ZDM

, Volume 48, Issue 3, pp 321–335 | Cite as

Brain activity associated with logical inferences in geometry: focusing on students with different levels of ability

Original Article

Abstract

Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various combinations of G and EM factors, while another group of seven students were considered to be ‘super mathematically gifted’ (S-MG). EM and G factors affected behavioral measures similarly: EM and G students were more accurate than their non-EM and non-G counterparts respectively. At the same time, G and EM factors affected electrophysiological measures differently, with significant interaction between G and EM factors associated with absolute ERP amplitudes at some of the solution stages. S-MG students exhibited significantly lower absolute ERP amplitude values, which we attribute to a neural efficiency effect in this research group. Based on the differences revealed, we suggest that our research demonstrates that G and EM factors are interrelated individual traits which are different in nature. Since the accuracy and strength of electrical potentials associated with solving the problems appeared to be of an accumulative nature, we argue that S-MG is an extreme expression of combined EM and G factors. Taking it one step further, we suggest that ability grouping in school mathematics must take into account both EM and G factors.

Keywords

Problem solving Logical inference Giftedness Excellence in mathematics Neuro-cognition Event related potentials (ERP) 

Notes

Acknowledgements

This project was made possible through the support of a grant 1447 from the John Templeton Foundation. The opinions expressed in this publication are those of the author(s) and do not necessarily reflect the views of the John Templeton Foundation. We are grateful to the University of Haifa for the generous support it has provided for this study.

