Children’s mathematical achievement depends on their domain-specific abilities and their domain-general skills such as executive functions (EFs) and visual-spatial skills (VSS). Research indicates that these two domain-general skills predict mathematical achievement. However, it is unclear whether these skills are differently associated with mathematical achievement across a large age range. The current cross-sectional study answered this question using a large, representative sample aged 5–20 years (N = 1754). EFs, VSS, and mathematical achievement were assessed using the Intelligence and Development Scales–2. Hierarchical regression analyses were computed with EFs and VSS as predictor variables and mathematical achievement as dependent variable. We examined (non-) linear effects and interactions of EFs and VSS with age. Results indicated that EFs and VSS were distinctly associated with mathematical achievement above and beyond effects of age, sex, maternal education, and verbal reasoning. Effects of EFs were linear and age-invariant. Effects of VSS were curvilinear and stronger in adolescents than in children. Our results indicated that EFs and VSS related differently to mathematical proficiency across age, suggesting a varying impact on mathematics across age.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
According to the instructions, the task was stopped when participants answered incorrectly in five subsequent items. Consequently, in some subjects, the termination of the test could also have been caused by geometry items. In order to achieve a complete correction of the test results with regard to the contributions of the geometry items, we estimated latent mathematical ability scores based on a two-parametric item-response model with the data of the completed math items only. We excluded all geometry items from the model. In this latent variable approach, the interaction term VSS*age showed a tendency (p = 0.057). The size of the effect, however, appears only slightly reduced as compared to the analyses with geometry items (βwithout geometry = 0.057 vs. βwith geometry = 0.070).
Aiken, L. S., West, S. G., & Reno, R. R. (1991). Multiple regression: testing and interpreting interactions. London: SAGE. https://doi.org/10.1037/10520-147.
Archibald, S. J., & Kerns, K. A. (1999). Identification and description of new tests of executive functioning in children. Child Neuropsychology, 5, 115–129.
Baddeley, A. (1996). Exploring the central executive. The Quarterly Journal of Experimental Psychology Section, 49A(1), 5–28. https://doi.org/10.1080/713755608.
Baird, K. (2012). Class in the classroom: the relationship between school resources and math performance among low socioeconomic status students in 19 rich countries. Education Economics, 20(5), 484–509.
Bull, R., & Lee, K. (2014). Executive functioning and mathematics achievement. Child Development Perspectives, 8(1), 36–41. https://doi.org/10.1111/cdep.12059.
Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: inhibition, switching, and working memory. Developmental Psychology, 19(3), 273–293. https://doi.org/10.1207/S15326942DN1903_3.
Casey, M., Nuttall, R., & Benbow, C. (1995). The influence of spatial ability on gender differences in mathematics college entrance test-scores across diverse samples. Developmental Psychology, 31(4), 697–705. https://doi.org/10.1037/0012-16126.96.36.1997.
Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 63–68. https://doi.org/10.1016/j.tine.2013.12.001.
Cragg, L., Keeble, S., Richardson, S., Roome, H. E., & Gilmore, C. (2017). Direct and indirect influences of executive functions on mathematics achievement. Cognition, 162, 12–26. https://doi.org/10.1016/j.cognition.2017.01.014.
Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. New York: Guilford Publications.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1–2), 1–42. https://doi.org/10.1016/0010-0277(92)90049-N.
Di Stefano, C., Zhu, M., & Mîndrilă, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research & Evaluation, 14(20), 1–11.
Diamond, A. (2013). Executive functions. Annual Review of Psychology, 64, 135–168. https://doi.org/10.1146/annurev-psych-113011-143750.
Erziehungsdirektoren-Konferenz (D-EDK) (2013). Lehrplan 21, Mathematik (Konsultationsfassung). Luzern: D-EDK
Field, A. (2013). Discovering Statistics Using SPSS (4th ed.). London: SAGE.
Frick, A. (2018). Spatial transformation abilities and their relation to later mathematics performance. Psychological Research. https://doi.org/10.1007/s00426-018-1008-5. (Advance online publication).
Geary, D. C. (2000). From infancy to adulthood: The development of numerical abilities. European Child and Adolescent Psychiatry, 9, 11–16. https://doi.org/10.1007/s007870070004.
Geary, D. C. (2011a). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental and Behavioral Pediatrics, 32(3), 250–263. https://doi.org/10.1097/DBP.0b013e318209edef.
Geary, D. C. (2011b). Cognitive predictors of achievement growth in mathematics: A five year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510.
Gelman, R. (1990). First principles organize attention to and learning about relevant data: Number and the animate-inanimate distinction as examples. Cognitive Science, 14, 79–106. https://doi.org/10.1207/s15516709cog1401_5.
Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., & Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLOS One, 8(6), e67374. https://doi.org/10.1371/journal.pone.0067374.
