Skip to main content
SpringerLink
Log in

Giftedness and High Ability in Mathematics

  • Living reference work entry
  • First Online:
Encyclopedia of Mathematics Education

Introduction

The mystery of mathematical giftedness has remained a subject of educational debate for many years. Initially, the analysis of the mathematical mind focused on the activities of prominent mathematicians. At the beginning of the twentieth century, Poincare (1908) – French mathematician, theoretical physicist, engineer, and philosopher of science – shared his introspective analysis on mathematicians’ thought in the keynote address before the French Psychological Society. He brought forward the importance of the analysis of mathematical thought and stressed that mathematical creation requires special abilities, including a feeling of mathematical order and mathematical intuition. Later, J Hadamard (1945/1954) – internationally known mathematician and awardee of the CNRS 1956 Gold medal, which is the highest scientific research award in France – examined “The Psychology of Invention in the Mathematical Field.” He investigated the creative practices of some of the greatest...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Amalric M, Dehaene S (2016) Origins of the brain networks for advanced mathematics in expert mathematicians. Proc Natl Acad Sci 113(18):4909–4917

    Article  Google Scholar 

  • Anderson JR, Betts S, Ferris JL, Fincham JM (2011) Cognitive and metacognitive activity in mathematical problem solving: prefrontal and parietal patterns. Cogn Affect Behav Neurosci 11(1):52–67

    Article  Google Scholar 

  • Arsalidou M, Taylor MJ (2011) Is 2+ 2= 4? Meta-analyses of brain areas needed for numbers and calculations. NeuroImage 54(3):2382–2393

    Article  Google Scholar 

  • Carlson MP, Bloom I (2005) The cyclic nature of problem solving: an emergent multidimensional problem-solving framework. Educ Stud Math 58(1):45–75

    Article  Google Scholar 

  • Chi MTH, Glaser R, Farr MJ (1988) The nature of expertise. Hillsdale, NJ: Erlbaum

    Google Scholar 

  • Cowan N (1998) Visual and auditory working memory capacity. Trends Cogn Sci 2(3):77

    Article  Google Scholar 

  • Csikszentmihalyi M (1988) Society, culture, and person: a systems view of creativity. In: Sternberg RJ (ed) The nature of creativity. Cambridge University Press, New York, pp 325–339

    Google Scholar 

  • Dark VJ, Benbow CP (1990) Enhanced problem translation and short-term memory: components of mathematical talent. J Educ Psychol 82(3):420

    Article  Google Scholar 

  • Davidson JE, Sternberg RJ (eds) (2003) The psychology of problem solving. Cambridge university press, Cambridge

    Google Scholar 

  • Desco M, Navas-Sanchez FJ, 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

    Google Scholar 

  • Dietrich A, Kanso R (2010) A review of EEG, ERP, and neuroimaging studies of creativity and insight. Psychol Bull 136(5):822

    Article  Google Scholar 

  • Dweck CS (2012) Mindset: the new psychology of success. Constable & Robinson Limited, New York

    Google Scholar 

  • Ericsson KA, Lehmann AC (1996) Expert and exceptional performance: evidence of maximal adaptation to task constraints. Annu Rev Psychol 47(1):273–305

    Article  Google Scholar 

  • Ervynck G (1991) Mathematical creativity. In: Tall D (ed) Advanced mathematical thinking. Kluwer, Dordrecht, pp 42–53

    Google Scholar 

  • Eysenck MW, Keane MT (2010) Attention and performance. In: Cognitive psychology: a student’s handbook, vol 7. Psychology Press, Hove, pp 195–253

    Google Scholar 

  • Gardner H (1983/2003) Frames of mind: the theory of multiple intelligences. Basic Books, New York

    Google Scholar 

  • Geary DC (2011) Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Dev Psychol 47(6):1539

    Article  Google Scholar 

  • Goldin GA (2009) The affective domain and students’ mathematical inventiveness. In: Leikin R, Berman A, Koichu B (eds) Creativity in mathematics and the education of gifted students. Sense Publishers, Rotterdam, pp 149–163 (in press)

    Google Scholar 

  • Grabner RH, Neubauer AC, Stern E (2006) Superior performance and neural efficiency: the impact of intelligence and expertise. Brain Res Bull 69(4):422–439

    Article  Google Scholar 

  • Hadamard J (1945/1954) The psychology of invention in the mathematical field. Dover Publications, New York

    Google Scholar 

  • Hindal HS (2014) Visual-spatial learning: a characteristic of gifted students. Eur Sci J 10(13):557–574

    Google Scholar 

  • Jensen AR (1993) Why is reaction time correlated with psychometric g? Curr Dir Psychol Sci 2(2):53–56

    Article  Google Scholar 

  • Johnson W, Bouchard TJ (2005) The structure of human intelligence: it is verbal, perceptual, and image rotation (VPR), not fluid and crystallized. Intelligence 33(4):393–416

