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.
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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).
Boaler, J. (1997). When even women are losers: evaluating the experiences of ‘top set’ students. Journal of Curriculum Studies, 29(2), 165–182.
Boaler, J. (2016). Mathematical mindsets: unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco: Jossey-Bass.
Bressoud, D., Camp, D., & Teague, D. (2012). Background to the MAA/NCTM statement on calculus. Reston: NCTM.
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.
Butterworth, B. (1999). What counts: How every brain is hardwired for math. New York: Simon and Schuster.
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).
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.
Devlin, K. (1997). Mathematics: the science of patterns: the search for order in life, mind and the universe. New York: Scientific American Library.
Devlin, K. (2000). The math gene: How mathematical thinking evolved and why numbers are like gossip. New York: Basic Books.
Dweck, C. (2006a). Mindset: the new psychology of success. New York: Random House.
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.
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.
Finn, C. E., Jr., & Wright, B. L. (2015). Failing our brightest kids: the global challenge of educating high-ability students. Cambridge: Harvard Education Press.
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.
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.
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.
Hadamard, J. (1954). The psychology of invention in the mathematical field. New York: Dover Publications.
Jenkins, M. D. (1936). A socio-psychological study of Negro children of superior intelligence. The Journal of Negro Education, 5(2), 175–190.
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.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
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.
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.
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.
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.
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.
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.
Sawyer, W. W. (1955). Prelude to mathematics. London: Penguin.
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.
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.
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.
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.
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.
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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
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DOI: https://doi.org/10.1007/s11858-016-0814-8