Skip to main content
Log in

Dangerous myths about “gifted” mathematics students

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

A number of myths about mathematically gifted students, mathematics itself, and programs designed to serve these students tend to inhibit educators, parents and students themselves from developing students’ mathematical creativity, expertise and enjoyment. This paper discusses some of the myths that can discourage students’ mathematical development, restrict their understanding of mathematics, and/or are well-intentioned solutions with unintended consequences and includes research results from a few mathematics programs and other studies designed to counteract these myths and maximize students’ mathematical achievement, engagement and innovation.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Abbreviations

AP:

Advanced placement

CCSS-M:

Common core state standards in mathematics

CERI:

Centre for Educational Research and Innovation

ESSA:

Every Student Succeeds Act

HS:

High school

MAA:

Mathematical Association of America

NAEP:

National Assessment of Educational Progress

NAGC:

National Association for Gifted Children

NCLB:

No Child Left Behind

NCSM:

National Council of Supervisors of Mathematics

NCTM:

National Council of Teachers of Mathematics

NSB:

National Science Board

OECD:

Organisation for Economic Co-operation and Development

PISA:

Programme for International Student Assessment

STEM:

Science, Technology, Engineering and Mathematics

TIMSS:

Trends in International Mathematics and Science Study

US:

United States

References

  • Binet, A. (1909). Les idées modernes sur les enfants. Paris: Flammarion. (Published in English as: Modern ideas about children. Menlo Park, CA: Suzanne Heisler, 1984).

    Google Scholar 

  • Boaler, J. (1997). When even women are losers: evaluating the experiences of ‘top set’ students. Journal of Curriculum Studies, 29(2), 165–182.

    Article  Google Scholar 

  • Boaler, J. (2016). Mathematical mindsets: unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco: Jossey-Bass.

    Google Scholar 

  • Bressoud, D., Camp, D., & Teague, D. (2012). Background to the MAA/NCTM statement on calculus. Reston: NCTM.

    Google Scholar 

  • Bush, V. (1945). Science—the endless frontier. A report to the President on a program for postwar scientific research. Washington, DC: U.S. Government Printing Office.

    Google Scholar 

  • Butterworth, B. (1999). What counts: How every brain is hardwired for math. New York: Simon and Schuster.

    Google Scholar 

  • Cepelewicz, J. (2016). How does a mathematician’s brain differ from that of a mere mortal?. Scientific American. http://www.scientificamerican.com/article/how-does-a-mathematician-s-brain-differ-from-that-of-a-mere-mortal/. Accessed 6 May 2016.

  • Collins, C. A., & Gan, L. (2013). Does sorting students improve scores? An analysis of class composition. Cambridge, MA: National Bureau of Economic Research (NBER).

    Book  Google Scholar 

  • Common Core State Standards for Mathematics. (2010). www.corestandards.org/Math/. Accessed 27 Nov 2015.

  • Dehaene, S. (1997). The number sense: how the mind creates mathematics. New York: Oxford University Press.

    Google Scholar 

  • Devlin, K. (1997). Mathematics: the science of patterns: the search for order in life, mind and the universe. New York: Scientific American Library.

    Google Scholar 

  • Devlin, K. (2000). The math gene: How mathematical thinking evolved and why numbers are like gossip. New York: Basic Books.

    Google Scholar 

  • Dweck, C. (2006a). Mindset: the new psychology of success. New York: Random House.

    Google Scholar 

  • Dweck, C. (2006b). Is math a gift? Beliefs that put females at risk. In S. J. Ceci & W. Williams (Eds.), Why aren’t more women in science? Top researchers debate the evidence. Washington, DC: American Psychological Association.

    Google Scholar 

  • Ellison, G., & Swanson, A. (2010). The gender gap in secondary school mathematics at high achievement levels: evidence from the American mathematics competitions. Journal of Economic Perspectives, 24(2), 109–128.

    Article  Google Scholar 

  • Finn, C. E., Jr., & Wright, B. L. (2015). Failing our brightest kids: the global challenge of educating high-ability students. Cambridge: Harvard Education Press.

    Google Scholar 

  • Gavin, M. K., Casa, T. M., Adelson, J. L., Carroll, S. R., & Sheffield, L. J. (2009). The impact of advanced curriculum on the achievement of mathematically promising elementary students. Gifted Child Quarterly, 53, 188–202.

    Article  Google Scholar 

  • Gavin, M. K., Casa, T. M., Adelson, J. L., & Firmender, J. M. (2013a). The impact of advanced geometry and measurement units on the achievement of grade 2 students. Journal for Research in Mathematics Education, 44(3), 478–510.

