system, involving both storage and processing, whereas STM involves only storage and no processing, as required in forward span tasks (Cornoldi and Vecchi, 2003; Swanson and Beebe-Frankenberger, 2004).”
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Hord, C., Tzur, R., Xin, Y. P., Si, L., Kenney, R. H., & Woodward, J. (2016) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2016.09.002 · Cited by 21
Mathematics, anxiety, and the brain
Moustafa, A. A., Tindle, R., Ansari, Z., Doyle, M. J., Hewedi, D. H., & Eissa, A. M. (2017) · Reviews in the Neurosciences · doi:10.1515/revneuro-2016-0065 · Cited by 19
Variability in the Precision of Children’s Spatial Working Memory
Weber, E. M. G., Dirk, J., & Schmiedek, F. (2018) · Journal of Intelligence · doi:10.3390/jintelligence6010008 · Cited by 24
Gordon, R., Smith-Spark, J. H., Newton, E. J., & Henry, L. A. (2019) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2019.104736 · Cited by 19
Kroesbergen, E. H., Noordende, J. E. V. '., & Kolkman, M. E. (2012) · Springer eBooks · doi:10.1007/978-94-007-4086-0_16 · Cited by 19
Proctor, B. E. (2012) · Journal of Learning Disabilities · doi:10.1177/0022219410392049 · Cited by 19
“…al., 2008; McGrew & Wendling, in press; Osmon, Smerz, Braun, & Plambeck, 2006; Passolunghi & Siegel, 2001; Rasmussen & Bisanz, 2005; Swanson, 1994; Swanson & Beebe-Frankenberger, 2004; Swanson & Jerman, 2006), the score for the clinical cluster of WM was also included to represent the CHC narrow…”
BackgroundVisual Processing in Generally Gifted and Mathematically Excelling Adolescents
Paz-Baruch, N., Лейкин, Р., & Leikin, M. (2016) · journal for the education of the gifted · doi:10.1177/0162353216657184 · Cited by 19
“…by the previous studies, which reported that processing speed is related both to quantitative knowledge (Berg, 2008; J. Johnson et al., 2003; Swanson & Beebe-Frankenberger, 2004) and G (Dark & Benbow, 1991; J. Johnson et al., 2003; Kranzler et al., 1994), and are also partly reported in our…”
BackgroundZhu, X., Tang, Y., Lu, J., Song, M., Yang, C., & Zhao, X. (2024) · Educational Psychology Review · doi:10.1007/s10648-024-09976-w · Cited by 24
“…featuring both typically developed children and children with developmental disability, but presented the results separately for each group (e.g., Swanson & Beebe-Frankenberger, 2004); (5) they included data from participants who did not receive any interventions (i.e., only baseline and control…”
Ramos-Galarza, C., Jadán-Guerrero, J. L., & Gómez-García, A. R. (2018) · Avances en Psicología Latinoamericana · doi:10.12804/revistas.urosario.edu.co/apl/a.5481 · Cited by 26
Xu, Z., Wang, L., Liu, D., Chen, Y., & Tao, L. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.01899 · Cited by 19
“, maintaining recently retrieved knowledge and integrating it with the present inputs (Swanson and Beebe-Frankenberger, 2004).”
BackgroundLendínez, C., Pelegrina, S., & Lechuga, M. T. (2015) · Acta Psychologica · doi:10.1016/j.actpsy.2015.02.015 · Cited by 18
Swanson, H. L., Orosco, M. J., & Kudo, M. F. (2015) · Journal of Learning Disabilities · doi:10.1177/0022219415618499 · Cited by 19
“…Gerber, 2006), the STM (phonological loop) component of WM (Forward Digit Span, Backward Digit Span, Word Span, and Pseudoword Span; Swanson, 2014, Swanson & Beebe-Frankenberger, 2004); phonological processing (Segmentation and Blending [Leafstedt & Gerber, 2005; Swanson, Rosston, Gerber, &…”
BackgroundSelf-citationThe Relation Between Inattentive and Hyperactive/Impulsive Behaviors and Early Mathematics Skills
Sims, D. M., Purpura, D. J., & Lonigan, C. J. (2012) · Journal of Attention Disorders · doi:10.1177/1087054712464390 · Cited by 18
“Past research has indicated that mathematics performance can be adversely impacted by a range of factors from both cognitive (Fuchs et al., 2005; Swanson & Beebe-Frankenberger, 2004; Swanson & Kim, 2007) and behavioral domains (Johnson, McGue, & Iacono, 2005; Willcutt & Pennington 2000).”