    Article  Google Scholar 

  • Krutetskii VA (1968/1976) The psychology of mathematical abilities in schoolchildren. (trans: Russian by Teller J; Edited by Kilpatrick J & Wirszup I). The University of Chicago Press, Chicago

    Google Scholar 

  • Lee K, Yeong SH, Ng SF, Venkatraman V, Graham S, Chee MW (2010) Computing solutions to algebraic problems using a symbolic versus a schematic strategy. ZDM - The International Journal on Mathematics Education 42(6):591–605

    Google Scholar 

  • Leikin M, Paz-Baruch N, Leikin R (2013) Memory Abilities in Generally Gifted and Excelling-in-mathematics Adolescents. Intelligence 41:566–578

    Google Scholar 

  • Leikin R (2009a) Bridging research and theory in mathematics education with research and theory in creativity and giftedness. In: Leikin R, Berman A, Koichu B (eds) Creativity in mathematics and the education of gifted students. Sense Publishers, Rotterdam, pp 383–409

    Google Scholar 

  • Leikin R (2009b) Exploring mathematical creativity using multiple solution tasks. In: Leikin R, Berman A, Koichu B (eds) Creativity in mathematics and the education of gifted students. (Ch. 9. Sense Publisher, Rotterdam, pp 129–145

    Google Scholar 

  • Leikin R (2013) Evaluating mathematical creativity: the interplay between multiplicity and insight. Psychol Test Assessment Model 55(4):385–400

    Google Scholar 

  • Paz-Baruch N, Leikin M, Aharon-Peretz J, Leikin R (2014) Speed of information processing in generally gifted and excelling in mathematics adolescents. High Abil Stud 25(2):143–167

    Google Scholar 

  • Leikin R (2016) Interplay between creativity and expertise in teaching and learning of mathematics. In Csíkos C, Rausch A, Szitányi J (eds) Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19–34). Szeged, Hungary: PME

    Google Scholar 

  • Leikin R, Leikin M, Paz-Baruch N, Waisman I, Lev M (2017) On the four types of characteristics of super mathematically gifted students. High Ability Studies, 28(1):107–125

    Google Scholar 

  • Leikin R, Sriraman B (eds) (2017) Creativity and giftedness: interdisciplinary perspectives from mathematics and beyond, Advances in mathematics education series. Springer, Basel

    Google Scholar 

  • Leikin R, Waisman I, Leikin M (2016) Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study. ZDM – Int J Math Educ 48(3):305–319

    Article  Google Scholar 

  • Lester FK (1994) Musings about mathematical problem-solving research: 1970–1994. J Res Math Educ 25(6):660–675

    Article  Google Scholar 

  • Logie RH (1995) Visuo-spatial working memory. Lawrence Erlbaum, Hove

    Google Scholar 

  • Lubinski D, Benbow CP (2006) Study of mathematically precocious youth after 35 years: uncovering antecedents for the development of math-science expertise. Perspect Psychol Sci 1:316–345

    Article  Google Scholar 

  • Metcalfe J, Wiebe D (1987) Intuition in insight and noninsight problem solving. Mem Cogn 15(3):238–246

    Article  Google Scholar 

  • Milgram R, Hong E (2009) Talent loss in mathematics: causes and solutions. In: Leikin R, Berman A, Koichu B (eds) Creativity in mathematics and the education of gifted students. Sense Publishers, Rotterdam, pp 149–163

    Google Scholar 

  • Myers T, Carey E, Szűcs D (2017) Cognitive and neural correlates of mathematical giftedness in adults and children: a review. Front Psychol 8:1646

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (1995) Report of the NCTM task force on the mathematically promising. NCTM News Bulletin, p. 32. Retrieved from http://www.lindajsheffield.com/resources/nctm-task-force

  • National Council of Teachers of Mathematics (2000) Principles and standards for school mathematics. Reston, VA: NCTM

    Google Scholar 

  • Neubauer AC, Fink A (2009) Intelligence and neural efficiency. Neurosci Biobehav Rev 33(7):1004–1023

    Article  Google Scholar 

  • O’Boyle MW (2005) Some current findings on brain characteristics of the mathematically gifted adolescent. Int Edu J 6(2):247–251

    Google Scholar 

  • Poincare H (1908/1952) Science and method. Dover Publications Inc, New York

    Google Scholar 

  • Prescott J, Gavrilescu M, Cunnington R, O’Boyle MW, Egan GF (2010) Enhanced brain connectivity in math-gifted adolescents: an fMRI study using mental rotation. Cogn Neurosci 1(4):277–288

    Article  Google Scholar 

  • Renzulli JS (1978) What makes giftedness? Reexamining a definition. Phi Delta Kappan 60(3):180

    Google Scholar 

  • Renzulli JS (2000) The identification and development of giftedness as a Paradign for school reform. J Sci Educ Technol 9(2):95–114

