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

Swanson, H. Lee; Beebe-Frankenberger, Margaret

doi:10.1037/0022-0663.96.3.471

Cited by 639Cognitive and developmental aspects of mathematical skillsDevelopmental and Educational NeuropsychologyCognitive Abilities and Testing

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

Swanson, H. Lee, Beebe-Frankenberger, Margaret·2004·Journal of Educational Psychology

DOI 10.1037/0022-0663.96.3.471

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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 consistent with other findings from studies of children with learning difficulties.
“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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Working memory, short-term memory, speech rate, word recognition and reading comprehension in learning disabled readers: does the executive system have a role?11The research was supported by Peloy Endowment Funds awarded by the first author. This work is truly a collaborative endeavor. First authorship primarily reflects responsibility for write-up and data analysis and second authorship reflects data collection. Data was collected by the second author in the Redlands Unified School District. The authors are thankful to staff at the Redlands School District and for the comments of Jerry Carlson, Richard Eyman, Kathy Wilson, Carole Lee, Randy Engle, and the two reviewers of this journal on an earlier draft. Inquiries and requests should be directed to H. Lee Swanson, Educational Psychology, School of Education, University of California, Riverside, CA., 92521-0128.
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Skills underlying mathematics: The role of executive function in the development of mathematics proficiency
Cragg, L., & Gilmore, C. K. (2014) · Trends in Neuroscience and Education · doi:10.1016/j.tine.2013.12.001 · Cited by 597 · see citing works
“…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).”
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
Krajewski, K., & Schneider, W. (2009) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2009.03.009 · Cited by 493 · see citing works
“…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).”
The Cognitive and Behavioral Characteristics of Children With Low Working Memory
Alloway, T. P., Gathercole, S. E., Kirkwood, H., & Elliott, J. (2009) · Child Development · doi:10.1111/j.1467-8624.2009.01282.x · Cited by 492 · see citing works
“…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).”
Background
A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics
Peng, P., Namkung, J., Barnes, M., & Sun, C. (2016) · Journal of Educational Psychology · doi:10.1037/edu0000079 · Cited by 557 · see citing works
The importance of number sense to mathematics achievement in first and third grades
Jordan, N. C., Glutting, J., & Ramineni, C. (2010) · Learning and Individual Differences · doi:10.1016/j.lindif.2009.07.004 · Cited by 471 · see citing works
“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).”
Background
Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade
Smedt, B. D., Janssen, R., Bouwens, K., Verschaffel, L., Boets, B., & Ghesquière, P. (2009) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2009.01.004 · Cited by 418 · see citing works
The Potential for School-Based Interventions That Target Executive Function to Improve Academic Achievement: A Review
Jacob, R., & Parkinson, J. (2015) · Review of Educational Research · doi:10.3102/0034654314561338 · Cited by 538 · see citing works
“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).”
Background
Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study
Krajewski, K., & Schneider, W. (2008) · Learning and Instruction · doi:10.1016/j.learninstruc.2008.10.002 · Cited by 405 · see citing works
Early literacy and early numeracy: The value of including early literacy skills in the prediction of numeracy development
Purpura, D. J., Hume, L. E., Sims, D. M., & Lonigan, C. J. (2011) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2011.07.004 · Cited by 404 · see citing works
“…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).”
Cognitive Characteristics of Children With Mathematics Learning Disability (MLD) Vary as a Function of the Cutoff Criterion Used to Define MLD
Murphy, M. M., Mazzocco, M. M. M., Hanich, L. B., & Early, M. C. (2007) · Journal of Learning Disabilities · doi:10.1177/00222194070400050901 · Cited by 366 · see citing works
“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…”
Background
Working memory and specific language impairment: an update on the relation and perspectives on assessment and treatment.
