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Self-Regulated Learning and Working Memory Determine Problem-Solving Accuracy in Math

Published online by Cambridge University Press:  26 September 2022

Paula Da Costa Ferreira Open the ORCID record for Paula Da Costa Ferreira [Opens in a new window] ,
Aristides I. Ferreira Open the ORCID record for Aristides I. Ferreira [Opens in a new window] ,
Ana Margarida Vieira Da Veiga Simão Open the ORCID record for Ana Margarida Vieira Da Veiga Simão [Opens in a new window] ,
Rui Prada Open the ORCID record for Rui Prada [Opens in a new window] ,
Ana Paula Paulino Open the ORCID record for Ana Paula Paulino [Opens in a new window]  and
Ricardo Rodrigues Open the ORCID record for Ricardo Rodrigues [Opens in a new window]
Paula Da Costa Ferreira*
Affiliation:
Universidade de Lisboa (Portugal)
Aristides I. Ferreira
Affiliation:
Instituto Universitário de Lisboa (ISCTE) (Portugal)
Ana Margarida Vieira Da Veiga Simão
Affiliation:
Universidade de Lisboa (Portugal)
Rui Prada
Affiliation:
Instituto Superior Técnico (INESC-ID) (Portugal)
Ana Paula Paulino
Affiliation:
Universidade Lusófona de Humanidades e Tecnologias (Portugal)
Ricardo Rodrigues
Affiliation:
Instituto Superior Técnico (INESC-ID) (Portugal)
*
Correspondence concerning this article should be addressed to Paula da Costa Ferreira. Universidade de Lisboa. Faculdade de Psicologia. Centro de Investigação em Ciência Psicológica (CICPSI). Alameda da Universidade. 1649–004 Lisboa (Portugal). E-mail: [email protected]
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Abstract

This study aims to understand the role of self-regulated learning (SRL) and its different processes in the relationship between working memory (WM) and problem-solving accuracy in math in primary school children. A sample of 269 primary school children (M age = 8.84, SD = 0.81, 58% boys) participated in this study. Tasks were used as intervention resources to assess children’s WM (i.e., reading and computation span tasks), SRL (i.e., a digital game), and performance (i.e., the performance in the game, as well as a traditional math problem). Through structural equation modeling, results revealed that WM predicted children’s SRL and their problem-solving accuracy in math, such that those with higher capability for temporary storage attained better accuracy. Accordingly, children’s SRL explained the relationship between WM capacity and problem-solving accuracy in math; such that the indirect effect of WM capacity through SRL was lower on problem-solving accuracy in math. Results indicated that the planning phase was a greater indicator of students’ SRL in problem-solving accuracy in math. These results highlight the importance of SRL competencies in explaining children’s performance in problem-solving in math.

Keywords

primary school childrenproblem-solving in mathself-regulated learningworking memory capacity
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 25 , 2022 , e23
Copyright
© Universidad Complutense de Madrid and Colegio Oficial de Psicólogos de Madrid 2022

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Footnotes

Paula Ferreira and Ana Margarida Veiga Simão work for Centro de Investigação em Ciência Psicológica (CICPSI), Faculdade de Psicologia, Universidade de Lisboa. Paula Paulino works for Digital Human-Environment Interaction Labs (HEI-Lab); Universidade Lusófona de Humanidades e Tecnologias, Lisboa. Rui Prada and Ricardo Rodrigues work for Instituto Superior Técnico, Instituto de Engenharia de Sistemas e Computadores: Investigação e Desenvolvimento em Lisboa (INESC-ID).

Funding Statement: This study received financing from national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference CICPSI–UIDB/04527/2020, UIDP/04527/2020; INESC–ID UIDB/50021/2020, and the participative budget of the Câmara Municipal de Lisboa (Agreement No. 15033699).

Conflicts of Interest: None.

