European Journal of Psychology of Education

, Volume 34, Issue 3, pp 665–683 | Cite as

Prediction of elementary mathematics grades by cognitive abilities

  • Sven HilbertEmail author
  • Georg Bruckmaier
  • Karin Binder
  • Stefan Krauss
  • Markus Bühner


In the present study, the relationship between the mathematics grade and the three basic cognitive abilities (inhibition, working memory, and reasoning) was analyzed regarding possible alterations during elementary school. In a sample of N = 244 children, the mathematics grade was best predicted by working memory performance in the second grade and by reasoning in the third and fourth grades. Differentiation of these abilities during elementary school was considered as a cause for this pattern but discarded after the analysis of structural equation models. Thus, with respect to output-orientated curricula, scholastic standards, and a large inter-individual heterogeneity of students, it is implied for teachers to account for different cognitive strengths and weaknesses of their students, using adequate tasks and teaching strategies like self-differentiating tasks and adaptive explorative learning.


Cognitive ability Mathematics Cognitive differentiation 



  1. Asch, S. E. (1936). A study of change in mental organization. Archives of Psychology, 28, 1–30.Google Scholar
  2. Baddeley, A. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417–423.Google Scholar
  3. Baumert, J., Lüdtke, O., Trautwein, U., & Brunner, M. (2009). Large-scale student assessment studies measure the results of processes of knowledge acquisition: Evidence in support of the distinction between intelligence and student achievement. Educational Research Review, 4(3), 165–176.Google Scholar
  4. Bjorklund, D. F., & Harnishfeger, K. K. (1990). The resources construct in cognitive development: Diverse sources of evidence and a theory of inefficient inhibition. Developmental Review, 10(1), 48–71.Google Scholar
  5. Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246–263.Google Scholar
  6. Blair, C., Gamson, D., Thorne, S., & Baker, D. (2005). Rising mean IQ: Cognitive demand of mathematics education for young children, population exposure to formal schooling, and the neurobiology of the prefrontal cortex. Intelligence, 33(1), 93–106.Google Scholar
  7. Blum, W., Galbraith, P., Henn, H.-W., & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education. New York: Springer.Google Scholar
  8. BMB – Bundesministerium für Bildung (2014). Lehrplan der Volksschule – Mathematik. Retrieved from
  9. Brunner, M. (2008). No g in education? Learning and Individual Differences, 18(2), 152–165.Google Scholar
  10. Brunner, M., Krauss, S., & Kunter, M. (2008). Gender differences in mathematics: Does the story need to be rewritten? Intelligence, 36, 403–421.Google Scholar
  11. Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19(3), 273–293.Google Scholar
  12. Bull, R., Espy, K. A., & Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33(3), 205–228.Google Scholar
  13. CCSSI – Common Core State Standards Initiative (2010). Common core state standards for mathematics. Retrieved from
  14. Cerda, G., Ortega, R., Pérez, C., Flores, C., & Melipillán, R. (2011). Inteligencia lógica y rendimiento académico en matemáticas: un estudio con estudiantes de Educación Básica y Secundaria de Chile. Anales de Psycología, Universidad de Murcia, 27(2), 389–398.Google Scholar
  15. Clark, C. A., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46(5), 1176–1191.Google Scholar
  16. Cobb, P., & Jackson, K. (2011). Assessing the quality of the common core state standards for mathematics. Educational Researcher, 40(4), 183–185.Google Scholar
  17. Connelly, S. L., Hasher, L., & Zacks, R. T. (1991). Age and reading: The impact of distraction. Psychology and aging, 6(4), 533.Google Scholar
  18. Conway, A. R. A., Cowan, N., Bunting, M. F., Therriault, D. J., & Minkoff, S. R. B. (2002). A latent variable analysis of working memory capacity, short-term memory capacity, processing speed, and general fluid intelligence. Intelligence, 30(2), 163–183.Google Scholar
  19. 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.Google Scholar
  20. Crone, E. A., Wendelken, C., Donohue, S., Van Leijenhorst, L., & Bunge, S. A. (2006). Neurocognitive development of the ability to manipulate information in working memory. Proceedings of the National Academy of Sciences, 103(24), 9315–9320.Google Scholar
  21. Davidson, M. C., Amso, D., Anderson, L. C., & Diamond, A. (2006). Development of cognitive control and executive functions from 4 to 13 years: Evidence from manipulations of memory, inhibition, and task switching. Neuropsychologia, 44(11), 2037–2078.Google Scholar
  22. Deary, I. J., Egan, V., Gibson, G. J., Austin, E. J., Brand, C. R., & Kellaghan, T. (1996). Intelligence and the differentiation hypothesis. Intelligence, 23(2), 105–132.Google Scholar