Montgomery, J., Magimairaj, B. M., & Finney, M. C. (2010) · American Journal of Speech-Language Pathology · doi:10.1044/1058-0360(2009/09-0028 · Cited by 358 · see citing works
The precursors of mathematics learning: Working memory, phonological ability and numerical competence
Passolunghi, M. C., Vercelloni, B., & Schadee, H. M. A. (2006) · Cognitive Development · doi:10.1016/j.cogdev.2006.09.001 · Cited by 326 · see citing works
Working Memory and Academic Learning: Assessment and Intervention
Dehn, M. J. (2008) · Cited by 323 · see citing works
The role of selective attention on academic foundations: A cognitive neuroscience perspective
Stevens, C., & Bavelier, D. (2011) · Developmental Cognitive Neuroscience · doi:10.1016/j.dcn.2011.11.001 · Cited by 330 · see citing works
“ry performance (Andersson and Lyxell, 2007; Fuchs et al., 006; Swanson and Beebe-Frankenberger, 2004; Swanson nd Jerman, 2006).”
Examining the mutual relations between language and mathematics: A meta-analysis.
Peng, P., Lin, X., Ünal, Z. E., Lee, K., Namkung, J. M., Chow, J. C., & Sales, A. (2020) · Psychological Bulletin · doi:10.1037/bul0000231 · Cited by 331 · see citing works
Developmental and Individual Differences in Understanding of Fractions
Siegler, R., & Pyke, A. A. (2012) · Developmental Psychology · doi:10.1037/a0031200 · Cited by 111 · see citing works
“Kover, 2007; Passolunghi & Pazzaglia, 2004, 2005; Swanson & Beebe-Frankenberger, 2004).”
Using Kindergarten Number Sense to Predict Calculation Fluency in Second Grade
Locuniak, M. N., & Jordan, N. C. (2008) · Journal of Learning Disabilities · doi:10.1177/0022219408321126 · Cited by 300 · see citing works
“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…”
Background
Improving at-risk learners’ understanding of fractions.
Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J. M., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R. S., Gersten, R. M., & Changas, P. C. (2013) · Journal of Educational Psychology · doi:10.1037/a0032446 · Cited by 279 · see citing works
“…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).”
Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders
Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., & Menon, V. (2010) · Learning and Individual Differences · doi:10.1016/j.lindif.2009.08.004 · Cited by 273 · see citing works
“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).”
BackgroundResult
Working memory deficit in children with mathematical difficulties: A general or specific deficit?
Andersson, U., & Lyxell, B. (2007) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2006.10.001 · Cited by 274 · see citing works
Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?
Fuchs, L. S., Fuchs, D., Stuebing, K. K., Fletcher, J. M., Hamlett, C. L., & Lambert, W. E. (2008) · Journal of Educational Psychology · doi:10.1037/0022-0663.100.1.30 · Cited by 273 · see citing works
“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.”
Background
Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?
Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., Bryant, J. D., & Schatschneider, C. (2010) · Developmental Psychology · doi:10.1037/a0020662 · Cited by 263 · see citing works
“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.”
Growth in working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties.
Swanson, H. L., Jerman, O., & Zheng, X. (2008) · Journal of Educational Psychology · doi:10.1037/0022-0663.100.2.343 · Cited by 258 · see citing works
“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.”
BackgroundMethodSelf-citation
Cogmed working memory training: Does the evidence support the claims?
Shipstead, Z., Hicks, K. L., & Engle, R. W. (2012) · Journal of Applied Research in Memory and Cognition · doi:10.1016/j.jarmac.2012.06.003 · Cited by 249 · see citing works
“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,…”
Background
The development of strategy use in elementary school children: Working memory and individual differences
Imbo, I., & Vandierendonck, A. (2007) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2006.09.001 · Cited by 244 · see citing works
“…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).”
A Meta-Analysis of Working Memory Deficits in Children With Learning Difficulties
Peng, P., & Fuchs, D. (2014) · Journal of Learning Disabilities · doi:10.1177/0022219414521667 · Cited by 244 · see citing works
“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).”