References

Aragón, E., Navarro, J. I., Aguilar, M., Cerda, G., & García-Sedeño, M. (2016). Predictive model for early math skills based on structural equations. Scandinavian Journal of Psychology, 57(6), 489–494. https://doi.org/10.1111/sjop.12317CrossRefGoogle ScholarPubMed
Baddeley, A. (2012). WM: Theories, models, and controversies. Annual Review of Psychology, 63(1), 1–29. https://doi.org/10.1146/annurev-psych-120710-100422CrossRefGoogle Scholar
Baddeley, A. D., Hitch, G. J., & Allen, R. J. (2021). A multicomponent model of working memory. In Logie, R., Camos, V., & Cowan, N. (Eds.), Working memory: State of the science (online Ed.). Oxford Academic. https://doi.org/10.1093/oso/9780198842286.003.0002CrossRefGoogle Scholar
Bandura, A. (2001). Social cognitive theory: An agentic perspective. Annual Review of Psychology, 52, 1–26. https://doi.org/10.1146/annurev.psych.52.1.1CrossRefGoogle Scholar
Barrett, L. F., Tugade, M. M., & Engle, R. W. (2004). Individual differences in WM capacity and dual-process theories of the mind. Psychological Bulletin, 130, 553–573. https://doi.org/10.1037/0033-2909.130.4.553CrossRefGoogle Scholar
Berkowitz, M., Edelsbrunner, P., & Stern, E. (2022). The relation between working memory and mathematics performance among students in math-intensive STEM programs. Intelligence, 92, Article 101649. https://doi.org/10.1016/j.intell.2022.101649CrossRefGoogle Scholar
Bridgett, D. J., Oddi, K. B., Laake, L. M., Murdock, K. W., & Bachmann, M. N. (2013). Integrating and differentiating aspects of self-regulation: Effortful control, executive functioning, and links to negative affectivity. Emotion, 13(1), 47–63. https://doi.org/10.1037/a0029536CrossRefGoogle ScholarPubMed
Bull, R., Espy, K. A., Wiebe, S. A., Sheffield, T. D., & Nelson, J. M. (2011). Using confirmatory factor analysis to understand executive control in preschool children: Sources of variation in emergent mathematic achievement. Developmental Science, 14(4), 679–692. https://doi.org/10.1111/j.1467-7687.2010.01012.xCrossRefGoogle ScholarPubMed
Byrne, B. M. (2013). Structural equation modeling with AMOS (2nd Ed.). Routledge. https://doi.org/10.4324/9780203805534CrossRefGoogle Scholar
Campos, I. S., Almeida, L. S., Ferreira, A. I., Martinez, L. F., & Ramalho, G. (2013). Cognitive processes and math performance: A study with children at third grade of basic education. European Journal of Psychology of Education, 28(2), 421–436. https://doi.org/10.1007/s10212-012-0121-xCrossRefGoogle Scholar
Clements, D. H., & Sarama, J. (2019). Executive function and early mathematical learning difficulties. In Fritz, A., Haase, V., & Räsänen, P. (Eds.), International handbook of mathematical learning difficulties (pp. 755–771). Springer. https://doi.org/10.1007/978-3-319-97148-3_43CrossRefGoogle Scholar
Clements, D. H., Sarama, J., & Germeroth, C. (2016). Learning executive functions and early mathematics: Directions of causal relations. Early Childhood Research Quarterly, 36, 79–90. https://doi.org/10.1016/j.ecresq.2015.12.009CrossRefGoogle Scholar
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). Erlbaum. https://doi.org/10.4324/9780203771587CrossRefGoogle Scholar
Conway, A. R. A., & Engle, R. W. (1994). Working memory and retrieval: A resource-dependent inhibition model. Journal of Experimental Psychology: General, 123, 354–373. https://doi.org/10.1037/0096-3445.123.4.354CrossRefGoogle ScholarPubMed
Conway, A. R. A., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R. W. (2005). Working memory span tasks: A methodological review and user’s guide. Psychonomic Bulletin & Review, 12(5), 769–786. https://doi.org/10.3758/BF03196772CrossRefGoogle ScholarPubMed
Cowan, N. (2015). George Miller’s magical number of immediate memory in retrospect: Observations on the faltering progression of science. Psychological Review, 122(3), 536–541. https://doi.org/10.1037/a0039035CrossRefGoogle ScholarPubMed
Das, J. P., Naglieri, J. A., & Kirby, J. R. (1994). Assessment of cognitive processes. The PASS theory of intelligence. Allyn & Bacon.Google Scholar
Day, S. L., & Connor, C. M. (2017). Examining the relations between self-regulation and achievement in third-grade students. Assessment for Effective Intervention, 42(2), 97–109. https://doi.org/10.1177/1534508416670367CrossRefGoogle ScholarPubMed
