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ZDM

, Volume 47, Issue 5, pp 801–811 | Cite as

The effect of inhibitory control on general mathematics achievement and fraction comparison in middle school children

  • David Maximiliano Gómez
  • Abelino Jiménez
  • Roberto Bobadilla
  • Cristián Reyes
  • Pablo Dartnell
Original Article
First Online:

Abstract

Individual differences in inhibitory control have been shown to relate to general mathematics achievement, but whether this relation varies for specific areas within mathematics is a question that remains open. Here, we evaluate if inhibitory processes play a specific role in the particular case of fraction comparison, where learners must ignore the potentially misleading information provided by the natural numbers composing fractions (e.g. 2/3 > 4/7 despite 2 < 4 and 3 < 7). To do this, we presented a sample of Chilean children (N = 450) from 5th, 6th, and 7th grade with a numerical comparison task tapping inhibitory and other processes. Results showed that both general math achievement and accuracy in comparing fractions were significantly predicted by inhibition. The former association, however, turned out to mediate the latter one. Another process, related to visual priming, predicted children’s likelihood to answer fraction comparison items focusing exclusively on the fraction components. This relation was, furthermore, not mediated by general math achievement. Altogether, these findings shed light on the mental processes underlying the early stages of the learning of fractions.

Keywords

Mathematics achievement Fraction comparison Inhibitory control Visual priming Numerical Stroop task Natural number bias 
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Notes

Acknowledgments

The authors are grateful to the administrators, teachers, parents, and children of the school network who took part in this study, to Benjamín Bossi and Sergio Orellana for their assistance in collecting the data, and to anonymous reviewers who made invaluable contributions to this manuscript. This project was funded by CONICYT’s Basal Funds for Centers of Excellence FB0003 and BASAL-CMM.