BackgroundMethod
Neuroanatomical correlates of developmental dyscalculia: combined evidence from morphometry and tractography
Rykhlevskaia, E. I. (2009) · Frontiers in Human Neuroscience · doi:10.3389/neuro.09.051.2009 · Cited by 239 · see citing works
“…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.,…”
Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory, and reading
Berg, D. H. (2008) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2007.12.002 · Cited by 238 · see citing works
Working memory training involves learning new skills
Gathercole, S. E., Dunning, D. L., Holmes, J., & Norris, D. (2019) · Journal of Memory and Language · doi:10.1016/j.jml.2018.10.003 · Cited by 225 · see citing works
The language of mathematics: Investigating the ways language counts for children’s mathematical development
Vukovic, R. K., & Lesaux, N. K. (2013) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2013.02.002 · Cited by 224 · see citing works
“…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).”
Result
Sources of group and individual differences in emerging fraction skills.
Hecht, S. A., & Vagi, K. J. (2010) · Journal of Educational Psychology · doi:10.1037/a0019824 · Cited by 220 · see citing works
“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).”
Background
“I think I can, but I'm afraid to try”: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency
Hoffman, B. H. (2010) · Learning and Individual Differences · doi:10.1016/j.lindif.2010.02.001 · Cited by 228 · see citing works
A Randomized Controlled Trial Examining the Effect of Mindfulness Meditation on Working Memory Capacity in Adolescents
Quach, D., Jastrowski Mano, K. E., & Alexander, K. (2016) · Journal of Adolescent Health · doi:10.1016/j.jadohealth.2015.09.024 · Cited by 213 · see citing works
“WMC is implicated in processes such as reasoning ability, mathematical problem solving, language, and reading comprehension, and many other aspects of learning [21,22].”
Background
Working Memory in Children With Developmental Disorders
Alloway, T. P., Rajendran, G., & Archibald, L. M. D. (2009) · Journal of Learning Disabilities · doi:10.1177/0022219409335214 · Cited by 203 · see citing works
A Systematic Review of Longitudinal Studies of Mathematics Difficulty
Nelson, G., & Powell, S. R. (2017) · Journal of Learning Disabilities · doi:10.1177/0022219417714773 · Cited by 205 · see citing works
“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…”
Background
Effects of general and broad cognitive abilities on mathematics achievement.
Taub, G. E., Keith, T. Z., Floyd, R. G., & McGrew, K. S. (2008) · School Psychology Quarterly · doi:10.1037/1045-3830.23.2.187 · Cited by 211 · see citing works
“…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).”
BackgroundInfluential
The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge.
Purpura, D. J., Baroody, A. J., & Lonigan, C. J. (2013) · Journal of Educational Psychology · doi:10.1037/a0031753 · Cited by 204 · see citing works
Working memory and language: Skill-specific or domain-general relations to mathematics?
Purpura, D. J., & Ganley, C. M. (2014) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2013.12.009 · Cited by 199 · see citing works
Remediating Number Combination and Word Problem Deficits Among Students With Mathematics Difficulties: A Randomized Control Trial
Fuchs, L., Powell, S. R., Seethaler, P. M., Cirino, P., Fletcher, J., Fuchs, D., Hamlett, C. L., & Zumeta, R. O. (2009) · Journal of Educational Psychology · doi:10.1037/a0014701 · Cited by 189 · see citing works
“…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…”
Background
Intensive Intervention for Students with Mathematics Disabilities: Seven Principles of Effective Practice
Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. T., & Fletcher, J. M. (2008) · Learning Disability Quarterly · doi:10.2307/20528819 · Cited by 194 · see citing works
“third graders, Swanson and Beebe-Frankenberger (2004) identified working memory as Intensive Intervention - 7”
Background
Skill development in different components of arithmetic and basic cognitive functions: Findings from a 3-year longitudinal study of children with different types of learning difficulties
Andersson, U. (2010) · Journal of Educational Psychology · doi:10.1037/a0016838 · Cited by 191 · see citing works
Informal Numeracy Skills
Purpura, D. J., & Lonigan, C. J. (2012) · American Educational Research Journal · doi:10.3102/0002831212465332 · Cited by 187 · see citing works
Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions
Andersson, U. (2008) · British Journal of Educational Psychology · doi:10.1348/000709907x209854 · Cited by 174 · see citing works
Cross-sectional and incremental changes in working memory and mathematical problem solving.
