Working memory and phonological processing as predictors of children’s mathematical problem solving at different ages
Abstract
The study explored the contribution of working memory (WM) to mathematical problem solving in younger (8-year-old) and older (11-year-old) children. The results showed that (1) significant age-related differences in WM performance were maintained when measures of phonological processing (i.e., digit naming speed, short-term memory, phonological deletion) were partialed from the analysis; (2) WM predicted solution accuracy of word problems independently of measures of problem representation, knowledge of operations and algorithms, phonological processing, fluid intelligence, reading, and math skill; and (3) a second-order WM factor was correlated with problem solving, suggesting that a general or executive system underlies age-related performance. The results were interpreted as support for the notion that the executive system was an important predictor of age-related changes in problem solving beyond the contribution of math and reading skills, and this system operates independently of the phonological system and domain-specific knowledge in predicting solution accuracy.
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EF have been shown to explain at least as much variance in academic achievement as intelligence.
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From Executive control training from middle childhood to adolescence (2014) · cites this paper as Swanson, 2004
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“For example, working memory is increasingly involved in arithmetic learning and math problem solving (Swanson, 2014).”
BackgroundA hand full of numbers: a role for offloading in arithmetics learning?
Costa, A. J. (2011) · Frontiers in Psychology · doi:10.3389/fpsyg.2011.00368 · Cited by 83 · see citing works
“Swanson (2004) has shown that effects of the slave systems in the multicomponential working memory model are attenuated when analyses include central executive measures.”
BackgroundInfluentialCui, J.-X., Georgiou, G. K., Zhang, Y.-Y., Li, Y.-X., Shu, H., & Zhou, X.-L. (2017) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2016.10.008 · Cited by 73 · see citing works
“This is important in light of the diverse use of RAN tasks in mathematics research (e.g., as a measure of processing speed: Berg, 2008; as a measure of phonological processing: Swanson, 2004; as a language-related skill: Mazzocco & Myers, 2003).”
BackgroundWorking 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-citationTam, Y. P., Wong, T. T., & Chan, W. W. L. (2018) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2018.10.007 · Cited by 61 · see citing works
Lin, X. (2020) · Educational Psychology Review · doi:10.1007/s10648-020-09554-w · Cited by 52 · see citing works
“A prior longitudinal study also suggested that nonverbal reasoning is a significant predictor of age-related differences in WPS accuracy controlling for mathematics computation, reading comprehension, phonological processing, and working memory (Swanson 2004).”
BackgroundInfluentialUsing video game play to improve education-majors’ mathematical performance: An experimental study
Novak, E., & Tassell, J. L. (2015) · Computers in Human Behavior · doi:10.1016/j.chb.2015.07.001 · Cited by 58 · see citing works
“Several studies have shown that a large proportion of variance in accuracy of the problem solving is due to working memory (LeBlanc & Weber-Russell, 1996; Swanson, 2004; Swanson & Sachse-Lee, 2001).”
BackgroundFung, W. W., & Swanson, H. L. (2017) · Memory & Cognition · doi:10.3758/s13421-017-0697-0 · Cited by 47 · see citing works
“Previous studies had attributed proficiency in word problem solving to naming speed (e.g., Cirino, 2011; Geary, 2011; Swanson & Kim, 2007) and problem representation(e.g.,Swanson,2004;Zhengetal.,2011), toname a few of the processes.”
BackgroundMethodSelf-citationThe Role of Executive Function in Arithmetic Problem-Solving Processes: A Study of Third Graders
Viterbori, P., Traverso, L., & Usai, M. C. (2017) · Journal of Cognition and Development · doi:10.1080/15248372.2017.1392307 · Cited by 47 · see citing works
“…word problems impose high demands on children’s cognitive abilities, as they involve an interplay of different skills and knowledge (Boonen, Van Der Schoot, Van Wesel, De Vries, & Jolles, 2013; Kintsch & Greeno, 1985; Lee, Ng, Ng, & Lim, 2004; Mayer & Hegarty, 1996; H. L. Swanson, 2004).”
BackgroundLee, K. L., Ning, F., & Goh, H. C. (2013) · Educational Psychology · doi:10.1080/01443410.2013.836158 · Cited by 45 · see citing works
“Indeed, most studies have found working memory to be more predictive of academic achievement than measures of intelligence (Andersson, 2008; Lee & Ng, 2009; Swanson, 2004) (cf.”