    Article  Google Scholar 

  • Rohde TE, Thompson LA (2007) Predicting academic achievement with cognitive ability. Intelligence 35(1):83–92

    Article  Google Scholar 

  • Royer JM, Tronsky LN, Chan Y, Jackson SJ, Marchant H III (1999) Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemp Educ Psychol 24(3):181–266

    Article  Google Scholar 

  • Schoenfeld AH (1992) Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook of research on mathematics teaching and learning 334–370

    Google Scholar 

  • Sheffield LJ (2017) Dangerous myths about “gifted” mathematics students. ZDM – Int J Math Educ 49(1):13–23

    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. Creat Res J 25(1):48–58

    Article  Google Scholar 

  • Sheppard LD, Vernon PA (2008) Intelligence and speed of information-processing: a review of 50 years of research. Personal Individ Differ 44(3):535–551

    Article  Google Scholar 

  • Silver EA (1997) Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM Int J Math Educ 29(3):75–80

    Article  Google Scholar 

  • Sriraman B (2005) Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. J Second Gift Educ 17:20–36

    Article  Google Scholar 

  • Star JR, Newton KJ (2009) The nature and development of experts’ strategy flexibility for solving equations. ZDM 41(5):557–567

    Article  Google Scholar 

  • Sternberg R (2001) Giftedness as developing expertise. In: Sternberg R (ed) International handbook of giftedness and talent. Elsevier Science Ltd, Oxford, pp 55–66

    Google Scholar 

  • Sternberg RJ (2005) Creativity or creativities? Int J Hum Comput Stud 63(4–5):370–382

    Article  Google Scholar 

  • Subotnik RF, Pillmeier E, Jarvin L (2009) The psychosocial dimensions of creativity in mathematics: implications for gifted education policy. In: Leikin R, Berman A, Koichu B (eds) Creativity in mathematics and the education of gifted students. Sense Publishers, Rotterdam, pp 165–179

    Google Scholar 

  • Sweller J, Mawer RF, Ward MR (1983) Development of expertise in mathematical problem solving. J Exp Psychol Gen 112(4):639

    Article  Google Scholar 

  • Tolar TD, Lederberg AR, Fletcher JM (2009) A structural model of algebra achievement: computational fluency and spatial visualisation as mediators of the effect of working memory on algebra achievement. Educ Psychol 29(2):239–266

    Article  Google Scholar 

  • Torrance EP (1974) Torrance tests of creative thinking. Directions manual and scoring guide, verbal test booklet B. Scholastic Testing Service, Bensenville

    Google Scholar 

  • Treffinger DJ, Renzulli JS (1986) Giftedness as potential for creative productivity: transcending IQ scores. Roeper Rev 8(3):150–154

    Article  Google Scholar 

  • Vogeli BR (ed) (2015) Special secondary schools for the mathematically talented: an international panorama, Series on mathematics education, vol 12. World Scientific, Denver

    Google Scholar 

  • Vygotsky LS (1930a) Imagination and its development in childhood. In: Davydov VV (ed) General problems of psychology. The collected works of L. S. Vygotsky, vol 2. Pedagogika, Moscow, pp 438–454 (in Russian)

    Google Scholar 

  • Vygotsky LS (1930b) Imagination and creativity in adolescent. In: Elkonin DB (ed) Child psychology. The collected works of L. S. Vygotsky, vol 4. Pedagogika, Moscow, pp 199–219 (in Russian)

    Google Scholar 

  • Waisman I, Leikin M, Leikin R (2016) Brain activity associated with logical inferences in geometry: Focusing on students with different levels of ability. Special issue on neuro-science and mathematics education - ZDM - The International Journal on Mathematics Education 48(3):321–335

    Google Scholar 

  • Weisberg RW (2015) Toward an integrated theory of insight in problem solving. Think Reason 21(1):5–39

    Article  Google Scholar 

  • Zeki S, Romaya JP, Benincasa DMT, Atiyah MF (2014) The experiences of mathematical beauty and its neural correlates. Front Hum Neurosci 8:68

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Education, Department of Mathematics Education, RANGE Center, Neuro-Cognitive Laboratory for the Investigation of Creativity, Ability and Giftedness, University of Haifa, Haifa, Israel

    Roza Leikin

Authors
  1. Roza Leikin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roza Leikin .

Editor information

Editors and Affiliations

  1. South Bank University Centre for Mathematics Education, London, United Kingdom

    Steve Lerman

Section Editor information

  1. Department of Science Teaching, The Weizmann Institute of Science, Rehovot, Israel

    Ruhama Even

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Leikin, R. (2018). Giftedness and High Ability in Mathematics. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_65-4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-77487-9_65-4

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77487-9

  • Online ISBN: 978-3-319-77487-9

  • eBook Packages: Springer Reference EducationReference Module Humanities and Social SciencesReference Module Education

Publish with us

Policies and ethics

Search

Navigation