Changing mathematical beliefs and achievement: The synergies of mindset ideas and effective teaching

Authors

DOI:

https://doi.org/10.48489/quadrante.32534

Keywords:

mathematics, mindsets, neuroscience, camp, math anxiety

Abstract

This paper reviews research showing the importance of changing students’ mindsets and mathematical beliefs, and the promising research that has shown the impact of infusing mindset ideas through the teaching of mathematics. Previous research has demonstrated increased motivation and brain activity in learners with a growth mindset when facing mathematics problems. This paper proposes a shift in focusing solely on positive mindset messages towards the reorganization of learning environments and teaching approaches, to what we call a Mathematical Mindset approach. It also presents the outcomes of a summer camp that was designed with a mathematical mindset approach and taught in 10 US districts and four countries.This paper reviews research showing the importance of changing students’ mindsets and mathematical beliefs, and the promising research that has shown the impact of infusing mindset ideas through the teaching of mathematics. Previous research has demonstrated increased motivation and brain activity in learners with a growth mindset when facing mathematics problems. This paper proposes a shift in focusing solely on positive mindset messages towards the reorganization of learning environments and teaching approaches, to what we call a Mathematical Mindset approach. It also presents the outcomes of a summer camp that was designed with a mathematical mindset approach and taught in 10 US districts and four countries. 

References

Aiken L. R. (1976). Update on attitudes and other affective variables in learning mathematics. Review of Educational Research, 46(2), 293–311. https://doi.org/10.3102/00346543046002293

Aiken, L. R., & Dreger, R. M. (1961). The effect of attitudes on performance in mathematics. Journal of Educational Psychology, 52(1), 19–24. https://doi.org/10.1037/h0041309

Bagès, C., Verniers, C., & Martinot, D. (2016). Virtues of a hardworking role model to improve girls’ mathematics performance. Psychology of Women Quarterly, 40(1), 55–64. https://doi.org/10.1177/0361684315608842

Beilock, S. (2015). How the body knows its mind: The surprising power of the physical environment to influence how you think and feel. Simon and Schuster.

Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246–263. https://doi.org/10.1111/j.1467-8624.2007.00995.x

Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. (International Perspectives on the Teaching and Learning of Mathematical Modelling) (pp. 15–30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3

Boaler, J. (2019). Prove it to me!. Mathematics Teaching in the Middle School, 24(7), 422–428. https://www.youcubed.org/wp-content/uploads/2019/05/prove-it-to-me-JB.pdf

Boaler, J. (2022). Mathematical mindsets: Unleashing students’ potential through creative mathematics, inspiring messages, and innovative teaching (2nd ed.). Jossey-Bass.

Boaler, J., Dieckmann, J. A., LaMar, T., Leshin, M., Selbach-Allen, M., & Pérez-Núñez, G. (2021). The transformative impact of a mathematical mindset experience taught at scale. Frontiers in Education, 6. https://doi.org/10.3389/feduc.2021.784393

Boaler, J., Dieckmann, J. A., Pérez-Núñez, G., Sun, K. L., & Williams, C. (2018). Changing students' minds and achievement in mathematics: The impact of a free online student course. Frontiers in Education, 3. https://doi.org/10.3389/feduc.2018.00026

Bonne, L., & Johnston, M. (2016). Students’ beliefs about themselves as mathematics learners. Thinking Skills and Creativity, 20, 17–28. https://doi.org/10.1016/j.tsc.2016.02.001

Boyd, P., & Ash, A. (2018). Mastery mathematics: Changing teacher beliefs around in-class grouping and mindset. Teaching and Teacher Education, 75, 214–223. https://doi.org/10.1016/j.tate.2018.06.016

Brez, C., Hampton, E. M., Behrendt, L., Brown, L., & Powers, J. (2020). Failure to replicate: Testing a growth mindset intervention for college student success. Basic and Applied Social Psychology, 42(6), 460–468. https://doi.org/10.1080/01973533.2020.1806845

Chen, L., Bae, S. R., Battista, C., Qin, S., Chen, T., Evans, T. M., & Menon, V. (2018). Positive attitude toward math supports early academic success: Behavioral evidence and neurocognitive mechanisms. Psychological Science, 29(3), 390–402. https://doi.org/10.1177/0956797617735528

Cheng, E. (2023, May 29). What if nobody is bad at maths? The Guardian. https://www.theguardian.com/books/2023/may/29/what-if-nobody-is-bad-at-maths

Chestnut, E. K., Lei, R. F., Leslie, S. J., & Cimpian, A. (2018). The myth that only brilliant people are good at math and its implications for diversity. Education Sciences, 8(2), 65. https://doi.org/10.3390/educsci8020065

Cimpian, A., & Leslie, S. J. (2017). The brilliance trap: How a misplaced emphasis on genius subtly discourages women and African-Americans from certain academic fields. Scientific American, 317, 60–65. https://www.jstor.org/stable/27109296

Daly, I., Bourgaize, J., & Vernitski, A. (2019). Mathematical mindsets increase student motivation: Evidence from the EEG. Trends in Neuroscience and Education, 15, 18–28. https://doi.org/10.1016/j.tine.2019.02.005

Doidge, N. (2007). The brain that changes itself: Stories of personal triumph from the frontiers of brain science. Penguin.

Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Heinemann.

Dweck, C. S. (2006). Mindset: The new psychology of success. Random House.

