Learning and solving algebra word problems: The roles of relational skills, arithmetic, and executive functioning
Abstract
Although algebra is a prerequisite for higher mathematics, few studies have examined the mathematical and cognitive capabilities that contribute to the development of algebra word problems solving skills. We examined changes in these relations from second to ninth grades. Using a cross-sequential design that spanned 4 years, children from 3 cohorts (Mage = 7.85, 10.05, and 12.32) were administered annual tests of algebra word problems, mathematical skills (mathematical relational tasks, arithmetic word problems), and cognitive capabilities (working memory, updating, inhibitory, task switching, and performance intelligence). The cross-sectional findings showed that ability to solve mathematical relational problems was associated strongly with performance in algebra word problems. Working memory and updating explained variance in the relational, but not the algebra problems. Using an autoregressive cross-lagged model with structured residuals to analyze the longitudinal data, we found relational and arithmetic performance predicted independently algebra performance from one year to the next. The strength of these relations was consistent across grades. These findings point to the importance of developing skills in relational problems as one of the tools for improving algebra performance. (PsycINFO Database Record
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Becoming proficient in tasks that require relational thinking, in various settings, enhances performance in algebra.
“It has been observed that becoming proficient in tasks that require relational thinking, in various settings, enhances performance in algebra [18].”
From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [18]
Cites
(2010) · Cited by 7,034 · see citing works
A critique of the cross-lagged panel model
Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. P. P. (2015) · Psychological Methods · doi:10.1037/a0038889 · Cited by 4,005 · see citing works
Testing the efficiency and independence of attentional networks
Fan, J., McCandliss, B. D., Sommer, T., Raz, A., & Posner, M. I. (2002) · Journal of Cognitive Neuroscience · doi:10.1162/089892902317361886 · Cited by 3,717 · see citing works
The interpretation of interaction in contingency tables
Simpson, E. H. (1951) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1951.tb00088.x · Cited by 2,301 · see citing works
Davidson, M. C., Amso, D., Anderson, L. C., & Diamond, A. (2006) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2006.02.006 · Cited by 2,226 · see citing works
Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study.
Geary, D. C. (2011) · Developmental Psychology · doi:10.1037/a0025510 · Cited by 836 · see citing works
Early Predictors of High School Mathematics Achievement
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012) · Psychological Science · doi:10.1177/0956797612440101 · Cited by 795 · see citing works
Berry, D., & Willoughby, M. T. (2017) · Child Development · doi:10.1111/cdev.12660 · Cited by 737 · see citing works
Developmental changes in executive functioning.
Lee, K., Bull, R., & Ho, R. M. H. (2013) · Child Development · doi:10.1111/cdev.12096 · Cited by 633 · see citing works
Self-citationWorking memory and mathematics in primary school children: A meta-analysis
den Bos, I. F., van der Ven, S. H. G., Kroesbergen, E. H., & Luit, J. E. H. V. (2013) · Educational Research Review · doi:10.1016/j.edurev.2013.05.003 · Cited by 587 · see citing works
Executive Functioning and Mathematics Achievement
Bull, R., & Lee, K. (2014) · Child Development Perspectives · doi:10.1111/cdep.12059 · Cited by 552 · see citing works
Self-citation(2001) · Cited by 506 · see citing works
Curran, P., Howard, A. L., Bainter, S. A., Lane, S. T., & Mcginley, J. (2013) · Journal of Consulting and Clinical Psychology · doi:10.1037/a0035297 · Cited by 443 · see citing works
Does Understanding the Equal Sign Matter? Evidence from Solving Equations
Knuth, E., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006) · Journal for Research in Mathematics Education · doi:10.2307/30034852 · Cited by 396 · see citing works
Early Childhood Mathematics Learning
Sarama, J., & Clements, D. H. (2009) · Routledge eBooks · doi:10.4324/9780203883785-1 · Cited by 317 · see citing works
Cole, D. A., Martin, N. C., & Steiger, J. H. (2005) · Psychological Methods · doi:10.1037/1082-989x.10.1.3 · Cited by 314 · see citing works
