# Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study

- 910 Downloads
- 9 Citations

## Abstract

We asked: “What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?” To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of insight-based problems were not related to the learning experience but rather to an “Aha!” moment. As learning-based problems, we employed tasks that require comparing the areas of geometric figures. The analysis was performed through the lens of mathematical performance in students who differed in the combination of levels of general giftedness (G) and excellence in school mathematics (EM). Alongside a quantitative analysis of the effects of EM and G factors on accuracy, reaction time, strength of the electrical potentials and their topographical distribution, we performed a qualitative comparison of the differences in the effects of EM and G factors associated with the two types of tests. We demonstrate that an analysis of the behavioral measures is insufficient and even misleading and argue that neurocognitive analysis is crucial for the understanding of the distinctions between mathematical processing associated with solving different types of problems. Analysis of the electrical potentials evoked when solving the two types of problems demonstrated that excellence in school mathematics affects learning-based problem solving but does not affect insight-based problem solving. Based on the observation of the increased activation of PO4–PO8 electrode site as related to G and EM factors, we further hypothesize that the ability to solve insight-based problems is a specific personal aptitude related mainly to general giftedness, while experience-based problem solving by experts involves insight-related components at the stage of problem understanding.

## Keywords

Insight-based problem solving Learning-based problem solving General giftedness Excellence in mathematics Neuro-cognition Event related potentials (ERP)## Notes