BackgroundPassolunghi, M. C., de Blas, G. D., Carretti, B., Veiga, I. G., Doz, E., & García-Madruga, J. A. (2022) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2022.105512 · Cited by 37 · see citing works
Cognitive processes and math performance: a study with children at third grade of basic education
Campos, I. S., Almeida, L. S., Ferreira, A. I., Martinez, L. F., & Ramalho, G. (2012) · European Journal of Psychology of Education · doi:10.1007/s10212-012-0121-x · Cited by 37 · see citing works
“executive cognitive functions, as proposed in the literature (Bull et al. 1999; Bull and Scerif 2001; Geary 2004; Holmes and Adams 2006; Maybery and Do 2003; Swanson 2004).”
BackgroundSwanson, H. L., Olide, A. F., & Kong, J. E. (2017) · Journal of Educational Psychology · doi:10.1037/edu0000252 · Cited by 36 · see citing works
“In a follow-up study, Swanson (2004) compared two age groups (7 and 11 years old) on WM and problem-solving measures.”
BackgroundMethodResultSelf-citationEndophenotypes for intelligence in children and adolescents
van Leeuwen, M., van den Berg, S. M., Hoekstra, R. A., & Boomsma, D. I. (2006) · Intelligence · doi:10.1016/j.intell.2006.09.008 · Cited by 36 · see citing works
“…ability (Cain, Oakhill, & Bryant, 2004; De Jonge & De Jonge, 1996; Gathercole, Alloway, Willis, & Adams, 2006) and solving mathematical problems (Adams & Hitch, 1997; Geary, Hoard, Byrd- Craven, & Catherine DeSoto, 2004; Swanson, 2004; Swanson & Beebe-Frankenberger, 2004; Lee, Ng, Ng, & Lim, 2004).”
BackgroundResultInfluentialThe association between working memory and mathematical problem solving: A three-level meta-analysis
Ji, Z., & Guo, K. (2023) · Frontiers in Psychology · doi:10.3389/fpsyg.2023.1091126 · Cited by 43 · see citing works
Gordon, R., & Ramani, G. B. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.650286 · Cited by 36 · see citing works
“, 2011), problem solving more broadly (Swanson, 2004), written and verbal calculation (Andersson, 2008), as well as mathematical word problem accuracy (Andersson, 2007; Zheng et al.”
BackgroundVilleneuve, E. F., Hajovsky, D. B., Mason, B. A., & Lewno, B. M. (2018) · School Psychology · doi:10.1037/spq0000267 · Cited by 29 · see citing works
Spencer, M., Fuchs, L. S., & Fuchs, D. (2019) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2019.101825 · Cited by 29 · see citing works
“word-problem solving over and above a variety of other cognitive skills (e.g., phonological processing, IQ, reading comprehension, and calculation skill; Swanson, 2004).”
BackgroundTraining-induced improvement in working memory tasks results from switching to efficient strategies
Malinovitch, T., Jakoby, H., & Ahissar, M. (2021) · Psychonomic Bulletin & Review · doi:10.3758/s13423-020-01824-6 · Cited by 29 · see citing works
“Indeed, WM capacity is strongly correlated with fluid intelligence (Engle, Laughlin, Tuholski, & Conway, 1999; Süß, Oberauer, Wittmann, Wilhelm, & Schulze, 2002) and with academic achievements (Baddeley, 1992a; Bayliss, Jarrold, Baddeley, & Gunn, 2005; Hitch, Towse, & Hutton, 2001; Swanson, 2004).”
Foster, M. E., Anthony, J. L., Zucker, T. A., & Branum-Martin, L. (2019) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2018.02.007 · Cited by 26 · see citing works
Daróczy, G., Meurers, D., Heller, J., Wolska, M. A., & Nürk, H.-C. (2020) · Cognitive Processing · doi:10.1007/s10339-019-00948-5 · Cited by 26 · see citing works
“2008; Swanson 2004).”
BackgroundInfluentialProcesses in the development of mathematics in kindergarten children from Title 1 schools.