BackgroundLiang, Z., Dong, P., Zhou, Y., Feng, S., & Zhang, Q. (2021) · British Journal of Educational Psychology · doi:10.1111/bjep.12454 · Cited by 26
Self-efficacy and short-term memory capacity as predictors of proportional reasoning
Kingston, J. A., & Lyddy, F. (2013) · Learning and Individual Differences · doi:10.1016/j.lindif.2013.01.017 · Cited by 20
“…Brown, & Gore, 1997; Pajares & Kranzler, 1995; Pajares & Miller, 1994; Williams & Williams, 2010) and working memory capacity (DeStefano & LeFevre, 2004; Jackson & Warrington, 1986; Klein & Bisanz, 2000; Seitz & Schumann-Hengsteler, 2000, 2002; Swanson, 2004; Swanson & Beebe-Frankenberger, 2004).”
BackgroundWorking memory and learning disabilities
Malekpour, M., Aghababaei, S., & Abedi, A. (2013) · International Journal of Developmental Disabilities · doi:10.1179/2047387711y.0000000011 · Cited by 19
“Swanson and Beebe-Frankenberger (2004) reported a correlation of 0.54 between working memory and mathematics problem solving.”
BackgroundInfluentialSiffredi, V., Barrouillet, P., Spencer‐Smith, M. M., Vaessen, M. J., Anderson, V. A., & Vuilleumier, P. O. (2017) · PLoS ONE · doi:10.1371/journal.pone.0179959 · Cited by 18
Predicting Visuospatial and Verbal Working Memory by Individual Differences in E-Learning Activities
Fellman, D., Lincke, A., Berge, E., & Jonsson, B. (2020) · Frontiers in Education · doi:10.3389/feduc.2020.00022 · Cited by 19
The Roles of Arithmetic Fluency and Executive Functioning in Mathematical Problem-Solving
Kaskens, J., Goei, S. L., Luit, J. V. V., Verhoeven, L., & Segers, E. (2022) · The Elementary school journal · doi:10.1086/721771 · Cited by 15
“…and accurate retrieval of arithmetic facts from long-term memory but also the efficient updating of information, the suppression of incorrect responding (inhibition), and accurate shifts between operations (1, –, #, ÷; Bull & Scerif, 2001; Bull et al., 1999; Swanson & Beebe-Frankenberger, 2004).”
BackgroundInfluentialComprensión lectora, memoria de trabajo, fluidez y vocabulario en escolares cubanos
Hernández, K. G., Paz, L. O., & Laguardia, A. M. C. (2015) · Actualidades Investigativas en Educación · doi:10.15517/aie.v16i1.21715 · Cited by 17
Improving short-term and working memory: Methods of memory training
Clair‐Thompson, H. S. (2008) · Northumbria Research Link (Northumbria University) · doi:10.25405/ncl.34210533 · Cited by 17
Jang, S., & Cho, S. (2018) · Learning and Individual Differences · doi:10.1016/j.lindif.2018.05.005 · Cited by 17
The role of inhibitory functioning in children’s reading skills
Booth, J. N., & Boyle, J. M. E. (2009) · Educational Psychology in Practice · doi:10.1080/02667360903315164 · Cited by 17
Working Memory in ADHD: A Comparison of British and South African Children
Alloway, T. P., & Cockcroft, K. (2014) · Journal of Attention Disorders · doi:10.1177/1087054711417397 · Cited by 16
Harrison, A. G., Beal, A., & Armstrong, I. (2020) · Clinical Neuropsychologist · doi:10.1080/13854046.2020.1842501 · Cited by 13
“Executive functions such as working memory have been shown to relate to reading comprehension (Daneman & Merikle, 1996) and math word problem solving performance (Swanson & Beebe-Frankenberger, 2004).”
Metadata
- Authors
- Swanson, H. L., & Beebe-Frankenberger, M.
- Affiliations
- University of California, Riverside (US)
- University of Montana (US)
- ORCID
- Swanson, H. Lee
- Venue
- Journal of Educational Psychology
- Published
- 2004-09
- Volume
- 96
- Issue
- 3
- Pages
- 471-491
- ISSN
- 0022-0663 (ISSN-L)
- 1939-2176
- OpenAlex
- W1965873661
- Cited by
- 638
- References
- 91
- Citations by year
- 2026: 18 · 2025: 17 · 2024: 18 · 2023: 25 · 2022: 25 · 2021: 26 · 2020: 64 · 2019: 39 · 2018: 27 · 2017: 38 · 2016: 36 · 2015: 41 · 2014: 51 · 2013: 39 · 2012: 36
- FWCI
- 11.50
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Educational Psychology (publishedVersion)
- Topics
- Social Sciences › Psychology › Developmental and Educational Psychology › Cognitive and developmental aspects of mathematical skills
- Social Sciences › Psychology › Neuropsychology and Physiological Psychology › Developmental and Educational Neuropsychology
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Abilities and Testing
- Keywords
- working memory, mathematical problem solving, vulnerable children, elementary school students, executive function, inhibition, phonological processing, semantic processing, age differences, individual differences
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