References

  1. Ayalon, M., & Even, R. (2010). Mathematics educators’ views on the role of mathematics learning in developing deductive reasoning. International Journal of Science and Mathematics Education, 8(6), 1131–1154.CrossRefGoogle Scholar
  2. Bonnefond, M., & Van der Henst, J.-B. (2013). Deduction electrified: eRPs elicited by the processing of words in conditional arguments. Brain and Language, 124(3), 244–256.CrossRefGoogle Scholar
  3. Davis, G. A., & Rimm, S. B. (2004). Education of the Gifted and Talented. Boston: Allyn & Bacon.Google Scholar
  4. 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
  5. Deal, L. J., & Wismer, M. G. (2010). NCTM Principles and Standards for mathematically talented students. Gifted Child Today, 33(3), 55–65.CrossRefGoogle Scholar
  6. Desco, M., Navas-Sanchez, F. J., Sanchez-González, J., Reig, S., Robles, O., Franco, C., et al. (2011). Mathematically gifted adolescents use more extensive and more bilateral areas of the fronto-parietal network than controls during executive functioning and fluid reasoning tasks. NeuroImage, 57(1), 281–292.CrossRefGoogle Scholar
  7. Donchin, E., & Coles, M. G. (1988). Is the P300 component a manifestation of context updating? Behavioral and rain sciences, 11(03), 357–374.CrossRefGoogle Scholar
  8. Doyle, M. C., Rugg, M. D., & Wells, T. (1996). A comparison of the electrophysiological effects of formal and repetition priming. Psychophysiology, 33(2), 132–147.CrossRefGoogle Scholar
  9. Dunst, B., Benedek, M., Jauk, E., Bergner, S., Koschutnig, K., Sommer, M., et al. (2014). Neural efficiency as a function of task demands. Intelligence, 42(1), 22–30.CrossRefGoogle Scholar
  10. Durand-Guerrier, V., Boero, P., Douek, N., Epp, S. S., & Tanguay, D. (2012). Examining the role of logic in teaching proof. In G. Hanna & M. De Villiers (Eds.), Proof and proving in mathematics education: The 19th ICMI Study (pp. 369–389). Dordrecht: Springer.Google Scholar
  11. Erez, M. M., & Yerushalmy, M. (2006). “If You Can Turn a Rectangle into a Square, You Can Turn a Square into a Rectangle…” Young Students Experience the Dragging Tool. International Journal of Computers for Mathematical Learning, 11(3), 271–299.CrossRefGoogle Scholar
  12. Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60–72.CrossRefGoogle Scholar
  13. Gardner, H. (2011). Multiple Intelligences: New Horizons in Theory and Practice. New York: Basic Books.Google Scholar
  14. Gevins, A., & Smith, M. E. (2000). Neurophysiological Measures of Working Memory and Individual Differences in Cognitive Ability and Cognitive Style. Cerebral Cortex, 10(9), 829–839.CrossRefGoogle Scholar
  15. Grabner, R. H., Neubauer, A. C., & Stern, E. (2006). Superior performance and neural efficiency: the impact of intelligence and expertise. Brain Research Bulletin, 69(4), 422–439.CrossRefGoogle Scholar
  16. Gratton, G., Coles, M. G. H., & Donchin, E. (1983). A new method for off-line removal of ocular artifact. Electroencephalography and Clinical Neurophysiology, 55(4), 468–484.CrossRefGoogle Scholar
  17. Gross, M. U. (2009). Highly gifted young people: development from childhood to adulthood. In L. Shavinina (Ed.), International handbook on giftedness (pp. 337–351). Netherlands: Springer.CrossRefGoogle Scholar
  18. Hanna, G., & De Villiers, M. (Eds.). (2012). Proofs and Proving in Mathematics Education. The 19th ICMI Study. New York: Springer.Google Scholar
  19. Hill, D., Saville, C. W., Kiely, S., Roberts, M. V., Boehm, S. G., Haenschel, C., & Klein, C. (2011). Early electro-cortical correlates of inspection time task performance. Intelligence, 39(5), 370–377.CrossRefGoogle Scholar
  20. Hoyles, C., & Kuchemann, D. (2002). Students’ understandings of logical implication. Educational Studies in Mathematics, 51(3), 193–223.CrossRefGoogle Scholar
  21. Jaušovec, N., & Jaušovec, K. (2000). Correlations between ERP parameters and intelligence: a reconsideration. Biological Psychology, 55(2), 137–154.CrossRefGoogle Scholar
  22. Jensen, A. R. (2006). Clocking the mind: Mental chronometry and individual differences. Amsterdam: Elsevier.Google Scholar
  23. Jolij, J., Huisman, D., Scholte, S., Hamel, R., Kemner, C., & Lamme, V. A. (2007). Processing speed in recurrent visual networks correlates with general intelligence. NeuroReport, 18(1), 39–43.CrossRefGoogle Scholar
  24. Juter, K., & Sriraman, B. (2011). Does High Achieving in Mathematics = Gifted and/or Creative in Mathematics? In B. Sriraman and K.H. Lee (Eds.), The Elements of Creativity and Giftedness in Mathematics (pp. 45–65). Rotterdam: Sense Publishers.Google Scholar
  25. Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren. Translated from Russian by J. Teller. In Kilpatrick J. & Wirszup (Eds.), Chicago: The University of Chicago Press.Google Scholar
  26. Leikin, M. (2002). Processing words’ syntactic functions in normal and dyslexic readers. Journal of Psycholinguistic Research, 31(2), 145–163.CrossRefGoogle Scholar
  27. Leikin, R. (2013). Evaluating mathematical creativity: the interplay between multiplicity and insight. Psychological Assessment and Test Modeling, 55(4), 385–400.Google Scholar
  28. Leikin, R. (2014). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Electronic Version: Springer.Google Scholar