References

  1. Aksu, M. (1997). Student performance in dealing with fractions. The Journal of Educational Research, 90(6), 375–380.CrossRefGoogle Scholar
  2. Baddeley, A. (1996). Exploring the central executive. The Quarterly Journal of Experimental Psychology, 49A(1), 5–28.CrossRefGoogle Scholar
  3. Baddeley, A., & Hitch, G. (1974). Working memory. In G. H. Bower (Ed.), Recent advances in learning and motivation (Vol. 8). New York: Academic Press.Google Scholar
  4. Besner, D., & Coltheart, M. (1979). Ideographic and alphabetic processing in skilled reading of English. Neuropsychologia, 17(5), 467–472.CrossRefGoogle Scholar
  5. Blair, C., & Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78(2), 647–663.CrossRefGoogle Scholar
  6. Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of fractions: real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410–1419.Google Scholar
  7. Bornemann, B., Foth, M., Horn, J., Ries, J., Warmuth, E., Wartenburger, I., & van der Meer, E. (2010). Mathematical cognition: individual differences in resource allocation. ZDM - The International Journal on Mathematics Education, 42(6), 555–567.CrossRefGoogle Scholar
  8. Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118, 32–44.CrossRefGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. Bull, R., Johnston, R. S., & Roy, J. A. (1999). Exploring the roles of the visual-spatial sketch pad and central executive in children’s arithmetical abilities: views from cognition and developmental neuropsychology. Developmental Neuropsychology, 15(3), 421–442.CrossRefGoogle 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.CrossRefGoogle Scholar
  12. Bush, G., Whalen, P. J., Rosen, B. R., Jenike, M. A., McInerney, S. C., & Rauch, S. L. (1998). The counting Stroop: an interference task specialized for functional neuroimaging—Validation study with functional MRI. Human Brain Mapping, 6, 270–282.CrossRefGoogle Scholar
  13. Censabella, S., & Noël, M.-P. (2007). The inhibition capacities of children with mathematical disabilities. Child Neuropsychology, 14(1), 1–20.CrossRefGoogle Scholar
  14. Clark, C. A. C., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46(5), 1176–1191.CrossRefGoogle Scholar
  15. 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, 63–68.CrossRefGoogle Scholar
  16. D’Amico, A., & Passolunghi, M. C. (2009). Naming speed and effortful and automatic inhibition in children with arithmetic learning disabilities. Learning and Individual Differences, 19, 170–180.CrossRefGoogle Scholar
  17. De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (2001). Verifying simple arithmetic sums and products: are the phonological loop and the central executive involved? Memory and Cognition, 29(2), 267–273.CrossRefGoogle Scholar
  18. De Smedt, B., Janssen, R., Bouwens, K., Verschaffel, L., Boets, B., & Ghesquière, P. (2009). Working memory and individual differences in mathematics achievement: a longitudinal study from first grade to second grade. Journal of Experimental Child Psychology, 103(2), 186–201.CrossRefGoogle Scholar
  19. De Smedt, B., & Verschaffel, L. (2010). Traveling down the road: from cognitive neuroscience to mathematics education… and back. ZDM - The International Journal on Mathematics Education, 42(6), 649–654.CrossRefGoogle Scholar
  20. Edwards, J. R. (2001). Ten difference score myths. Organizational Research Methods, 4(3), 265–287.CrossRefGoogle Scholar
  21. Espy, K. A., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A., & Senn, T. E. (2004). The contribution of executive functions to emergent mathematic skills in preschool children. Developmental Neuropsychology, 26(1), 465–486.CrossRefGoogle Scholar
  22. Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., et al. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? Developmental Psychology, 46(6), 1731–1746.CrossRefGoogle Scholar
  23. Gabriel, F., Szűcs, D., & Content, A. (2013). The mental representation of fractions: adults’ same-different judgments. Frontiers in Psychology, 4, 385. doi: 10.3389/fpsyg.2013.00385.Google Scholar
  24. Ganor-Stern, D., Karasik-Rivkin, I., & Tzelgov, J. (2011). Holistic representation of unit fractions. Experimental Psychology, 58(3), 201–206.CrossRefGoogle Scholar
  25. Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., et al. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS One, 8(6), e67374.CrossRefGoogle Scholar
  26. Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76(2), 104–122.CrossRefGoogle Scholar
  27. Gómez, D. M., Jiménez, A., Bobadilla, R., Reyes, C., & Dartnell, P. (2014). Exploring fraction comparison in school children. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 3, pp. 185–192). Vancouver, Canada: PME.Google Scholar
  28. Henik, A., & Tzelgov, J. (1982). Is three greater than five: the relation between physical and semantic size in comparison tasks. Memory and Cognition, 10(4), 389–395.CrossRefGoogle Scholar
  29. Kallai, A. Y., & Tzelgov, J. (2012). When meaningful components interrupt the processing of the whole: the case of fractions. Acta Psychologica, 139(2), 358–369.CrossRefGoogle Scholar
  30. Landy, D. H., & Goldstone, R. L. (2010). Proximity and precedence in arithmetic. Quarterly Journal of Experimental Psychology, 63(10), 1953–1968.CrossRefGoogle Scholar
  31. 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.CrossRefGoogle Scholar
  32. MacLeod, C. M., Dodd, M. D., Sheard, E. D., Wilson, D. E., & Bibi, U. (2003). In opposition to inhibition. In B. H. Ross (Ed.), The psychology of learning and motivation (Vol. 43, pp. 163–214). San Diego, CA: Academic Press.Google Scholar
  33. Mallinckrodt, B., Abraham, W. T., Wei, M., & Russell, D. W. (2006). Advances in testing the statistical significance of mediation effects. Journal of Counseling Psychology, 53(3), 372–378.CrossRefGoogle Scholar
  34. 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, 599. doi: 10.3389/fpsyg.2014.00599.CrossRefGoogle Scholar
  35. Meert, G., Grégoire, J., & Noël, M.-P. (2010). Comparing the magnitude of two fractions with common components: which representations are used by 10- and 12-year-olds? Journal of Experimental Child Psychology, 107(3), 244–259.CrossRefGoogle Scholar
  36. Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., & Menon, V. (2010). Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders. Learning and Individual Differences, 20(2), 101–109.CrossRefGoogle Scholar
  37. 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(1), 49–100.CrossRefGoogle Scholar
  38. Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52.CrossRefGoogle Scholar
  39. Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72.CrossRefGoogle Scholar
  40. Pansky, A., & Algom, D. (2002). Comparative judgment of numerosity and numerical magnitude: attention preempts automaticity. Journal of Experimental Psychology. Learning, Memory, and Cognition, 28(2), 259–274.CrossRefGoogle Scholar
  41. 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.CrossRefGoogle Scholar
  42. 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.CrossRefGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. Shallice, T., & Burgess, P. W. (1991). Higher-order cognitive impairments and frontal lobe lesions in man. In H. S. Levin, H. M. Eisenberg, & A. L. Benton (Eds.), Frontal lobe function and dysfunction (pp. 125–138). New York: Oxford University Press.Google Scholar
  45. Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., et al. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697.CrossRefGoogle Scholar
  46. Sprute, L., & Temple, E. (2011). Representations of fractions: evidence for accessing the whole magnitude in adults. Mind, Brain, and Education, 5(1), 42–47.CrossRefGoogle Scholar
  47. St Clair-Thompson, H. L., & Gathercole, S. E. (2006). Executive functions and achievements in school: shifting, updating, inhibition, and working memory. The Quarterly Journal of Experimental Psychology, 59(4), 745–759.CrossRefGoogle Scholar
  48. Szűcs, D., & Soltész, F. (2007). Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm. Neuropsychologia, 45(14), 3190–3202.CrossRefGoogle Scholar
  49. Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344–355.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2015

Authors and Affiliations

  • David Maximiliano Gómez
    • 1
  • Abelino Jiménez
    • 1
  • Roberto Bobadilla
    • 2
  • Cristián Reyes
    • 1
    • 3
  • Pablo Dartnell
    • 1
    • 2
    • 4
  1. 1.Centro de Investigación Avanzada en Educación (CIAE)Universidad de ChileSantiagoChile
  2. 2.Departamento de Ingeniería Matemática (DIM)Universidad de ChileSantiagoChile
  3. 3.Departamento de Estudios Pedagógicos (DEP)Universidad de ChileSantiagoChile
  4. 4.Centro de Modelamiento Matemático (CMM)Universidad de ChileSantiagoChile

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