# BRAIN ACTIVITY ASSOCIATED WITH TRANSLATION BETWEEN GRAPHICAL AND SYMBOLIC REPRESENTATIONS OF FUNCTIONS IN GENERALLY GIFTED AND EXCELLING IN MATHEMATICS ADOLESCENTS

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## Abstract

In this study, we examine the impact and the interplay of general giftedness (G) and excellence in mathematics (EM) on high school students’ mathematical performance associated with translations from graphical to symbolic representations of functions, as reflected in cortical electrical activity (by means of ERP—event-related potentials—methodology). We report on findings of comparative data analysis based on 75 right-handed male high school students (16 – 18 years old) divided into four research groups designed by a combination of EM and G factors. Effects of EM factor appeared at the behavioral and electrophysiological levels. The fifth group of participants included 9 students with extraordinary mathematical abilities (S-MG: super mathematically gifted). We found that in EM participants, the G factor has no impact on the performance associated with translation between representations of the functions. The highest overall electrical activity is found in excelling in mathematics students who are not identified as generally gifted (NG-EM students). This increased electrical activity can be an indicator of increased cognitive load in this group of students. We identified accumulative and unique characteristics of S-MG at the behavioral and electrophysiological levels. We explain the findings by the nature of the tasks used in the study. We argue that a combination of the ERP techniques along with more traditional educational research methods enables obtaining reliable measures on the mental processing involved in learning mathematics and mathematical problem solving.

## KEY WORDS

event-related potentials (ERP) excellence in mathematics functions giftedness graphical and symbolic representations## Preview