Swanson, H. L. (2006) · Journal of Educational Psychology · doi:10.1037/0022-0663.98.2.265 · Cited by 174 · see citing works
Self-citation
The Cognitive and Academic Profiles of Reading and Mathematics Learning Disabilities
Compton, D. L., Fuchs, L. S., Fuchs, D., Lambert, W. E., & Hamlett, C. L. (2011) · Journal of Learning Disabilities · doi:10.1177/0022219410393012 · Cited by 173 · see citing works
“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…”
Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills
Hannula‐Sormunen, M. M., Lepola, J., & Lehtinen, E. (2010) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2010.06.004 · Cited by 172 · see citing works
The Contributions of Numerosity and Domain-General Abilities to School Readiness
Fuchs, L., Geary, D., Compton, D. L., Fuchs, D., Hamlett, C. L., & Bryant, J. D. (2010) · Child Development · doi:10.1111/j.1467-8624.2010.01489.x · Cited by 160 · see citing works
“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.”
Result
Executive function as a mediator between SES and academic achievement throughout childhood
Lawson, G. M., & Farah, M. J. (2015) · International Journal of Behavioral Development · doi:10.1177/0165025415603489 · Cited by 171 · see citing works
“…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).”
Working memory abilities and children's performance in laboratory analogues of classroom activities
Gathercole, S. E., Durling, E., Evans, M. K., Jeffcock, S., & Stone, S. (2007) · Applied Cognitive Psychology · doi:10.1002/acp.1407 · Cited by 166 · see citing works
“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).”
Processing speed and working memory underlie academic attainment in very preterm children
Mulder, H., Pitchford, N. J., & Marlow, N. (2010) · Archives of Disease in Childhood Fetal & Neonatal · doi:10.1136/adc.2009.167965 · Cited by 162 · see citing works
Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children
Swanson, H. L. (2011) · Journal of Educational Psychology · doi:10.1037/a0025114 · Cited by 161 · see citing works
Self-citation
Examining the relations between spatial skills and mathematical performance: A meta-analysis
Atit, K., Power, J., Pigott, T., Lee, J., Geer, E. A., Uttal, D. H., Ganley, C. M., & Sorby, S. (2021) · Psychonomic Bulletin & Review · doi:10.3758/s13423-021-02012-w · Cited by 174 · see citing works
“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…”
Background
Cognitive components of a mathematical processing network in 9‐year‐old children
Szűcs, D., Devine, A., Soltész, F., Nobes, A., & Gabriel, F. C. (2014) · Developmental Science · doi:10.1111/desc.12144 · Cited by 158 · see citing works
“More recently, Swanson and Beebe-Frankenberger (2004) and Simmons, Singleton and Horne (2008) reported similar results.”
Result
Working memory components as predictors of children's mathematical word problem solving.
Zheng, X.-H., Swanson, H. L., & Marcoulides, G. (2011) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2011.06.001 · Cited by 161 · see citing works
Self-citation
Normative data on the n-back task for children and young adolescents
Pelegrina, S., Lechuga, M. T., García-Madruga, J. A., Elosúa, M. R., Macizo, P., Carreiras, M., Fuentes, L. J., & Bajo, M. T. (2015) · Frontiers in Psychology · doi:10.3389/fpsyg.2015.01544 · Cited by 155 · see citing works
The influence of self-efficacy and working memory capacity on problem-solving efficiency
Hoffman, B. H., & Schraw, G. J. (2008) · Learning and Individual Differences · doi:10.1016/j.lindif.2008.08.001 · Cited by 162 · see citing works
Is Word-Problem Solving a Form of Text Comprehension?