  23. Dempster, F. N., Corkill, A. J., & Jacobi, K. (1995). Individual differences in resistance to interference. In Annual Meeting of the Psychonomic Society, Los Angeles.Google Scholar
  24. Der, G., & Deary, I. J. (2003). IQ, reaction time and the differentiation hypothesis. Intelligence, 31(5), 491–503.Google Scholar
  25. Engle, R. W., Tuholski, S. W., Laughlin, J. E., & Conway, A. R. (1999). Working memory, short-term memory, and general fluid intelligence: A latent-variable approach. Journal of Experimental Psychology: General, 128(3), 309–331.Google Scholar
  26. Facon, B. (2006). Does age moderate the effect of IQ on the differentiation of cognitive abilities during childhood? Intelligence, 34(4), 375–386.Google Scholar
  27. Filella, J. F. (1960). Educational and sex differences in the organization of abilities in technical and academic students in Colombia, South America. Genetic Psychology Monographs, 61, 115–163.Google Scholar
  28. Floyd, R. G., Evans, J. J., & McGrew, K. S. (2003). Relations between measures of Cattell-Horn-Carroll (CHC) cognitive abilities and mathematics achievement across the school-age years. Psychology in the Schools, 40(2), 155–171.Google Scholar
  29. Garrett, H. E. (1946). A developmental theory of intelligence. American Psychologist, 1(9), 372–378.Google Scholar
  30. Hammer, S., Reiss, K., Lehner, M. C., Heine, J. H., Sälzer, C., & Heinze, A. (2015). Mathematische Kompetenz in PISA 2015: Ergebnisse, Veränderungen und Perspektiven. PISA, 219–248.Google Scholar
  31. Heene, M., Hilbert, S., Draxler, C., Ziegler, M., & Bühner, M. (2011). Masking misfit in confirmatory factor analysis by increasing unique variances: A cautionary note on the usefulness of cutoff values of fit indices. Psychological Methods, 16(3), 319.Google Scholar
  32. Houdé, O. (2000). Inhibition and cognitive development: Object, number, categorization, and reasoning. Cognitive Development, 15(1), 63–73.Google Scholar
  33. Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55.Google Scholar
  34. Hülür, G., Wilhelm, O., & Robitzsch, A. (2011). Intelligence differentiation in early childhood. Journal of Individual Differences, 32(3), 170.Google Scholar
  35. Hyde, J. S., Fennema, E., & Lamon, S. J. (1990). Gender differences in mathematics performance: A meta-analysis.Google Scholar
  36. Johnson, W., Bouchard Jr., T. J., Krueger, R. F., McGue, M., & Gottesman, I. I. (2004). Just one g: Consistent results from three test batteries. Intelligence, 32(1), 95–107.Google Scholar
  37. Juan-Espinosa, M., García, L. F., Colom, R., & Abad, F. J. (2000). Testing the age related differentiation hypothesis through the Wechsler’s scales. Personality and Individual Differences, 29(6), 1069–1075.Google Scholar
  38. Kelley, K. (2018). MBESS: The MBESS R Package. R package version 4.4.3. Retrieved: June 11th, 2018.
  39. KMK – Ständige Konferenz der Kultusminister der Länder in der Bundesrepublik Deutschland (Hrsg.) (2004). Bildungsstandards im Fach Mathematik für den Primarbereich. Darmstadt: Luchterhand.Google Scholar
  40. Krumm, S., Schmidt-Atzert, L., Bühner, M., Ziegler, M., Michalczyk, K., & Arrow, K. (2009). Storage and non-storage components of working memory predicting reasoning: A simultaneous examination of a wide range of ability factors. Intelligence, 37(4), 347–364.Google Scholar
  41. Kunter, M., & Voss, T. (2013). The model of instructional quality in COACTIV: A multicriteria analysis. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers. Results from the COACTIV project (pp. 97–124). New York: Springer.Google Scholar
  42. Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 105(3), 805–820. Scholar
  43. Kyllonen, P. C., & Christal, R. E. (1990). Reasoning ability is (little more than) working-memory capacity. Intelligence, 14(4), 389–433.Google Scholar
  44. Leder, G., & Forgasz, H. (2008). Mathematics education: New perspectives on gender. ZDM, 40(4), 513–518.Google Scholar
  45. Leuders, T., Philipp, K., & Leuders, J., (2018). Diagnostic competence of mathematics teachers—unpacking a complex construct in teacher education and teacher practice. Cham: Springer.Google Scholar
  46. Limerick, B., Clarke, J., & Daws, L. (1997). Problem-based learning within a post-modern framework: A process for a new generation? Teaching in Higher Education, 2(3), 259–272.Google Scholar
  47. MacLeod, C. M. (2007). The concept of inhibition in cognition. In D. S. Gorfein & C. M. MacLeod (Eds.), Inhibition in cognition (pp. 3–23). Washington, DC: American Psychological Association.
  48. Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. International Association for the Evaluation of Educational Achievement. Herengracht 487, Amsterdam, 1017 BT, The Netherlands.Google Scholar
  49. O’Grady, K. E. (1990). A confirmatory maximum likelihood factor analysis of the WPPSI. Personality and Individual Differences, 11(2), 135–140.Google Scholar