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## REFERENCES

- Anderson, J. R., Betts, S., Ferris, J. L. & Fincham, J. M. (2011). Cognitive and metacognitive activity in mathematical problem solving: Prefrontal and parietal patterns.
*Cognitive, Affective, & Behavioral Neuroscience, 11*(1), 52–67.CrossRefGoogle Scholar - Callahan, C. M. (2000). Intelligence and giftedness. In R. J. Sternberg (Ed.),
*Handbook of intelligence*(pp. 159–175). New York, NY: Cambridge University Press.CrossRefGoogle Scholar - Da Ponte, J. P. (1992). The history of the concept of function and some educational implications.
*The Mathematics Educator, 3*(2), 3–8.Google Scholar - Dai, D. Y., Swanson, J. A. & Cheng, H. (2011). State of research on giftedness and gifted education: A survey of empirical studies published during 1998–2010.
*Gifted Child Quarterly, 55*(2), 126–138.CrossRefGoogle Scholar - Danker, J. F. & Anderson, J. R. (2007). The roles of prefrontal and posterior parietal cortex in algebra problem solving: A case of using cognitive modelling to inform neuroimaging data.
*NeuroImage, 35*(3), 1365–1377.CrossRefGoogle Scholar - De Smedt, B. & Verschaffel, L. (2010). Travelling down the road from cognitive neuroscience to education.... and back.
*ZDM The International Journal on Mathematics Education, 42*, 49–65.CrossRefGoogle Scholar - Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2003). Three parietal circuits for number processing.
*Cognitive Neuropsychology, 20*(3–6), 487–506.CrossRefGoogle Scholar - Dietrich, A. & Kanso, R. (2010). A review of EEG, ERP, and neuroimaging studies of creativity and insight.
*Psychological Bulletin, 136*(5), 822–848.CrossRefGoogle Scholar - Donchin, E. & Coles, M. G. (1988). Is the P300 component a manifestation of context updating?
*Behavioral and Brain Sciences, 11*(03), 357–374.CrossRefGoogle Scholar - 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 - Feldman, D. (2003). A developmental, evolutionary perspective on giftedness. In J. H. Borland (Ed.),
*Rethinking gifted education*(pp. 9–33). New York, NY: Teachers College Press.Google Scholar - Ferrara, F., Pratt, D. & Robutti, O. (2006). The role and uses of technologies for the teaching of algebra and calculus. In A. Gutierrez & P. Boero (Eds.),
*Handbook of research on the psychology of mathematics education*(pp. 237–273). Rotterdam: Sense.Google Scholar - Frey, M. C. & Detterman, D. K. (2004). Scholastic assessment or g? The relationship between the scholastic assessment test and general cognitive ability.
*Psychological Science, 15*(6), 373–378.CrossRefGoogle Scholar - Gagatsis, A. & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving.
*Educational Psychology, 24*(5), 645–657.CrossRefGoogle Scholar - Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F. & Neuper, C. (2009). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving.
*Neuropsychologia, 47*(2), 604–608.CrossRefGoogle Scholar - Grabner, R. H., Reishofer, G., Koschutnig, K. & Ebner, F. (2011). Brain correlates of mathematical competence in processing mathematical representations.
*Frontiers in Human Neuroscience, 5*, 130. doi: 10.3389/fnhum.2011.00130.CrossRefGoogle Scholar - 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 - Halgren, E. (1990). Insights from evoked potentials into the neuropsychological mechanisms of reading. In A. B. Scheibel & A. F. Wechsler (Eds.),
*Neurobiology of higher cognitive function*. NY: Guilford Press.Google Scholar - Handy, T. C. (2005). Basic principles of ERP quantification. In T. C. Handy (Ed.),
*Event-related potentials: A methods handbook*(pp. 33–56). Cambridge: MIT Press.Google Scholar - Heinze, H. J. & Mangun, G. R. (1995). Electrophysiological signs of sustained and transient attention to spatial locations.
*Neuropsychologia, 33*(7), 889–908.CrossRefGoogle Scholar - Heinze, A., Star, J. R. & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education.
*ZDM, 41*(5), 535–540.CrossRefGoogle Scholar - Janvier, C. (1987). Translation processes in mathematics education. In C. Janvier (Ed.),
*Problems of representation in the teaching and learning of mathematics*(pp. 27–32). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Jensen, A. R. (2006).
*Clocking the mind: Mental chronometry and individual differences*. Amsterdam, the Netherlands: Elsevier.Google Scholar - Kaan, E. (2007). Event‐related potentials and language processing: A brief overview.
*Language and Linguistics Compass, 1*(6), 571–591.CrossRefGoogle Scholar - Kaput, J. J. (1998). Representations, inscriptions, descriptions, and learning: A kaleidoscope of windows.
*Journal of Mathematical Behavior, 17*(2), 265–281.CrossRefGoogle Scholar - Krutetskii, V. A. (1976).
*The psychology of mathematical abilities in schoolchildren.*(Translated from Russian by Teller, J.; Edited by Kilpatrick J. & Wirszup). Chicago, IL: The University of Chicago Press.Google Scholar - Kutas, M., McCarthy, G. & Donchin, E. (1977). Augmenting mental chronometry: The P300 as a measure of stimulus evaluation time.
*Science, 197*(4305), 792–795.CrossRefGoogle Scholar - Lee, K., Lim, Z. Y., Yeong, S. H., Ng, S. F., Venkatraman, V. & Chee, M. W. (2007). Strategic differences in algebraic problem solving: Neuroanatomical correlates.