Fuchs, L. S., Fuchs, D., Compton, D. L., Hamlett, C. L., & Wang, A. Y. (2015) · Scientific Studies of Reading · doi:10.1080/10888438.2015.1005745 · Cited by 151 · see citing works
“…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).”
Background
Using Nonword Repetition Tasks for the Identification of Language Impairment in Spanish‐English‐Speaking Children: Does the Language of Assessment Matter?
Gutiérrez‐Clellen, V. F., & Simon‐Cereijido, G. (2010) · Learning Disabilities Research and Practice · doi:10.1111/j.1540-5826.2009.00300.x · Cited by 149 · see citing works
“…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).”
Background
Understanding the Cognition Related to Mathematics Difficulties: A Meta-Analysis on the Cognitive Deficit Profiles and the Bottleneck Theory
Peng, P., Wang, C., & Namkung, J. M. (2018) · Review of Educational Research · doi:10.3102/0034654317753350 · Cited by 147 · see citing works
“…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).”
BackgroundMethodInfluential
The effects of strategic counting instruction, with and without deliberate practice, on number combination skill among students with mathematics difficulties
Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., & Hamlett, C. L. (2009) · Learning and Individual Differences · doi:10.1016/j.lindif.2009.09.003 · Cited by 141 · see citing works
“…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.”
Method
Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school
van de Weijer‐Bergsma, E., Kroesbergen, E. H., & Luit, J. E. H. V. (2014) · Memory & Cognition · doi:10.3758/s13421-014-0480-4 · Cited by 141 · see citing works
“…& 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, &…”
Social networking sites and cognitive abilities: Do they make you smarter?
Alloway, T. P., Horton, J., Alloway, R. G., & Dawson, C. (2013) · Computers & Education · doi:10.1016/j.compedu.2012.10.030 · Cited by 136 · see citing works
“In typically developing children, scores on working memory tasks predict reading achievement independently of measures of phonological skills (Swanson & Beebe-Frankenberger, 2004).”
Background
The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability.
Cowan, R., & Powell, D. (2013) · Journal of Educational Psychology · doi:10.1037/a0034097 · Cited by 138 · see citing works
“Number estimation has been found to be impaired in children with number difficulties (Geary et al., 2008).”
The importance of working memory in children with Dyscalculia and Ageometria
Galitskaya, V., & Drigas, A. S. (2021) · Scientific Electronic Archives · doi:10.36560/141020211449 · Cited by 220 · see citing works
Working memory and executive function profiles of individuals with borderline intellectual functioning
Alloway, T. P. (2010) · Journal of Intellectual Disability Research · doi:10.1111/j.1365-2788.2010.01281.x · Cited by 136 · see citing works
Training working memory in kindergarten children: Effects on working memory and early numeracy
Kroesbergen, E. H., Noordende, J. E. V. '., & Kolkman, M. E. (2012) · Child Neuropsychology · doi:10.1080/09297049.2012.736483 · Cited by 131 · see citing works
“…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).”
Background
Executive function deficits in kindergarten predict repeated academic difficulties across elementary school
Morgan, P. L., Farkas, G., Wang, Y., Hillemeier, M. M., Oh, Y., & Maczuga, S. (2018) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2018.06.009 · Cited by 134 · see citing works
Different components of working memory have different relationships with different mathematical skills
Simmons, F. R., Willis, C., & Adams, A.-M. (2011) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2011.08.011 · Cited by 128 · see citing works
Preschool Children’s Spontaneous Focusing on Numerosity, Subitizing, and Counting Skills as Predictors of Their Mathematical Performance Seven Years Later at School
Hannula‐Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015) · Mathematical Thinking and Learning · doi:10.1080/10986065.2015.1016814 · Cited by 134 · see citing works
“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).”
Background
Mathematical competencies in children with different types of learning difficulties.
Andersson, U. (2008) · Journal of Educational Psychology · doi:10.1037/0022-0663.100.1.48 · Cited by 131 · see citing works
Number Magnitude Processing and Basic Cognitive Functions in Children with Mathematical Learning Disabilities.