  50. Oberauer, K., Süß, H. M., Wilhelm, O., & Wittman, W. W. (2003). The multiple faces of working memory: Storage, processing, supervision, and coordination. Intelligence, 31(2), 167–193.Google Scholar
  51. Passolunghi, M. C., & Siegel, L. S. (2001). Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80(1), 44–57.Google Scholar
  52. R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Retrieved from
  53. Raghubar, K. P., Barnes, M. A., & Hecht, S. A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20(2), 110–122.Google Scholar
  54. Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187–202.Google Scholar
  55. Raven, J. C. (1941). Standardization of progressive matrices, 1938. Psychology and Psychotherapy: Theory, Research and Practice, 19(1), 137–150.Google Scholar
  56. Raven, J., Raven, J. C., & Court, J. H. (2000). Standard progressive matrices. Oxford: Oxford Psychologists.Google Scholar
  57. Rindermann, H. (2007). The g-factor of international cognitive ability comparisons: The homogeneity of results in PISA, TIMSS, PIRLS and IQ-tests across nations. European Journal of Personality, 21(5), 667–706.Google Scholar
  58. Rindermann, H. (2008). Relevance of education and intelligence for the political development of nations: Democracy, rule of law and political liberty. Intelligence, 36(4), 306–322.Google Scholar
  59. Rohde, T. E., & Thompson, L. A. (2007). Predicting academic achievement with cognitive ability. Intelligence, 35(1), 83–92.Google Scholar
  60. Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36.Google Scholar
  61. Sackett, P. R., & Yang, H. (2000). Correction for range restriction: An expanded typology. Journal of Applied Psychology, 85(1), 112–118.Google Scholar
  62. Saß, S., Kampa, N., & Köller, O. (2017). The interplay of g and mathematical abilities in large-scale assessments across grades. Intelligence, 63, 33–44.Google Scholar
  63. Saxe, G. B. (2015). Culture and cognitive development: Studies in mathematical understanding. Hillsdale: Lawrence Erlbaum Associates, Inc.Google Scholar
  64. Schmid, V. (2010). TEMEKKO (Doctoral dissertation, Ludwig-Maximilians-University of Munich).Google Scholar
  65. Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children’s success, methods and strategies. Educational Studies in Mathematics, 47(2), 145–173.Google Scholar
  66. Shaw, P., Greenstein, D., Lerch, J., Clasen, L., Lenroot, R., Gogtay, N., et al. (2006). Intellectual ability and cortical development in children and adolescents. Nature, 30, 676–679.Google Scholar
  67. Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60(4), 973–980.Google Scholar
  68. Spearman, C. (1926). Some issues in the theory of “G” (including the law of diminishing returns). Paper presented at the British Association Section J-Psychology, Southampton.Google Scholar
  69. Spinath, B., Spinath, F. M., Harlaar, N., & Plomin, R. (2006). Predicting school achievement from general cognitive ability, self-perceived ability, and intrinsic value. Intelligence, 34(4), 363–374.Google Scholar
  70. Stamovlasis, D., & Tsaparlis, G. (2005). Cognitive variables in problem solving: A nonlinear approach. International Journal of Science and Mathematics Education, 3(1), 7–32.Google Scholar
  71. Stanovich, K. E., Cunningham, A. E., & Feeman, D. J. (1984). Intelligence, cognitive skills, and early reading progress. Reading Research Quarterly, 19(3), 278–303.Google Scholar
  72. Tartre, L. A., & Fennema, E. (1995). Mathematics achievement and gender: A longitudinal study of selected cognitive and affective variables [grades 6–12]. Educational Studies in Mathematics, 28(3), 199–217.Google Scholar
  73. Tideman, E., & Gustafsson, J. E. (2004). Age-related differentiation of cognitive abilities in ages 3-7. Personality and Individual Differences, 36(8), 1965–1974.Google Scholar
  74. Tucker-Drob, E. M. (2009). Differentiation of cognitive abilities across the life span. Developmental psychology, 45(4), 1097.Google Scholar
  75. Van Dooren, W., & Inglis, M. (2015a). Inhibitory control in mathematical thinking, learning and problem solving. ZDM, 47(5).Google Scholar
  76. Van Dooren, W., & Inglis, M. (2015b). Inhibitory control in mathematical thinking, learning and problem solving: A survey. ZDM, 47(5), 713–721.Google Scholar
  77. Wilson, K. M., & Swanson, H. L. (2001). Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit? Journal of Learning Disabilities, 34(3), 237–248.Google Scholar

Copyright information

© Instituto Superior de Psicologia Aplicada, Lisboa, Portugal and Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Faculty of Psychology, Educational Science, and Sport ScienceUniversity of RegensburgRegensburgGermany
  2. 2.School for Teacher Education, Institute for Primary EducationUniversity of Applied Sciences Northwestern SwitzerlandLiestalSwitzerland
  3. 3.Faculty of Mathematics, Department of Mathematics EducationUniversity of RegensburgRegensburgGermany
  4. 4.Department of Psychology, Psychological Methods and AssessmentLMU MunichMunichGermany

Personalised recommendations