### Acknowledgments

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

- 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 and Behavioral Neuroscience,**11*(1), 52–67.CrossRefGoogle Scholar - Arsalidou, M., & Taylor, M. J. (2011). Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations.
*Neuroimage,**54*(3), 2382–2393.CrossRefGoogle Scholar - Avancini, C., Soltész, F., & Szűcs, D. (2015). Separating stages of arithmetic verification: An ERP study with a novel paradigm.
*Neuropsychologia,**75*, 322–329.CrossRefGoogle Scholar - Bowden, E. M., & Jung-Beeman, M. (2007). Methods for investigating the neural components of insight.
*Methods,**42*(1), 87–99.CrossRefGoogle Scholar - Braunstein, V., Ischebeck, A., Brunner, C., Grabner, R. H., Stamenov, M., & Neuper, C. (2012). Investigating the influence of proficiency on semantic processing in bilinguals: An ERP and ERD/S analysis.
*Acta Neurobiologiae Experimentalis,**72*, 421–438.Google Scholar - Colom, R., Karama, S., Jung, R. E., & Haier, R. J. (2010). Human intelligence and brain networks.
*Dialogues in Clinical Neuroscience,**12*(4), 489–501.Google Scholar - Da Ponte, J. P. (2007). Investigations and explorations in the mathematics classroom.
*ZDM - The International Journal on Mathematics Education,**39*(5–6), 419–430.CrossRefGoogle Scholar - Davidson, J. E., & Sternberg, R. J. (2003).
*The psychology of problem solving*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Desco, M., Navas-Sanchez, F. J., Sanchez-González, J., Reig, S., Robles, O., Franco, C., & Arango, C. (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 - 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 - Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.),
*Advanced mathematical thinking*(pp. 42–53). Dordrecht: Kluwer.Google Scholar - Eysenck, M. W., & Keane, M. T. (2000).
*Cognitive psychology: A student’s handbook*. Philadelphia: Taylor and Francis.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 - 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 - 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 - Guthormsen, A. M., Fisher, K. J., Bassok, M., Osterhout, L., DeWolf, M., & Holyoak, K. J. (2015). Conceptual integration of arithmetic operations with real-world knowledge: Evidence from event-related potentials.
*Cognitive Science,*. doi: 10.1111/cogs.12238.Google Scholar - Hadamard, J. (1945).
*The psychology of invention in the mathematical field*. New York: Dover Publications.Google Scholar - Hajcak, G., Dunning, J. P., & Foti, D. (2009). Motivated and controlled attention to emotion: Time-course of the late positive potential.
*Clinical Neurology,**120*(3), 505–510.Google Scholar - Jausovec, N., & Jausovec, K. (2000). Correlations between ERP parameters and intelligence: A reconsideration.
*Biological Psychology,**55*(2), 137–154.CrossRefGoogle Scholar - Jung-Beeman, M., Bowden, E. M., Haberman, J., Frymiare, J. L., Arambel-Liu, S., Greenblatt, R., & Kounios, J. (2004). Neural activity when people solve verbal problems with insight.
*PLoS Biology,**2*(4), 500–510.CrossRefGoogle Scholar - Juottonen, K., Revonsuo, A., & Lang, H. (1996). Dissimilar age influences on two ERP waveforms (LPC and N400) reflecting semantic context effect.
*Cognitive Brain Research,**4*(2), 99–107.CrossRefGoogle Scholar - Kaan, E. (2007). Event-related potentials and language processing: A brief overview.
*Language and Linguistics Compass,**1*(6), 571–591.CrossRefGoogle Scholar - Kaiser, G., Blum, W., Ferri, R. B., & Stillman, G. (Eds.). (2011).
*Trends in teaching and learning of mathematical modelling: ICTMA14*(Vol. 1). New York: Springer Science & Business Media.Google Scholar - Kelly, A. C., & Garavan, H. (2005). Human functional neuroimaging of brain changes associated with practice.
*Cerebral Cortex,**15*(8), 1089–1102.CrossRefGoogle Scholar - Krutetskii, V. A. (1976).
*The psychology of mathematical abilities in schoolchildren*(translated from Russian by Teller, J.; edited by Kilpatrick, J., & Wirszup, I). Chicago: The University of Chicago Press.Google Scholar - Kutas, M., & Hillyard, S. A. (1984). Event-related brain potentials (ERPs) elicited by novel stimuli during sentence processinga.
*Annals of the New York Academy of Sciences,**425*(1), 236–241.CrossRefGoogle Scholar - Lee, K., Yeong, S. H., Ng, S. F., Venkatraman, V., Graham, S., & Chee, M. W. (2010). Computing solutions to algebraic problems using a symbolic versus a schematic strategy.
*ZDM - The International Journal on Mathematics Education,**42*(6), 591–605.CrossRefGoogle Scholar - Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight.
*Psychological Test and Assessment Modeling,**55*(4), 385–400.Google Scholar - Leikin, R. (2014). Giftedness and high ability in mathematics. In S. Lerman (Ed.),
*Encyclopedia of mathematics education*. Berlin: Springer.**(electronic version)**.Google Scholar - 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 - Leikin, M., Paz-Baruch, N., & Leikin, R. (2013b). Memory abilities in generally gifted and excelling-in-mathematics adolescents.
*Intelligence,**41*(5), 566–578.CrossRefGoogle Scholar - Lesh, R. A. (2003). A models and modeling perspective on problem solving. In R. Lesh & H. Doerr (Eds.),
*Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching*(pp. 317–336). Mahwah: Lawrence Erlbaum Associates.Google Scholar - Mai, X. Q., Luo, J., Wu, J. H., & Luo, Y. J. (2004). “Aha!” effects in a guessing riddle task: An event-related potential study.
*Human Brain Mapping,**22*(4), 261–270.CrossRefGoogle Scholar - Metcalfe, J., & Wiebe, D. (1987). Intuition in insight and non-insight problem solving.
*Memory and Cognition,**15*(3), 238–246.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 - 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 - Olofsson, J. K., Nordin, S., Sequeira, H., & Polich, J. (2008). Affective picture processing: an integrative review of ERP findings.
*Biological Psychology,**77*(3), 247–265.CrossRefGoogle Scholar - 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 - Paz-Baruch, N., Leikin, M., & Leikin, R. (2016). Visual processing in generally gifted and excelling in school mathematics adolescents.
*Journal for the Education of the Gifted***(forthcoming)**.Google Scholar - Polich, J. (2011). Neuropsychology of P300. In S. J. Luck & E. S. Kappenman (Eds.),
*Oxford handbook of event-related potential components*(pp. 159–188). Oxford: Oxford University Press.Google Scholar - Polya, G. (1973).
*How to solve it. A new aspect of mathematical method*. Princeton: Princeton University Press.Google Scholar - 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 - Qiu, J., Li, H., Yang, D., Luo, Y., Li, Y., Wu, Z., & Zhang, Q. (2008). The neural basis of insight problem solving: An event-related potential study.
*Brain and Cognition,**68*(1), 100–106.CrossRefGoogle Scholar - Raven, J., Raven, J. C., & Court, J. H. (2000).
*Manual for Raven’s progressive matrices and vocabulary scales*. Oxford: Oxford Psychologists.Google Scholar - Schneider, W., Eschman, A., & Zuccolotto, A. (2002).
*E-prime Computer Software (Version 1.0)*. Pittsburgh: Psychology Software Tools.Google Scholar - Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.),
*Handbook for research on mathematics teaching and learning*(pp. 334–370). New York: MacMillan.Google Scholar - Shen, W., Liu, C., Zhang, X., Zhao, X., Zhang, J., Yuan, Y., & Chen, Y. (2013). Right hemispheric dominance of creative insight: an event-related potential study.
*Creativity Research Journal,**25*(1), 48–58.CrossRefGoogle Scholar - Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing.
*ZDM,**29*(3), 75–80.CrossRefGoogle Scholar - Silver, E. A. (Ed.). (2003).
*Teaching and learning mathematical problem solving: Multiple research perspectives*. New York: Routladge.Google Scholar - Silverman, L. K. (2009). The measurement of giftedness. In L. V. Shavinina (Ed.),
*International handbook on giftedness*(pp. 947–970). Amsterdam: Springer.CrossRefGoogle Scholar - Spencer, K. M., Abad, E. V., & Donchin, E. (2000). On the search for the neurophysiological manifestation of recollective experience.
*Psychophysiology,**37*(4), 494–506.CrossRefGoogle Scholar - Sriraman, B., & English, L. (Eds.). (2010).
*Theories of mathematics education: Seeking new frontiers*. Heidelberg: Springer.Google Scholar - Star, J. R., & Newton, K. J. (2009). The nature and development of experts’ strategy flexibility for solving equations.
*ZDM - The International Journal on Mathematics Education,**41*(5), 557–567.CrossRefGoogle Scholar - 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 - Sternberg, R. J. (1985).
*Beyond IQ*. Cambridge: Cambridge University Press.Google Scholar - Võ, M. L. H., & Wolfe, J. M. (2013). Differential electrophysiological signatures of semantic and syntactic scene processing.
*Psychological Science,**24*(9), 1816–1823.CrossRefGoogle Scholar - 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 - Wang, T., Zhang, Q., Li, H., Qiu, J., Tu, S., & Yu, C. (2009). The time course of Chinese riddles solving: Evidence from an ERP study.
*Behavioural Brain Research,**199*(2), 278–282.CrossRefGoogle Scholar - Weisberg, R. W. (2015). Toward an integrated theory of insight in problem solving.
*Thinking and Reasoning,**21*(1), 5–39.CrossRefGoogle Scholar - Wieth, M., & Burns, B. D. (2006). Incentives improve performance on both incremental and insight problem solving.
*The Quarterly Journal of Experimental Psychology,**59*(8), 1378–1394.CrossRefGoogle Scholar - Yerushalmy, M. (2009). Educational technology and curricular design: Promoting mathematical creativity for all students. In R. Leikin, A. Berman, & B. Koichu (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 101–113). Rotterdam: Sense Publishers.Google Scholar - Zhang, M., Tian, F., Wu, X., Liao, S., & Qiu, J. (2011). The neural correlates of insight in Chinese verbal problems: An event related-potential study.
*Brain Research Bulletin,**84*(3), 210–214.CrossRefGoogle Scholar - Zhang, Z., Xing, Q., Li, H., Warren, C. M., Tang, Z., & Che, J. (2015). Chunk decomposition contributes to forming new mental representations: An ERP study.
*Neuroscience Letters,**598*, 12–17.CrossRefGoogle Scholar - Zhao, Y., Tu, S., Lei, M., Qiu, J., Ybarra, O., & Zhang, Q. (2011). The neural basis of breaking mental set: an event-related potential study.
*Experimental Brain Research,**208*(2), 181–187.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