*Brain Research, 1155*, 163–171.CrossRefGoogle Scholar - Lehmann, D. & Skrandies, W. (1984). Spatial analysis of evoked potentials in man—a review.
*Progress in Neurobiology, 23*(3), 227–250.CrossRefGoogle Scholar - Leikin, R. (2014). Giftedness and high ability in mathematics. In S. Lerman (Ed.),
*Encyclopedia of Mathematics Education*. Springer. Electronic Version.Google Scholar - Leikin, R., Leikin, M., Waisman, I., & Shaul, S. (2013). 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.Google Scholar - Leikin, R., Waisman, I., Shaul, S. & Leikin, M. (2012). An ERP study with gifted and excelling male adolescents: Solving short Insight-based problems. In T. Y. Tso (Ed.)
*The Proceedings of the 36th International Conference for the Psychology of Mathematics Education*(v. 3, pp. 83–90). Taiwan, Taipei.Google Scholar - Moreno-Armella, L., Hegedus, S. J. & Kaput, J. J. (2008). From static to dynamic mathematics: Historical and representational perspectives.
*Educational Studies in Mathematics, 68*(2), 99–111.CrossRefGoogle Scholar - Neubauer, A. C. & Fink, A. (2009). Intelligence and neural efficiency.
*Neuroscience and Biobehavioral Reviews, 33*(7), 1004–1023.CrossRefGoogle Scholar - Neville, H. J., Coffey, S. A., 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 - Newman, S. D., Willoughby, G. & Pruce, B. (2011). The effect of problem structure on problem-solving: An fMRI study of word versus number problems.
*Brain Research, 1410*, 77–88.CrossRefGoogle Scholar - Nittono, H., Nageishi, Y., Nakajima, Y. & Ullsberger, P. (1999). Event-related potential correlates of individual differences in working memory capacity.
*Psychophysiology, 36*(06), 745–754.CrossRefGoogle Scholar - Piirto, J. (1999).
*Talented children and adults: Their development and education*(2nd ed.). Columbus, OH: Prentice Hall/Merrill.Google Scholar - Polich, J. (2012). Neuropsychology of P300. In S. J. Luck & E. Kappenman (Eds.),
*The Oxford handbook of event-related potential components*(pp. 159–188). New York, NY: Oxford University Press.Google Scholar - Raven, J., Raven, J. C. & Court, J. H. (2000).
*Manual for Raven’s progressive matrices and vocabulary scales*. Oxford: Oxford Psychologists.Google Scholar - Renzulli, J. S. (1978). What makes giftedness? Reexamination of a definition.
*Phi Delta Kappa, 60*, 180–184.Google Scholar - Ruchkin, D. S., Johnson, R., Jr., Mahaffey, D. & Sutton, S. (1988). Towards a functional categorization of slow waves.
*Psychophysiology, 25*(3), 339–353.CrossRefGoogle Scholar - Schneider, W., Eschman, A. & Zuccolotto, A. (2002).
*E-prime computer software (version 1.0)*. Pittsburgh, PA: Psychology Software Tools.Google Scholar - Shiffrin, R. M. & Schneider, W. (1977). Controlled and automatic human information processing: II. Perceptual learning, automatic attending, and a general theory.
*Psychological Review, 84*(2), 127–190.CrossRefGoogle Scholar - Silverman, L. K. (2009). The measurement of giftedness. In L. V. Shavinina (Ed.),
*International handbook on giftedness*(pp. 947–970). Amsterdam: Springer Science and Business Media.CrossRefGoogle Scholar - Sohn, M. H., Goode, A., Koedinger, K. R., Stenger, V. A., Carter, C. S. & Anderson, J. R. (2004). Behavioral equivalence does not necessarily imply neural equivalence: Evidence in mathematical problem solving.
*Nature Neuroscience, 7*(11), 1193–1194.CrossRefGoogle Scholar - Sternberg, R. J. (1997).
*Successful intelligence*. New York: Plume.Google Scholar - Thomas, M. O., Wilson, A. J., Corballis, M. C., Lim, V. K. & Yoon, C. (2010). Evidence from cognitive neuroscience for the role of graphical and algebraic representations in understanding function.
*ZDM, 42*(6), 607–619.CrossRefGoogle Scholar - Vaivre-Douret, L. (2011). Developmental and cognitive characteristics of “high-level potentialities” (highly gifted) children.
*International Journal of Pediatrics, 2011*, 1–14.CrossRefGoogle Scholar - Wilson, G. F., Swain, C. R. & Ullsperger, P. (1998). ERP components elicited in response to warning stimuli: The influence of task difficulty.
*Biological Psychology, 47*(2), 137–158.CrossRefGoogle Scholar - Yerushalmy, M. (2006). Slower algebra students meet faster tools: Solving algebra word problems with graphing software.
*Journal for Research in Mathematics Education, 37*(5), 356–387.Google Scholar - Yerushalmy, M. & Shternberg, B. (2001). Charting a visual course to the concept of function. In A. A. Cuoco & F. R. Curcio (Eds.),
*The roles of representation in school mathematics*(pp. 251–267). Reston, VA: The National Council of Teachers of Mathematics.Google Scholar - Zacks, J. M. (2008). Neuroimaging studies of mental rotation: a meta-analysis and review.
*Journal of Cognitive Neuroscience, 20*(1), 1–19.Google Scholar - Zamarian, L., Ischebeck, A. & Delazer, M. (2009). Neuroscience of learning arithmetic—Evidence from brain imaging studies.
*Neuroscience and Biobehavioral Reviews, 33*(6), 909–925.CrossRefGoogle Scholar - Ziegler, A. & Raul, T. (2000). Myth and reality: A review of empirical studies on giftedness.
*High Ability Studies, 11*(2), 113–136.CrossRefGoogle Scholar - Zohar, A. (1990).
*Mathematical reasoning ability: Its structure, and some aspects of its genetic transmission*. Unpublished Doctoral Dissertation, Hebrew University, Jerusalem.Google Scholar