    Article  Google Scholar 

  • Gavin, M. K., Casa, T. M., Firmender, J. M., & Carroll, S. R. (2013b). The impact of advanced geometry and measurement units on the mathematics achievement of first-grade students. Gifted Child Quarterly, 57(2), 71–84.

    Article  Google Scholar 

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

    Google Scholar 

  • Jenkins, M. D. (1936). A socio-psychological study of Negro children of superior intelligence. The Journal of Negro Education, 5(2), 175–190.

    Article  Google Scholar 

  • Johnsen, S., & Sheffield, L. J. (Eds.). (2012). Using the common core state standards for mathematics with gifted and advanced learners. Washington, DC: National Association for Gifted Children.

    Google Scholar 

  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.

    Google Scholar 

  • Liljedahl, P. (2009). In the words of the creators. In R. Leikin, A. Berman and B. Koichu (eds.). Creativity in mathematics and the education of gifted students. pp 51–69.

  • Loveless, T. (2009). Tracking and detracking: high achievers in Massachusetts middle schools. Washington, DC: The Thomas B. Fordham Institute.

    Google Scholar 

  • Loveless, T. (2013). 2013 Brown Center report on American education: How well are American students learning? Part III: Advanced math in eighth grade. http://www.brookings.edu/research/reports/2013/03/18-brown-center-report-loveless. Accessed 17 Nov 2015.

  • Mann, E. (2006). Creativity: the essence of mathematics. Journal for the Education of the Gifted., 30(2), 236–260.

    Google Scholar 

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

    Google Scholar 

  • National Assessment of Educational Progress (NAEP). (2014). Technology and Engineering Literacy Overall Results. www.nationsreportcard.gov/. Accessed 26 May 2016.

  • National Council of Teachers of Mathematics. (1980). An agenda for action. Reston: NCTM.

    Google Scholar 

  • National Science Board (NSB). (2010). Preparing the next generation of STEM innovators: Identifying and developing our nation’s human capital. (NSB-10-33). Washington, DC: NSF.

    Google Scholar 

  • OECD (2015). The ABC of gender equality in education, aptitude, behavior, confidence. PISA: OEDC Publishing. https://www.oecd.org/pisa/keyfindings/pisa-2012-results-gender-eng.pdf. Accessed 14 March 2015.

  • OECD/CERI. (2007). Understanding the brain: the birth of a learning science. http://www.oecd.org/site/educeri21st/40554190.pdf. Accessed 2 May 2016.

  • Perry, M. J. (2015). 2015 SAT test results confirm pattern that’s persisted for 40+ years—high school boys are better at math than girls. https://www.aei.org/publication/2015-sat-test-results-confirm-pattern-thats-persisted-for-40-years-high-school-boys-are-better-at-math-than-girls/. Accessed 26 May 2016.

  • Picciotto, H. (2016). Hyper-acceleration. http://www.mathedpage.org/teaching/acceleration.html. Accessed 4 May 2016.

  • Polya, G. (1945). How to solve it: a new aspect of mathematical method. Princeton: Princeton University Press.

    Google Scholar 

  • Sawyer, W. W. (1955). Prelude to mathematics. London: Penguin.

    Google Scholar 

  • Sheffield, L. J., Bennett, J., Berriozabal, M., DeArmond, M., & Wertheimer, R. (1999). Report of the NCTM task force on the mathematically promising. In L. J. Sheffield (Ed.), Developing mathematically promising students (pp. 309–316). Reston: NCTM.

    Google Scholar 

  • Sheffield, L. J., Firmender, J., Gavin, M. K., & Casa, T. M. (2012). Project M2: mentoring young mathematicians. The 7th MCG International Conference Proceedings (pp. 269–276). Busan: Mathematical Creativity and Giftedness.

    Google Scholar 

  • Shenk, D. (2010). The genius in all of us: why everything you’ve been told about genetics, talent, and IQ is wrong. New York: Doubleday.

    Google Scholar 

  • Tyre, P. (2016). The math revolution. The Atlantic. http://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/. Accessed 15 April 2016.

  • Velez, W. Y., Maxwell, J. W., & Rose, C. (2013). Report on the 2012–2013 new doctoral recipients. Notices of the American Mathematical Society, 61(8), 874–884.

    Google Scholar 

  • Yong, E. (2016). The genetics of staying in school. The Atlantic. http://www.theatlantic.com/science/archive/2016/05/the-genetics-of-staying-in-school/482052/. Accessed 16 May 2016.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Linda Jensen Sheffield.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheffield, L.J. Dangerous myths about “gifted” mathematics students. ZDM Mathematics Education 49, 13–23 (2017). https://doi.org/10.1007/s11858-016-0814-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-016-0814-8

Keywords

Navigation