The development of executive functions and early mathematics: A dynamic relationship
Van der Ven, S. H. G., Kroesbergen, E. H., Boom, J., & Leseman, P. P. M. (2012) · British Journal of Educational Psychology · doi:10.1111/j.2044-8279.2011.02035.x · Cited by 295 · see citing works
Introduction: Methodologies and Models in the Study of Executive Function
Rabbitt, P. (2004) · Routledge eBooks · doi:10.4324/9780203344187-5 · Cited by 262 · see citing works
Learning executive function and early mathematics: Directions of causal relations
Clements, D. H., Sarama, J. H., & Germeroth, C. (2015) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2015.12.009 · Cited by 246 · see citing works
Learning the Algebraic Method of Solving Problems
Stacey, K., & MacGregor, M. (1999) · The Journal of Mathematical Behavior · doi:10.1016/s0732-3123(99)00026-7 · Cited by 200 · see citing works
Geary, D. C., Nicholas, A., Li, Y., & Sun, J. (2017) · Journal of Educational Psychology · doi:10.1037/edu0000159 · Cited by 190 · see citing works
Lee, K. L., Ng, E. L., & Ng, S. F. (2009) · Journal of Educational Psychology · doi:10.1037/a0013843 · Cited by 181 · see citing works
Self-citationFunctional Thinking as a Route Into Algebra in the Elementary Grades
Blanton, M. L., & Kaput, J. J. (2011) · Advances in Mathematics Education · doi:10.1007/978-3-642-17735-4_2 · Cited by 177 · see citing works
(2017) · Routledge eBooks · doi:10.4324/9781315097435 · Cited by 162 · see citing works
Working memory and literacy as predictors of performance on algebraic word problems
Lee, K. L., Ng, S. F., Ng, E. L., & Lim, Z. Y. (2004) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2004.07.001 · Cited by 157 · see citing works
Self-citationDevelopmental changes in working memory, updating, and math achievement.
Lee, K. L., & Bull, R. (2015) · Journal of Educational Psychology · doi:10.1037/edu0000090 · Cited by 157 · see citing works
Self-citationEmerging Understanding of Patterning in 4-Year-Olds
Rittle‐Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013) · Journal of Cognition and Development · doi:10.1080/15248372.2012.689897 · Cited by 141 · see citing works
Sex differences in problem solving.
Johnson, E. S. (1984) · Journal of Educational Psychology · doi:10.1037/0022-0663.76.6.1359 · Cited by 138 · see citing works
Tolar, T. D., Lederberg, A. R., & Fletcher, J. M. (2009) · Educational Psychology · doi:10.1080/01443410802708903 · Cited by 119 · see citing works
Kieran, C., Jeongsuk, P., Schifter, D., & Ng, S. F. (2016) · ICME-13 topical surveys · doi:10.1007/978-3-319-32258-2 · Cited by 106 · see citing works
Self-citationRisky business: Correlation and causation in longitudinal studies of skill development.
Bailey, D. H., Duncan, G. J., Watts, T. W., Clements, D. H., & Sarama, J. H. (2018) · American Psychologist · doi:10.1037/amp0000146 · Cited by 103 · see citing works
Lee, K. L., Ng, S. F., Bull, R., Pe, M. L., & Ho, R. M.-H. (2011) · Journal of Educational Psychology · doi:10.1037/a0023068 · Cited by 95 · see citing works
Self-citationDoes calculation or word-problem instruction provide a stronger route to prealgebraic knowledge?
Fuchs, L. S., Powell, S. R., Cirino, P. T., Schumacher, R. F., Marrin, S., Hamlett, C. L., Fuchs, D., Compton, D. L., & Changas, P. C. (2014) · Journal of Educational Psychology · doi:10.1037/a0036793 · Cited by 95 · see citing works
Fuchs, L. S., Compton, D. L., Fuchs, D., Powell, S. R., Schumacher, R. F., Hamlett, C. L., Vernier, E., Namkung, J. M., & Vukovic, R. K. (2012) · Developmental Psychology · doi:10.1037/a0027475 · Cited by 89 · see citing works
The development of studients' algebraic thinking in earlier grades:
Cai, J., Lew, H. C., Morris, A., et al. (2005) · ZDM · doi:10.1007/bf02655892 · Cited by 88 · see citing works
Geary, D. C., Hoard, M. K., & Nugent, L. D. (2012) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2012.03.003 · Cited by 87 · see citing works
van de Schoot, R., Sijbrandij, M., Depaoli, S., Winter, S. D., Olff, M., & van Loey, N. E. (2018) · Multivariate Behavioral Research · doi:10.1080/00273171.2017.1412293 · Cited by 85 · see citing works
Fuchs, L. S., Gilbert, J. K., Powell, S. R., Cirino, P. T., Fuchs, D., Hamlett, C. L., Seethaler, P. M., & Tolar, T. D. (2016) · Developmental Psychology · doi:10.1037/dev0000227 · Cited by 81 · see citing works
Recursive and explicit rules: How can we build student algebraic understanding?