Foster, M., Anthony, J. L., Clements, D., & Sarama, J. (2015) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2015.07.004 · Cited by 23 · see citing works
Specific language or working memory impairments: A small scale observational study
Archibald, L. M. D., Joanisse, M. F., & Edmunds, A. L. (2011) · Child Language Teaching and Therapy · doi:10.1177/0265659010396779 · Cited by 23 · see citing works
“These findings are consistent with reports of poor academic achievement in children with learning disabilities known to have working memory difficulties (Swanson, 1993, 2004).”
ResultDifferences in mathematical reasoning between typically achieving and gifted children
Berg, D. H., & McDonald, P. A. (2018) · Journal of Cognitive Psychology · doi:10.1080/20445911.2018.1457034 · Cited by 23 · see citing works
“While the reliabilities of the verbal working memory and visual-spatial working memory tasks were low in comparison to the other measures in this study, they are consistent with other studies that have employed these measures (e.g. Berg, 2008; Swanson, 2004; Swanson & Kim, 2007).”
ResultSwanson, H. L., Kong, J. E., Moran, A., & Orosco, M. J. (2019) · Learning Disabilities Research & Practice · doi:10.1111/ldrp.12194 · Cited by 25 · see citing works
“Based on a factor analysis of this measure (Swanson, 2004),”
MethodSelf-citationMousavi, S., Radmehr, F., & Alamolhodaei, H. (2018) · Electronic Journal of Research in Educational Psychology · doi:10.25115/ejrep.v10i28.1532 · Cited by 22 · see citing works
“…& 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).”
Increasing the Utility of EF Assessment of Executive Function in Children.
Salimpoor, V. N., & Desrocher, M. E. (2006) · Cited by 22 · see citing works
Layes, S., Lalonde, R., Bouakkaz, Y., & Rebai, M. A. (2017) · Cognitive Processing · doi:10.1007/s10339-017-0853-2 · Cited by 23 · see citing works
“Indeed, performing mental arithmetic and understanding mathematical problems require information storage while it is being processed or integrated with information retrieved from long-term memory (Swanson 2004; Tronsky 2005).”
BackgroundNon-Routine Problems in Primary Mathematics Workbooks from Romania.
Zsoldos-Marchiş, I. (2012) · Acta Didactica Napocensia · Cited by 20 · see citing works
Fang, P., Gao, Y., Li, Y., Li, C., Zhang, T., Wu, L., Zhu, Y., & Xie, Y. (2024) · NeuroImage · doi:10.1016/j.neuroimage.2024.120785 · Cited by 18 · see citing works
“It is crucial role for various higher cognitive processes, such as problem-solving, learning, and decision-making (Halford et al., 2007; Swanson, 2004).”
BackgroundSelf-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 18 · see citing works
“…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).”
Vessonen, T., Dahlberg, M., Hellstrand, H., Widlund, A., Söderberg, P., Korhonen, J., Pirjo Aunio, A., & Laine, A. (2025) · Review of Education · doi:10.1002/rev3.70045 · Cited by 17 · see citing works
Development of Cognitive Control across Childhood and Adolescence
Zanolie, K., & Crone, E. A. (2018) · Wiley eBooks · doi:10.1002/9781119170174.epcn405 · Cited by 15 · see citing works
“The ability to keep information in mind is essential for a wide variety of cognitive abilities, including mathematical calculation, reading, problem-solving, and reasoning (Bayliss, Jarrold, Baddeley, & Gunn, 2005; Swanson, 2004).”
BackgroundIS READING COMPREHENSION ASSOCIATED WITH MATHEMATICS SKILLS: A META-ANALYSIS RESEARCH
Akın, A. (2022) · International Online Journal of Primary Education · doi:10.55020/iojpe.1052559 · Cited by 14 · see citing works
“However, some studies (e.g., Swanson, 2004; Bullen et al., 2020) show that there is a greater relationship between reading In the literature, the relationship between reading comprehension and mathematics skills, mathematics achievement is measured by mathematics tasks that span the domain of…”
BackgroundLiu, S., Cheng, C., Wu, P., Zhang, L.-M., Wang, Z.-J., Wei, W., Chen, Y., & Zhao, J. (2021) · Journal of Learning Disabilities · doi:10.1177/00222194211063650 · Cited by 12 · see citing works
“When pattern recognition is being processed, an executive function consisting of inhibition, working memory, and so on is activated (Burgoyne et al., 2019), which also plays an important role in arithmetic operation (Swanson, 2004).”