DeFlorio, L., Klein, A., Starkey, P., Swank, P. R., Taylor, H. B., Halliday, S. E., Beliakoff, A., & Mulcahy, C. (2019). A study of the developing relations between self-regulation and mathematical knowledge in the context of an early math intervention. Early Childhood Research Quarterly, 46, 33–48. https://doi.org/10.1016/j.ecresq.2018.06.008CrossRefGoogle Scholar
Engle, R. W., Cantor, J., & Carullo, J. J. (1992). Individual differences in working memory and comprehension: A test of four hypotheses. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18(5), 972–992. https://doi.org/10.1037/0278-7393.18.5.972Google ScholarPubMed
Ferreira, A. I., Almeida, L. S., & Prieto, G. (2011). The role of processes and contents in human memory: An item response theory approach. Journal of Cognitive Psychology, 23(7), 873–885. https://doi.org/10.1080/20445911.2011.584692CrossRefGoogle Scholar
Fuchs, L., Fuchs, D., Seethaler, P. M., & Barnes, M. A. (2020). Addressing the role of working memory in mathematical word-problem solving when designing intervention for struggling learners. ZDM Mathematics Education, 52(1), 87–96. https://doi.org/10.1007/s11858-019-01070-8CrossRefGoogle Scholar
Fung, W., & Swanson, H. L. (2017). WM components that predict word problem-solving: Is it merely a function of reading, calculation, and fluid intelligence? Memory & Cognition, 45, 804–823. https://doi.org/10.3758/s13421-017-0697-0CrossRefGoogle ScholarPubMed
Gathercole, S. E. (1999). Cognitive approaches to the development of short-term memory. Trends in Cognitive Science, 3, 410–418. https://doi.org/10.1016/S1364-6613(99)01388-1CrossRefGoogle Scholar
Hadwin, A., Järvelä, S., & Miller, M. (2017). Self-regulation, co-regulation and shared regulation in collaborative learning environments. In Alexander, P. A., Schunk, D. H., & Greene, J. A. (Eds.), Handbook of self-regulation of learning and performance (2nd Ed.). Routledge. http://doi.org/10.4324/9781315697048-6Google Scholar
Hofmann, W., Schmeichel, B. J., & Baddeley, A. D. (2012). Executive functions and self-regulation. Trends in Cognitive Sciences, 16(3), 174–180. https://doi.org/10.1016/j.tics.2012.01.006CrossRefGoogle ScholarPubMed
Knouse, L. E., Feldman, G., & Blevins, E. J. (2014). Executive functioning difficulties as predictors of academic performance: Examining the role of grade goals. Learning and Individual Differences, 36, 19–26. https://doi.org/10.1016/j.lindif.2014.07.001CrossRefGoogle Scholar
Kroesbergen, E. H., van Luit, J. E. H., Naglieri, J. A., Taddei, S., & Franchi, E. (2010). PASS processes and early mathematics skills in Dutch and Italian kindergarteners. Journal of Psychoeducational Assessment, 28(6), 585–593. https://doi.org/10.1177/0734282909356054CrossRefGoogle Scholar
Lin, X. (2020). Investigating the unique predictors of word-problem solving using meta-analytic structural equation modeling. Educational Psychology Review, 33, 1097–1124. https://doi.org/10.1007/s10648-020-09554-wCrossRefGoogle Scholar
Little, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association, 83(404), 1198–1202. https://doi.org/10.1080/01621459.1988.10478722CrossRefGoogle Scholar
da Silva, A. L., Simão, A. M. V., & Sá, I. (2004). Auto-regulação da aprendizagem: Estudos teóricos e empíricos [The self-regulation of learning: Theoretical and empirical studies]. Intermeio: Revista do Mestrado em Educação da Universidade de Mato Grosso, 10(19), 59–74.Google Scholar
Mayoral-Rodríguez, S., Timoneda-Gallart, C., & Pérez-Álvarez, F. (2018). Effectiveness of experiential learning in improving cognitive Planning and its impact on problem-solving and mathematics performance. Cultura y Educación, 30(2), 308–337. https://doi.org/10.1080/11356405.2018.1457609CrossRefGoogle Scholar
McClelland, M. M., Cameron, C. E., Duncan, R., Bowles, R. P., Acock, A. C., Miao, A., & Pratt, M. E. (2014). Predictors of early growth in academic achievement: The Head-Toes-Knees-Shoulders task. Frontiers in Psychology, 5, Article 599. https://doi.org/10.3389/fpsyg.2014.00599CrossRefGoogle ScholarPubMed
McCormack, T., & Atance, C. M. (2011). Planning in young children: A review and synthesis. Developmental Review, 31(1), 1–31. https://doi.org/10.1016/j.dr.2011.02.002CrossRefGoogle Scholar
Ministério da Educação e Ciência. (2013). Programa de Matemática ensino básico [Basic education Mathematics program]. https://www.dge.mec.pt/sites/default/files/Basico/Metas/Matematica/programa_matematica_basico.pdfGoogle Scholar