Grieder, S., & Grob, A. (2019). Exploratory factor analysis of the intelligence and development scales–2: Implications for theory and practice. Assessment., 1, 1. https://doi.org/10.1177/1073191119845051. (Advance online publication).
Grob, A., & Hagmann-von Arx, P. (2018). Intelligence and developmental Scales—2 (IDS-2). Bern: Hogrefe.
Grob, A., Meyer, C. S., & Hagmann-von Arx, P. (2009). Intelligence and Development Scales (IDS). Bern: Huber.
Gross, J., Hudson, C., & Price, D. (2009). The Long Term Costs of Numeracy Difficulties. London: Every Child a Chance Trust.
Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. https://doi.org/10.1037/a0027433.
Hagmann-von Arx, P., Grob, A., Petermann, F., & Daseking, M. (2012). Konkurrente Validität des HAWIK-IV und der Intelligence and Development Scales (IDS). Zeitschrift für Kinder- und Jugendpsychiatrie und Psychotherapie, 40, 41–50. https://doi.org/10.1024/1422-4917/a000148.
Hagmann-von Arx, P., Meyer, C. S., & Grob, A. (2008). Assessing intellectual giftedness with the WISC-IV and the IDS. Journal of Psychology, 216, 173–180.
Hagmann-von Arx, P., Petermann, F., & Grob, A. (2013). Konvergente und diskriminante Validität der WISC-IV und der Intelligence and Development Scales (IDS) bei Kindern mit Migrationshintergrund. Diagnostica, 59, 170–182. https://doi.org/10.1026/0012-1924/a000091.
Hawes, Z., Moss, J., Caswell, B., Seo, J., & Ansari, D. (2018). Relations between numerical, spatial, and executive function skills and mathematics achievement: A latent-variable approach. Cognitive Psychology, 109, 1–23.
Hoff, E. (2013). Interpreting the early language trajectories of children from low SES and language minority homes: Implications for closing achievement gaps. Developmental Psychology, 49(1), 4–14. https://doi.org/10.1037/a0027238.
Holmes, J., & Adams, J. W. (2006). Working Memory and Children’s Mathematical Skills: Implications for mathematical development and mathematics curricula. Educational Psychology, 26(3), 339–366.
Jirout, J. J., & Newcombe, N. S. (2015). Building blocks for developing spatial skills: Evidence from a large, Representative U.S. Sample. Psychological Science, 26(3), 302–310. https://doi.org/10.1177/0956797614563338.
Kuncel, N. R., Hezlett, S. A., & Ones, D. S. (2004). Academic performance, career potential, creativity, and job performance: Can one construct predict them all? Journal of Personality and Social Psychology, 86(1), 148–161.
Kyttälä, M., Aunio, P., Lehto, J. E., Van Luit, J., & Hautamaki, J. (2003). Visuospatial working memory and early numeracy. Educational and Child Psychology, 20, 65–76.
Lauer, J. E., & Lourenco, S. F. (2016). Spatial processing in infancy predicts both spatial and mathematical aptitude in childhood. Psychological Science, 27(10), 1291–1298. https://doi.org/10.1177/0956797616655977.
LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753–1767.
Lehto, J. E., Juujärvi, P., Kooistra, L., & Pulkkinen, L. (2003). Dimensions of executive functioning: Evidence from children. British Journal of Developmental Psychology, 21, 59–80.
Levine, S. C., Dulaney, A., Lourenco, S. F., Ehrlich, S., & Ratliff, K. (2016). Sex differences in spatial cognition: Advancing the conversation. WIREs Cognitive Science, 7, 127–155.
Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35, 940–949.
Levine, S. C., Vasilyeva, M., Lourenco, S., Newcombe, N., & Huttenlocher, J. (2005). Socioeconomic status modifies the sex difference in spatial skill. Psychological Science, 16, 841–845.
Li, Y., & Geary, D. C. (2013). Developmental gains in visuospatial memory predict gains in mathematics achievement. PLoS One, 8(7), e70160. https://doi.org/10.1371/journal.pone.0070160.
Lindberg, S. M., Hyde, J. S., Petersen, J. L., & Linn, M. C. (2010). New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, 136(6), 1123–1135. https://doi.org/10.1037/a0021276.
Markey, S. M. (2010). The relationship between visual-spatial reasoning ability and math and geometry problem solving. Dissertation Abstracts International: Section B: The Sciences and Engineering, 70, 7874.
McCrink, K., & Opfer, J. E. (2014). Development of spatial-numerical associations. Psychological Science, 23(6), 439–445. https://doi.org/10.1177/0963721414549751.
Mix, K. S., & Cheng, Y. L. (2012). The relation between space and math: developmental and educational implications. In J. B. Benson (Ed.), Advances in Child Development and Behavior (Vol. 42, pp. 197–243). San Diego: Elsevier Academic Press Inc. https://doi.org/10.1016/b978-0-12-394388-0.00006-x.
Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C., Hambrick, D. Z., Ping, R., & Konstantopoulos, S. (2016). The latent structure of spatial skills and mathematics across development: Highly correlated but separate domains. JEP General, 145(9), 1206–1227.
Miyake, A., & Friedman, N. P. (2012). The nature and organization of individual differences in executive functions. Current Directions in Psychological Science, 21(1), 8–14. https://doi.org/10.1006/cogp.1999.0734.
Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41, 49–100.
Möhring, W., Newcombe, N. S., & Frick, A. (2015). The relation between spatial thinking and proportional reasoning in preschoolers. Journal of Experimental Child Psychology, 132, 213–220. https://doi.org/10.1016/j.jecp.2015.01.005.
Neuenschwander, R., Röthlisberger, M., Cimeli, P., & Roebers, C. M. (2012). How do different aspects of self-regulation predict successful adaptation to school? Journal of Experimental Child Psychology, 113(3), 353–371. https://doi.org/10.1016/j.jecp.2012.07.004.
Newcombe, N. S., & Shipley, T. F. (2015). Thinking about spatial thinking: New typology, new assessments. In Studying Visual and Spatial Reasoning for Design Creativity (p. 179–192). Dordrecht: Springer. https://doi.org/10.1007/978-94-017-9297-4_10
O’brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673–690.
Peng, P., Wang, T., Wang, C., & Lin, X. (2018). A meta-analysis on the relation between fluid intelligence and reading/mathematics: Effects of tasks, age, and social economics status. Psychological Bulletin, 145, 189–236.
Röthlisberger, M., Neuenschwander, R., Cimeli, P., & Roebers, C. M. (2013). Executive functions in 5-to 8-year olds: Developmental changes and relationship to academic achievement. Journal of Educational and Developmental Psychology, 3, 153–167. https://doi.org/10.5539/jedp.v3n2p153.
Röthlisberger, M., Neuenschwander, R., Michel, E., & Roebers, M. (2010). Exekutive Funktionen: Zugrundeliegende kognitive Prozesse und deren Korrelate bei Kindern im späten Vorschulalter. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 42(2), 99–110.
Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment, 8(4), 350–353. https://doi.org/10.1037/1040-35188.8.131.520.
Stipek, D., & Valentino, R. A. (2015). Early childhood memory and attention as predictors of academic growth trajectories. Journal of Educational Psychology, 107(3), 771–788. https://doi.org/10.1037/edu0000004.
Stroop, J. R. (1935). Studies of interference in serial verbal reactions. Journal of Experimental Psychology, 18, 643–662. https://doi.org/10.1037/h0054651.
Van de Weijer-Bergsma, E., Kroesbergen, E., & Van Luit, J. H. (2015). Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school. Memory & Cognition, 43, 367–368.
Van der Elst, W., Hurks, P., Wassenberg, R., Meijs, C., & Jolles, J. (2011). Animal verbal fluency and design fluency in school-aged children: Effects of age, sex, and mean level of parental education, and regression-based normative data. Journal of Clinical and Experimental Neuropsychology, 33(9), 1005–1015. https://doi.org/10.1080/13803395.2011.589509.
Verdine, B. N., Irwin, C. M., Golinkoff, R. M., & Hirsh-Pasek, K. (2014). Contributions of executive function and spatial skills to preschool mathematics achievement. Journal of Experimental Child Psychology, 126, 37–51. https://doi.org/10.1016/j.jecp.2014.02.012.
Wechsler, D. (2003). Wechsler Intelligence Scale for Children (4th ed.). San Antonio: The Psychological Corporation.
Wolfgang, C. H., Stannard, L. L., & Jones, I. (2001). Block play performance among preschoolers as a predictor of later school achievement in mathematics. Journal of Research in Childhood Education, 15(2), 173–180. https://doi.org/10.1080/02568540109594958.
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749–750. https://doi.org/10.1038/358749a0.
Yeniad, N., Malda, M., Mesman, J., van IJzendoorn, M. H., & Pieper, S. (2013). Shifting ability predicts math and reading performance in children: A meta-analytical study. Learning and Individual Differences, 23, 1–9. https://doi.org/10.1016/j.lindif.2012.10.004.
We are grateful to Priska Hagmann-von Arx and Nora Newcombe for their input on the present research questions. Further, we thank our colleagues of the Division of Developmental and Personality Psychology for their helpful feedback during the brown bag meetings. A special thank goes to the research assistants who were in charge of data collection.
Conflict of interest
The authors declare that they had no conflicts of interest with respect to their authorship or the publication of this article.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
About this article
Cite this article
Kahl, T., Grob, A., Segerer, R. et al. Executive Functions and Visual-Spatial Skills Predict Mathematical Achievement: Asymmetrical Associations Across Age. Psychological Research 85, 36–46 (2021). https://doi.org/10.1007/s00426-019-01249-4