BackgroundWorking memory and science education: exploring the compatibility of theoretical approaches
Clair‐Thompson, H. S., & Botton, C. (2009) · Research in Science & Technological Education · doi:10.1080/02635140902853616 · Cited by 14 · see citing works
Gamo, S., Nogry, S., & Sander, E. (2014) · Psychologie Française · doi:10.1016/j.psfr.2014.02.002 · Cited by 13 · see citing works
Short-term and Working Memory in Children with Specific L anguage Impairment
Archibald, L. M. D. (2006) · Durham e-Theses (Durham University) · Cited by 13 · see citing works
Park, S., Dotan, P. L., & Esposito, A. G. (2022) · International Journal of Bilingual Education and Bilingualism · doi:10.1080/13670050.2022.2116973 · Cited by 15 · see citing works
“demic achievement than intelligence (Alloway, Bibile, and Lau 2013; Swanson 2004).”
BackgroundHeterogeneidade cognitiva nas dificuldades de aprendizagem da matemática: uma revisão bibliográfica
Haase, V. G., Costa, A. J., Antunes, A. M., & Starling‐Alves, I. (2012) · Revista Psicologia em Pesquisa · doi:10.5327/z1982-12472012000200007 · Cited by 33 · see citing works
Do measures of working memory predict academic proficiency better than measures of intelligence
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Ayuso, D. M. R., Toledano-González, A., Segura‐Fragoso, A., Triviño-Juárez, J. M., & Rodríguez-Martínez, M. D. C. (2020) · Frontiers in Pediatrics · doi:10.3389/fped.2020.00275 · Cited by 10 · see citing works
“In the school environment, high academic performance has been associated with an optimal development of executive functions (EF), (30), especially relevant in subjects such as mathematics (35) and language (reading) (36, 37).”
BackgroundLin, X., & Powell, S. R. (2023) · Child Development · doi:10.1111/cdev.13970 · Cited by 9 · see citing works
Theobald, M., Koerner, J. K. A., Breitwieser, J., Buhr, L., Karbach, J., Könen, T., Nobbe, L., Reinelt, T., Schaaf, M., Schmiedek, F., et al. (2026) · Educational Psychology Review · doi:10.1007/s10648-026-10157-0 · Cited by 10 · see citing works
Howard, S. J., Johnson, J., & Pascual‐Leone, J. (2013) · Research Online (University of Wollongong) · Cited by 9 · see citing works
Cognitive Diversity and the Design of Classroom Tests for All Learners.
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Batool, T., Habiba, U. E., & Saeed, A. (2019) · Cited by 8 · see citing works
Träff, U., Skagerlund, K., & Skagenholt, M. (2025) · Educational Psychology · doi:10.1080/01443410.2025.2463930 · Cited by 8 · see citing works
“…word problem-solving involves a complex interplay of reading processes, language comprehension, modelling (i.e., establishing a problem representation), as well as selection and execution of calculation operations (Fuchs et al., 2016; Kintsch & Greeno, 1985; Mayer & Hegarty, 1996; Swanson, 2004).”
Self-Regulated Learning and Working Memory Determine Problem-Solving Accuracy in Math
Ferreira, P. C., Ferreira, A. I., Simão, A. M. V., Prada, R., Paulino, P., & Rodrigues, R. (2022) · The Spanish Journal of Psychology · doi:10.1017/sjp.2022.19 · Cited by 6 · see citing works
“…has found that WM influences the means through which knowledge is activated (Conway & Engle, 1994) and therefore, children’s capacity to identify the appropriate operations and algorithms, aswell as numerical and irrelevant information come into play when solving math problems (Swanson, 2004).”
BackgroundLongitudinal cognitive correlates of advanced mathematical performance in primary school children
Zhang, J., Yang, X., Yu, X., Xu, J., Jiang, J., & Chen, Y. (2023) · Current Psychology · doi:10.1007/s12144-023-04648-4 · Cited by 6 · see citing works
“Second, three aspects of general cognitive factors were considered simultaneously in this study while previous studies only included one or two sets cognitive skills (e.g., Berg & McDonald 2018; Swanson, 2004; Swanson et al., 2021).”