  29. Leikin, R., Leikin, M., Waisman, I., & Shaul, S. (2013a). Effect of the presence of external representations on accuracy and reaction time in solving mathematical double-choice problems by students of different levels of instruction. International Journal of Science and Mathematics Education, 11(5), 1049–1066.CrossRefGoogle Scholar
  30. Leikin, R., Paz-Baruch, N., & Leikin, M. (2014). Cognitive characteristics of students with superior performance in mathematics. Journal of Individual Differences, 35(3), 119–129.CrossRefGoogle Scholar
  31. Leikin, M., Waisman, I., & Leikin, R. (2013b). How brain research can contribute to the evaluation of mathematical giftedness. Psychological Assessment and Test Modeling, 55(4), 415–437.Google Scholar
  32. Luck, S. J. (2014). An introduction to the event-related potential technique. Cambridge: MIT press.Google Scholar
  33. Mathieu, R., Booth, J. R., & Prado, J. (2015). Distributed neural representations of logical, arguments in school-age children. Human Brain Mapping, 36(3), 996–1009.CrossRefGoogle Scholar
  34. Neubauer, A. C., & Fink, A. (2009). Intelligence and neural efficiency. Neuroscience and Biobehavioral Reviews, 33(7), 1004–1023.CrossRefGoogle Scholar
  35. Neville, H. J., Coffey, S., Holcomb, P. J., & Tallal, P. (1993). The neurobiology of sensory and language processing in language-impaired children. Journal of Cognitive Neuroscience, 5(2), 235–253.CrossRefGoogle Scholar
  36. Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., & Carraher, J. (2007). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology, 25(1), 147–166.CrossRefGoogle Scholar
  37. O’Boyle, M. W. (2005). Some current findings on brain characteristics of the mathematically gifted adolescent. International Educational Journal, 6(2), 247–251.Google Scholar
  38. Paz-Baruch, N., Leikin, R., Aharon-Peretz, J., & Leikin, M. (2014). Speed of information processing in generally gifted and excelling in mathematics adolescents. High Abilities Studies, 25(2), 143–167.CrossRefGoogle Scholar
  39. Polich, J. (2012). Neuropsychology of P300. In S. J. Luck & E. S. Kappenman (Eds.), Oxford Handbook of Event-related Potential Components (pp. 159–188). New York: Oxford University Press.Google Scholar
  40. Polich, J., & Kok, A. (1995). Cognitive and biological determinants of P300: an integrative review. Biological psychology, 41(2), 103–146.CrossRefGoogle Scholar
  41. Polya, G. (1973). How to solve it. A new aspect of mathematical method. Princeton: Princeton University Press.Google Scholar
  42. Prado, J., Chadha, A., & Booth, J. R. (2011). The brain network for deductive reasoning: a quantitative meta-analysis of 28 neuroimaging studies. Journal of Cognitive Neuroscience, 23(11), 3483–3497.CrossRefGoogle Scholar
  43. Prescott, J., Gavrilescu, M., Cunnington, R., O’Boyle, M. W., & Egan, G. F. (2010). Enhanced brain connectivity in math-gifted adolescents: an fMRI study using mental rotation. Cognitive Neuroscience, 1(4), 277–288.CrossRefGoogle Scholar
  44. Qiu, J., Li, H., Huang, X., Zhang, F., Chen, A., Luo, Y., et al. (2007). The neural basis of conditional reasoning: an event-related potential study. Neuropsychologia, 45(7), 1533–1539.CrossRefGoogle Scholar
  45. Raven, J., Raven, J. C., & Court, J. H. (2000). Manual for Raven’s Progressive Matrices and Vocabulary Scales. Oxford: Oxford Psychologists.Google Scholar
  46. Schneider, W., Eschman, A., & Zuccolotto, A. (2002). E-prime Computer Software (Version 1.0). Pittsburgh: Psychology Software Tools.Google Scholar
  47. Silverman, L. K. (1989). Invisible gifts, invisible handicaps. Roeper Review, 12(1), 37–42.CrossRefGoogle Scholar
  48. Steiner, H. H., & Carr, M. (2003). Cognitive development in gifted children: toward a more precise understanding of emerging differences in intelligence. Educational Psychology Review, 15(3), 215–246.CrossRefGoogle Scholar
  49. Vinner, S. (1991). The role of definitions in the learning and teaching of mathematics. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 65–81). Dordrecht: Kluwer.Google Scholar
  50. Waisman, I., Leikin, M., Shaul, S., & Leikin, R. (2014). Brain activity associated with translation between graphical and symbolic representations of functions in generally gifted and excelling in mathematics adolescents. International Journal of Science and Mathematics Education, 12(3), 669–696.CrossRefGoogle Scholar
  51. Zhang, Q., Shi, J., Luo, Y., Liu, S., Yang, J., & Shen, M. (2007). Effect of task complexity on intelligence and neural efficiency in children: an event-related potential study. NeuroReport, 18(15), 1599–1602.CrossRefGoogle Scholar
  52. Ziegler, A., & Raul, T. (2000). Myth and Reality: a review of empirical studies on giftedness. High Ability Studies, 11(2), 113–137.CrossRefGoogle Scholar
  53. Zohar, A. (1990). Mathematical reasoning ability: Its structure, and some aspects of its genetic transmission. Unpublished Doctoral Dissertation, Hebrew University, Jerusalem.Google Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  1. 1.Neuro-cognitive Laboratory for the Investigation of Creativity, Ability and Giftedness RANGE (Research and Advancement of Giftedness and Excellence) Center, Faculty of EducationUniversity of HaifaHaifaIsrael
  2. 2.Shaanan CollegeHaifaIsrael

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