Andersson, U., & Östergren, R. (2012) · Learning and Individual Differences · doi:10.1016/j.lindif.2012.05.004 · Cited by 121 · see citing works
“…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).”
BackgroundResult
Working memory deficits in developmental dyscalculia: The importance of serial order
Attout, L., & Majerus, S. (2015) · Child Neuropsychology: A Journal of Normal and Abnormal Development in Childhood and Adolescence · doi:10.1080/09297049.2014.922170 · Cited by 109 · see citing works
Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension
Fuchs, L. S., Gilbert, J. K., Fuchs, D., Seethaler, P. M., & Martin, B. N. (2017) · Scientific Studies of Reading · doi:10.1080/10888438.2017.1398259 · Cited by 128 · see citing works
“…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.”
BackgroundResult
Academic and Cognitive Characteristics of Persistent Mathematics Difficulty from First through Fourth Grade
Vukovic, R., & Siegel, L. (2010) · Learning Disabilities Research and Practice · doi:10.1111/j.1540-5826.2009.00298.x · Cited by 118 · see citing works
“…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.…”
Background
How preschool executive functioning predicts several aspects of math achievement in Grades 1 and 3: A longitudinal study
Viterbori, P., Usai, M. C., Traverso, L., & Franchis, V. D. (2015) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2015.06.014 · Cited by 118 · see citing works
Selective Spatial Working Memory Impairment in a Group of Children With Mathematics Learning Disabilities and Poor Problem-Solving Skills
Passolunghi, M., & Mammarella, I. (2012) · Journal of Learning Disabilities · doi:10.1177/0022219411400746 · Cited by 122 · see citing works
The contribution of working memory to children's mathematical word problem solving
Andersson, U. (2006) · Applied Cognitive Psychology · doi:10.1002/acp.1317 · Cited by 117 · see citing works
How Working Memory Capacity Affects Problem Solving
Wiley, J., & Jarosz, A. F. (2012) · The Psychology of learning and motivation/The psychology of learning and motivation · doi:10.1016/b978-0-12-394393-4.00006-6 · Cited by 116 · see citing works
“Numerous other studies have supported that WMC is related to word problem solving (Passolunghi & Siegel, 2004; Swanson, 2006; Swanson & Beebe-Frankenberger, 2004).”
Background
Remapping the cognitive and neural profiles of children who struggle at school
Astle, D. E., Bathelt, J., the CALM team, & Holmes, J. (2018) · Developmental Science · doi:10.1111/desc.12747 · Cited by 114 · see citing works
“…(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).”
Background
The relative importance of two different mathematical abilities to mathematical achievement
Nuñes, T., Bryant, P., Barros, R., & Sylva, Κ. (2011) · British Journal of Educational Psychology · doi:10.1111/j.2044-8279.2011.02033.x · Cited by 116 · see citing works
Working memory and early numeracy training in preschool children
Passolunghi, M. C., & Costa, H. M. (2014) · Child Neuropsychology · doi:10.1080/09297049.2014.971726 · Cited by 114 · see citing works
“…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).”
Background
Working memory, learning, and academic achievement.
Swanson, H. L., & Alloway, T. P. (2012) · APA educational psychology handbook, Vol 1: Theories, constructs, and critical issues. · doi:10.1037/13273-012 · Cited by 118 · see citing works
Self-citation
Cognitive processes that underlie mathematical precociousness in young children
Swanson, H. L. (2005) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2005.09.006 · Cited by 111 · see citing works
Self-citation
Learning disabilities: The need for neuropsychological evaluation
Silver, C., Ruff, R. M., Iverson, G. L., Barth, J. T., Broshek, D. K., BUSH, S., Koffler, S. P., & REYNOLDS, C. (2007) · Archives of Clinical Neuropsychology · doi:10.1016/j.acn.2007.09.006 · Cited by 111 · see citing works
“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).”