Soltani, A., & Mirhosseini, S. (2019) · International Journal of Disability Development and Education · doi:10.1080/1034912x.2019.1619673 · Cited by 6 · see citing works
QEEG coherence patterns related to mathematics ability in children
Anzalone, C., Luedke, J. C., Green, J. J., & Decker, S. L. (2020) · Applied Neuropsychology Child · doi:10.1080/21622965.2020.1830403 · Cited by 5 · see citing works
“The Applied Problem subtest involves listening to verbal math problems, thus intruding on one’s ability to engage in the phonological rehearsal strategies that are crucial for some children to remember and perform the steps to complete basic math problems (Swanson, 2004; Swanson & Kim, 2007).”
Malinovitch, T., Albouy, P., Zatorre, R. J., & Ahissar, M. (2022) · Cerebral Cortex · doi:10.1093/cercor/bhac175 · Cited by 5 · see citing works
“The ability to keep accessible and manipulate recent information (working memory [WM]) is essential for most high-level cognitive processes, including reading, mathematical calculations, and problem-solving (Swanson 2004; Bayliss et al. 2005).”
Saga, M., Rkhaila, A., Oubaha, D., & Ounine, K. (2022) · Applied Neuropsychology Child · doi:10.1080/21622965.2022.2105146 · Cited by 5 · see citing works
“Indeed, the execution of mental calculations and understanding mathematical problems involve storing information, while it is being processed or linked to information retrieved from long-term memory (Swanson, 2004; Tronsky, 2005), which is not the case for dyscalculic children.”
BackgroundLinguistic Influences on Mathematical Cognition
Nuerk, H., & Dowker, A. (2017) · Frontiers research topics · doi:10.3389/978-2-88945-200-2 · Cited by 5 · see citing works
Children's solving of mathematical word problems: The contribution of working memory
Pavlin-Bernardić, N. (2008) · University of Zagreb University Computing Centre (SRCE) · Cited by 5 · see citing works
McGonnell, M., Orr, M., Backman, J. E., Johnson, S. A., Davidson, F., & Corkum, P. V. (2024) · Acta Psychologica · doi:10.1016/j.actpsy.2024.104246 · Cited by 5 · see citing works
Mertens, A. T., Myers, K., Sherman, D., Ladouceur, C. D., & Doucet, G. E. (2025) · Cerebral Cortex · doi:10.1093/cercor/bhaf218 · Cited by 3 · see citing works
“Previous research also suggests that WM is required for the development of skills in r easoning, problem solving, and reading comprehension (Baddeley 1992; Swanson 2004; Barrouillet et al. 2008; Arrington et al. 2014).”
Processing Speed and Attentional Resources
Cohen, R. A. (2013) · Springer eBooks · doi:10.1007/978-0-387-72639-7_23 · Cited by 3 · see citing works
Yang, Y.-W., Zhang, X., & Huo, S. (2023) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2022.09.007 · Cited by 2 · see citing works
- Authors
- Swanson, H. L.
- Affiliations
- University of California, Riverside (US)
- Corresponding author
- Swanson, H. Lee
- ORCID
- Swanson, H. Lee
- Venue
- Memory & Cognition
- Published
- 2004-06
- Volume
- 32
- Issue
- 4
- Pages
- 648-661
- ISSN
- 0090-502X (ISSN-L)
- 1532-5946
- OpenAlex
- W2132792816
- Cited by
- 139
- References
- 69
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 4 · 2023: 3 · 2022: 11 · 2021: 4 · 2020: 7 · 2019: 6 · 2018: 8 · 2017: 10 · 2016: 4 · 2015: 10 · 2014: 5 · 2013: 12 · 2012: 10
- FWCI
- 4.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Memory & Cognition (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Abilities and Testing
- Social Sciences › Psychology › Neuropsychology and Physiological Psychology › Developmental and Educational Neuropsychology
- Keywords
- working memory, phonological processing, mathematical problem solving, children, age differences, word problems, solution accuracy, executive function, short-term memory, phonological deletion, fluid intelligence, reading skills, mathematical skills
- MeSH terms
- Age Factors, Child, Female, Humans, Male, Mathematics, Memory, Phonetics, Problem Solving, Prospective Studies
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