Miyake, A., & Friedman, N. P. (2012). The nature and organization of individual differences in executive functions: Four general conclusions. Current Directions in Psychological Science, 21, 8–14. http://doi.org/10.1177/0963721411429458CrossRefGoogle ScholarPubMed
Muñez, D., Lee, K., Bull, R., Khng, K. H., Cheam, F., & Rahim, R. A. (2022). Working memory and numeracy training for children with math learning difficulties: Evidence from a large-scale implementation in the classroom [Supplemental material]. Journal of Educational Psychology. Advance online publication. https://doi.org/10.1037/edu0000732.suppCrossRefGoogle Scholar
Núñez Castellar, E., All, A., de Marez, L., & van Looy, J. (2015). Cognitive abilities, digital games and arithmetic performance enhancement: A study comparing the effects of a math game and paper exercises. Computers & Education, 85, 123–133. https://doi.org/10.1016/j.compedu.2014.12.021CrossRefGoogle Scholar
Nyroos, M., Jonsson, B., Korhonen, J., & Eklöf, H. (2015). Children’s mathematical achievement and how it relates to working memory, test anxiety and self-regulation: A person-centred approach. Education Inquiry, 6(1), Article 26026. https://doi.org/10.3402/edui.v6.26026CrossRefGoogle Scholar
Offergeld, T., Martinez, L. F., & Ferreira, A. I. (2020). A train of thought in product experientiality: Working memory, distraction, and inconsistencies in cue order effects. Journal of Retailing & Consumer Services, 53, Article 101971. https://doi.org/10.1016/j.jretconser.2019.101971CrossRefGoogle Scholar
Otto, B. (2007). SELVES - Schüler, eltern- und lehrertrainings zur vermittlung effektiver selbstregulation [SELVES - student, parent and teacher training for teaching effective self-regulation]. Logos.Google Scholar
Packwood, S., Hodgetts, H. M., & Tremblay, S. (2011). A multiperspective approach to the conceptualization of executive functions. Journal of Clinical and Experimental Neuropsycholy, 33, 456–470. https://doi.org/10.1080/13803395.2010.53315CrossRefGoogle Scholar
Patterson, F., Rowett, E., Hale, R., Grant, M., Roberts, C., Cousans, F., & Martin, S. (2016). The predictive validity of a situational judgement test and multiple-mini interview for entry into postgraduate training in Australia. BMC Medical Education, 16, Article 87. https://doi.org/10.1186/s12909-016-0606-4CrossRefGoogle ScholarPubMed
Perels, F., Dignath, C., & Schmitz, B. (2009). Is it possible to improve mathematical achievement by means of self-regulation strategies? Evaluation of an intervention in regular math classes. European Journal of Psychology of Education, 24(1), Article 17. https://doi.org/10.1007/BF03173472CrossRefGoogle Scholar
Passolunghi, M. C., Cargnelutti, E., & Pellizzoni, S. (2019). The relation between cognitive and emotional factors and arithmetic problem-solving. Educational Studies in Mathematics, 100(3), 271–290. https://doi.org/10.1007/s10649-018-9863-yCrossRefGoogle Scholar
Passolunghi, M.C., & Siegel, L.S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of experimental child psychology, 88(4), 348–367. https://doi.org/10.1016/j.jecp.2004.04.002CrossRefGoogle ScholarPubMed
Perlow, R., & Jattuso, M. (2018). A comparison of computation span and reading working memory measures’ relations with problem-solving criteria. Psychological Reports, 121(3), 430–444.CrossRefGoogle ScholarPubMed
Polya, G. (2004). How to solve it: A new aspect of mathematical method (Vol. 85). Princeton University Press.Google Scholar
Polya, G. (1981). Mathematical discovery: On understanding, learning and teaching problem-solving (2 volumes combined). John Wiley & Sons. (Original work published 1965).Google Scholar
Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879–891. https://doi.org/10.3758/BRM.40.3.879CrossRefGoogle ScholarPubMed
Schmitt, S. A., Geldhof, G. J., Purpura, D. J., Duncan, R., & McClelland, M. M. (2017). Examining the relations between executive function, math, and literacy during the transition to kindergarten: A multi-analytic approach. Journal of Educational Psychology, 109, 1120–1140. https://doi.org/10.1037/edu0000193CrossRefGoogle Scholar
Schutz, P. A., Distefano, C., Benson, J., & Davis, H. A. (2004). The Emotional Regulation during Test-taking scale. Anxiety, Stress, & Coping: An International Journal, 17(3), 253–269. https://doi.org/10.1080/10615800410001710861CrossRefGoogle Scholar
Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7(4), 422–445. https://doi.org/10.1037//1082-989X.7.4.422CrossRefGoogle ScholarPubMed
Shukor, N. A., Abu, M. S., & Ahmad, N. (2015). A preliminary study on socially shared regulation during online collaborative mathematics learning. IEEE Conference on e-Learning, e-Management and e-Services, (2015), 1–7. https://doi.org/10.1109/IC3e.2015.7403477CrossRefGoogle Scholar
Silverman, S., & Ashkenazi, S. (2022). The unique role of spatial working memory for mathematics performance. Journal of Numerical Cognition, 8(1), 226–243. https://doi.org/10.5964/jnc.7159CrossRefGoogle Scholar
Swanson, H. L. (2004). Working memory and phonological processing as predictors of children’s mathematical problem-solving at different ages. Memory and Cognition, 32, 648–661. https://doi.org/10.3758/BF03195856CrossRefGoogle ScholarPubMed
Swanson, H. L. (2016). Word problem-solving, WM and serious math difficulties: Do cognitive strategies really make a difference? Journal of Applied Research in Memory and Cognition, 5, 368–383. https://doi.org/10.1016/j.jarmac.2016.04.012CrossRefGoogle Scholar
Swanson, H. L., & Alloway, T. P. (2012). Working memory, learning, and academic achievement. In Harris, K. R., Graham, S., Urdan, T., McCormick, C. B., Sinatra, G. M., & Sweller, J. (Eds.), APA educational psychology handbook , Vol. 1: Theories, constructs, and critical issues (pp. 327–366). American Psychological Association. http://doi.org/10.1037/13273-012Google Scholar
Swanson, H. L., Arizmendi, G. D., & Li, J.-T. (2021). Working memory growth predicts mathematical problem-solving growth among emergent bilingual children. Journal of Experimental Child Psychology, 201, Article 104988. https://doi.org/10.1016/j.jecp.2020.104988Google Scholar
Swanson, H. L., & Fung, W. (2016). Working memory components and problem-solving accuracy: Are there multiple pathways? Journal of Educational Psychology, 108(8), 1153–1177. https://doi.org/10.1037/edu0000116CrossRefGoogle Scholar
Taub, M., Mudrick, N. V., Azevedo, R., Millar, G. C., Rowe, J., Lester, J. (2017). Using multi-channel data with multi-level modeling to assess in-game performance during gameplay with Crystal Island. Computers in Human Behavior, 76, 641–655. https://doi.org/10.1016/j.chb.2017.01.038CrossRefGoogle Scholar
Thalmann, M., & Oberauer, K. (2017). Domain-specific interference between storage and processing in complex span is driven by cognitive and motor operations. Quarterly Journal of Experimental Psychology, 70(1), 109–126. https://doi.org/10.1080/17470218.2015.1125935CrossRefGoogle ScholarPubMed
Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28(2), 127–154. https://doi.org/10.1016/0749-596X(89)90040-5CrossRefGoogle Scholar
Simão, A. M. V., da Silva, A. L., Marques, J., Ferreira, P., & Paulino, P. (2015). Projeto resolução dos problemas - Relatório final. [Problem-solving project - Final Report] Faculdade de Psicologia da Universidade de Lisboa, Câmara Municipal de Lisboa.Google Scholar
von Bastian, C. C., & Oberauer, K. (2013). Distinct transfer effects of training different facets of working memory capacity. Journal of Memory and Language, 69(1), 36–58. https://doi.org/10.1016/j.jml.2013.02.002CrossRefGoogle Scholar
Vuontela, V., Carlson, S., Troberg, A.-M., Fontell, T., Simola, P., Saarinen, S., & Aronen, E. T. (2013). Working memory, attention, inhibition, and their relation to adaptive functioning and behavioral/emotional symptoms in school-aged children. Child Psychiatry & Human Development, 44(1), 105–122. https://doi.org/10.1007/s10578-012-0313-2CrossRefGoogle ScholarPubMed
Zheng, X., Swanson, H. L., & Marcoulides, G. A. (2011). Working memory components as predictors of children’s mathematical problem-solving. Journal of Experimental Child Psychology, 110, 481–498. https://doi.org/10.1016/j.jecp.2011.06.001CrossRefGoogle Scholar
Zimmerman, B. J. (2013). From cognitive modeling to self-regulation: A social cognitive career path. Educational Psychologist, 48(3), 135–147. https://doi.org/10.1080/00461520.2013.794676CrossRefGoogle Scholar
Zimmerman, B. J. (2000). Attainment of self-regulation: A social cognitive perspective. In Boekaerts, M., Pintrich, P. R., & Zeidner, M. (Eds.), Handbook of self-regulation, research, and applications (pp. 13–39). Academic Press. https://doi.org/10.1016/B978-012109890-2/50031-7CrossRefGoogle Scholar