Background
Functional brain organization of working memory in adolescents varies in relation to family income and academic achievement
Finn, A. S., Minas, J. E., Leonard, J., Mackey, A. P., Salvatore, J., Goetz, C., West, M. R., Gabrieli, C. F. O., & Gabrieli, J. D. E. (2016) · Developmental Science · doi:10.1111/desc.12450 · Cited by 108 · see citing works
Reaching the Mountaintop: Addressing the Common Core Standards in Mathematics for Students with Mathematics Difficulties
Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013) · Learning Disabilities Research and Practice · doi:10.1111/ldrp.12001 · Cited by 109 · see citing works
“This is problematic because research indicates that many students with MD have limitations in working memory (Passolunghi & Cornoldi, 2008; Swanson & Beebe-Frankenberger, 2004).”
Background
Academic Achievement of Children and Adolescents With Oral Clefts
Wehby, G. L., Collett, B., Barron, S., Romitti, P. A., Ansley, T. N., & Speltz, M. L. (2014) · PEDIATRICS · doi:10.1542/peds.2013-3072 · Cited by 108 · see citing works
U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems.
McNeil, N. (2007) · Developmental Psychology · doi:10.1037/0012-1649.43.3.687 · Cited by 120 · see citing works
Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?
Imbo, I., & Vandierendonck, A. (2007) · Psychological Research · doi:10.1007/s00426-007-0112-8 · Cited by 108 · see citing works
“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.”
Result
Early childhood memory and attention as predictors of academic growth trajectories.
Stipek, D. J., & Valentino, R. A. (2014) · Journal of Educational Psychology · doi:10.1037/edu0000004 · Cited by 107 · see citing works
“…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…”
Background
Mobile Application Tools for Students in Secondary Education. An Evaluation Study.
Karabatzaki, Z., Stathopoulou, A., Kokkalia, G., Dimitriou, E., Loukeri, P. I., Economou, A., & Drigas, A. S. (2018) · International Journal of Interactive Mobile Technologies (iJIM) · doi:10.3991/ijim.v12i2.8158 · Cited by 105 · see citing works
Spatial Working Memory and Arithmetic Deficits in Children With Nonverbal Learning Difficulties
Mammarella, I., Lucangeli, D., & Cornoldi, C. (2010) · Journal of Learning Disabilities · doi:10.1177/0022219409355482 · Cited by 104 · see citing works
Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving
Passolunghi, M., & Mammarella, I. (2010) · The European Journal of Cognitive Psychology · doi:10.1080/09541440903091127 · Cited by 108 · see citing works
“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…”
Background

Growth in working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties.
Swanson, H. L., Jerman, O., & Zheng, X. (2008) · Journal of Educational Psychology · doi:10.1037/0022-0663.100.2.343 · Cited by 258 · see citing works
Self-citation
Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children
Swanson, H. L. (2011) · Journal of Educational Psychology · doi:10.1037/a0025114 · Cited by 161 · see citing works
Self-citation
Working memory components as predictors of children's mathematical word problem solving.
Zheng, X.-H., Swanson, H. L., & Marcoulides, G. (2011) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2011.06.001 · Cited by 161 · see citing works
Self-citation
Working memory components and problem-solving accuracy: are there multiple pathways?
Swanson, H. L., & Fung, W. W. (2016) · Journal of Educational Psychology · doi:10.1037/edu0000116 · Cited by 63 · see citing works
Self-citation
Cross-sectional and incremental changes in working memory and mathematical problem solving.
Swanson, H. L. (2006) · Journal of Educational Psychology · doi:10.1037/0022-0663.98.2.265 · Cited by 174 · see citing works
Self-citation

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
Publisher: American Psychological Association (APA)
Published: 2004-09
Volume: 96
Issue: 3
Pages: 471-491
ISSN: 0022-0663 (ISSN-L)
1939-2176
DOI: 10.1037/0022-0663.96.3.471
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: Physical Sciences › Mathematics › Statistics and Probability › 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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The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties.

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