Dweck, C. S. (2015). Carol Dweck revisits the growth mindset. Education Week, 35(5), 20–24.

Dweck, C. S., & Yeager, D. S. (2019). Mindsets: A view from two eras. Perspectives on Psychological Science, 14(3), 481–496. https://doi.org/10.1177/1745691618804166

Gross-Loh, C. (2016, December 16). How praise became a consolation prize. The Atlantic. https://www.theatlantic.com/education/archive/2016/12/how-praise-became-a-consolation-prize/510845/

Gutierrez, R. (2000). Advancing African-American, urban youth in mathematics: Unpacking the success of one math department. American Journal of Education, 109(1), 63–111. https://doi.org/10.1086/444259

Hecht, C. A., Murphy, M. C., Dweck, C. S., Bryan, C. J., Trzesniewski, K. H., Medrano, F., Gianni, M. M., Mhatre, P., & Yeager, D. S. (2023). Shifting the mindset culture to address global educational disparities. Science of Learning, 8. https://doi.org/10.1038/s41539-023-00181-y

Iuculano, T., Rosenberg-Lee, M., Richardson, J., Tenison, C., Fuchs, L., Supekar, K., & Menon, V. (2015). Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities. Nature Communications, 6(1), 8453. https://doi.org/10.1038/ncomms9453

Kohn, A. (2015). The "Mindset" mindset: What we miss by focusing on kids’ attitudes. https://www.alfiekohn.org/article/mindset/

Leshin, M., LaMar, T., & Boaler, J. (in press). "When you let kids have a little bit of freedom, they'll surprise you": The role of reasoning in raising teacher expectations of student potential.

Letchford, L. (2018). Reversed: A memoir. Acorn Publishing.

Merzenich, M. (2013). Soft-wired: How the new science of brain plasticity can change your life. Parnassus.

OECD. (2019). Skills matter: Additional results from the survey of adult skills. OECD Publishing. https://doi.org/10.1787/9789264258051-en

O'Rourke, E., Haimovitz, K., Ballweber, C., Dweck, C., & Popović, Z. (2014, April). Brain points: A growth mindset incentive structure boosts persistence in an educational game. In CHI 14: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 3339–3348). https://doi.org/10.1145/2556288.2557157

Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86, 193–203. https://doi.org/10.1037/0022-0663.86.2.193

Ramirez, G., Shaw, S. T., & Maloney, E. A. (2018). Math anxiety: Past research, promising interventions, and a new interpretation framework. Educational Psychologist, 53(3), 145–164. https://doi.org/10.1080/00461520.2018.1447384

Rienzo, C., Rolfe, H., & Wilkinson, D. (2015). Changing mindsets: Evaluation report and executive summary. Education Endowment Foundation. https://eric.ed.gov/?id=ED581132

Schoenfeld, A. H., & Sloane, A. H. (Eds.). (2016). Mathematical thinking and problem solving. Routledge.

Singh, K., Granville, M., & Dika, S. (2002). Mathematics and science achievement: Effects of motivation, interest, and academic engagement. Journal of Educational Research, 95(6), 323–332. https://doi.org/10.1080/00220670209596607

Steele, C. M. (2011). Whistling Vivaldi: How stereotypes affect us and what we can do. W. W. Norton & Company.

Suárez-Pellicioni, M., Núñez-Peña, M. I., & Colomé, À. (2016). Math anxiety: A review of its cognitive consequences, psychophysiological correlates, and brain bases. Cognitive, Affective, & Behavioral Neuroscience, 16, 3–22. https://doi.org/10.3758/s13415-015-0370-7

Suri, M. (2023). The Big Bang of Numbers. W. W. Norton & Company.

Wang, A. Y., Fuchs, L. S., Fuchs, D., Gilbert, J. K., Krowka, S., & Abramson, R. (2019). Embedding self-regulation instruction within fractions intervention for third graders with mathematics difficulties. Journal of Learning Disabilities, 52(4), 337–348. https://doi.org/10.1177/0022219419851750

Yeager, D. S., Hanselman, P., Walton, G. M., Murray, J. S., Crosnoe, R., Muller, C., … & Dweck, C. S. (2019). A national experiment reveals where a growth mindset improves achievement. Nature, 573, 364–369. https://doi.org/10.1038/s41586-019-1466-y

Yeager, D. S., Trzesniewski, K. H., & Dweck, C. S. (2013). An implicit theories of personality intervention reduces adolescent aggression in response to victimization and exclusion. Child Development, 84(3), 970–988. https://doi.org/10.1111/cdev.12003

Young, C. B., Wu, S. S., & Menon, V. (2012). The neurodevelopmental basis of math anxiety. Psychological Science, 23(5), 492–501. https://doi.org/10.1177/0956797611429134

Zahrt, O. H., & Crum, A. J. (2020). Effects of physical activity recommendations on mindset, behavior and perceived health. Preventive Medicine Reports, 17, 101027. https://doi.org/10.1016/j.pmedr.2019.101027

Downloads

Published

2023-12-31

How to Cite

Boaler, J., Dieckmann, J., & Loos, R. A. (2023). Changing mathematical beliefs and achievement: The synergies of mindset ideas and effective teaching. Quadrante, 32(2), 195–208. https://doi.org/10.48489/quadrante.32534

Issue

Section

Articles