Lannin, J. K., Barker, D. D., & Townsend, B. E. (2006) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2006.11.004 · Cited by 76 · see citing works
Inhibiting interference from prior knowledge: Arithmetic intrusions in algebra word problem solving
Khng, K. H., & Lee, K. L. (2009) · Learning and Individual Differences · doi:10.1016/j.lindif.2009.01.004 · Cited by 65 · see citing works
Self-citationAlgebraic Thinking with and without Algebraic Representation: A Pathway for Learning
Britt, M. S., & Irwin, K. C. (2011) · Advances in mathematics education · doi:10.1007/978-3-642-17735-4_10 · Cited by 44 · see citing works
Working memory, worry, and algebraic ability
Trezise, K., & Reeve, R. A. (2014) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2013.12.001 · Cited by 44 · see citing works
Geary, D. C., Hoard, M. K., Nugent, L. D., & Rouder, J. N. (2015) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2015.07.010 · Cited by 38 · see citing works
Nathan, M. J., & Kim, S. (2007) · Mathematical Thinking and Learning · doi:10.1080/10986060701360886 · Cited by 38 · see citing works
Sequential development of algebra knowledge: A cognitive analysis
Pillay, H. K., Wilss, L. A., & Boulton‐Lewis, G. M. (1998) · Mathematics Education Research Journal · doi:10.1007/bf03217344 · Cited by 36 · see citing works
Navigating Through Algebra in Grades 3-5
Cuevas, G. J., & Yeatts, K. L. (2001) · Cited by 31 · see citing works
Elementary and middle school students’ analyses of pictorial growth patterns
Walkowiak, T. A. (2013) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2013.09.004 · Cited by 27 · see citing works
Navigating Through Algebra in Grades 6-8
Friel, S. N., Rachlin, S., Doyle, D., et al. (2001) · Cited by 24 · see citing works
Fong, N. S., Lee, K. L., Yin, A. S., et al. (2006) · BRILL eBooks · doi:10.1163/9789087900977_017 · Cited by 16 · see citing works
Self-citationUnderstanding Children’s Difficulties with Mathematical Equivalence
McNeil, N. M., Hornburg, C. B., Fuhs, M. W., & O’Rear, C. D. (2017) · Elsevier eBooks · doi:10.1016/b978-0-12-805086-6.00008-4 · Cited by 13 · see citing works
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Third Grade Students’ Use of Relational Thinking
Molina, M., & Castro, E. (2021) · Mathematics · doi:10.3390/math9020187 · Cited by 12 · see citing works
“It has been observed that becoming proficient in tasks that require relational thinking, in various settings, enhances performance in algebra [18].”
Background
- Authors
- Lee, K., Ng, S. F., & Bull, R.
- Affiliations
- Education University of Hong Kong (HK)
- Nanyang Technological University (SG)
- Venue
- Developmental Psychology
- Published
- 2018-09
- Volume
- 54
- Issue
- 9
- Pages
- 1758-1772
- ISSN
- 0012-1649 (ISSN-L)
- 1939-0599
- OpenAlex
- W2888908847
- Cited by
- 33
- References
- 50
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 3 · 2023: 7 · 2022: 4 · 2021: 4 · 2020: 4 · 2019: 2
- FWCI
- 2.08
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Developmental Psychology (publishedVersion)
- PubMed (publishedVersion)
- NIE Digital Repository (National Institute of Education, Nanyang Technological University) (acceptedVersion)
- Funders
- Centre for Research in Pedagogy and Practice (8/05KL 4/07KL)
- Office of Educational Research (2/08KL, 49/08KL)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Abilities and Testing
- Keywords
- algebra word problems, algebra learning, relationship skills, arithmetic word problems, working memory, updating, executive function, inhibitory control, task switching, performance intelligence, mathematical development
- MeSH terms
- Adolescent, Child, Psychology, Child, Child, Preschool, Cross-Sectional Studies, Female, Humans, Inhibition, Psychological, Intelligence, Language, Learning, Longitudinal Studies, Male, Memory, Short-Term, Problem Solving, Mathematical Concepts, Executive Function
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