Relationship between mathematical flexibility and success in national examinations

Peter Hästö 1 2 * , Riikka Palkki 2, Dimitri Tuomela 2, Jon R. Star 3
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1 University of Turku, Department of Mathematics and Statistics
2 University of Oulu, Department of Mathematical Sciences
3 Harvard University, Faculty of Education
* Corresponding Author
EUR J SCI MATH ED, Volume 7, Issue 1, pp. 1-13. https://doi.org/10.30935/scimath/9530
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ABSTRACT

Flexibility is an important element in learning mathematics. The purpose of this study was to investigate whether flexibility in linear equation solving predicts future academic achievement in mathematics and other subjects. Participants were 149 Finnish high-school students. Results show that flexibility was related to grades in both tracks of mathematics, chemistry, and mother tongue, as well as the total number of exams taken in the national matriculation examination. However, when controlling for accuracy in equation solving, only basic level mathematics and, to some degree, chemistry grade were related to flexibility. On the other hand, flexibility had an impact on students’ choice to participate in the mathematics and physics exams. A theoretical analysis shows that student selection may mask part of the relationship between flexibility and grade.
Keywords: flexibility, equation solving, national matriculation examination, student choice

CITATION

Hästö, P., Palkki, R., Tuomela, D., & Star, J. R. (2019). Relationship between mathematical flexibility and success in national examinations. European Journal of Science and Mathematics Education, 7(1), 1-13. https://doi.org/10.30935/scimath/9530

REFERENCES

  • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), Studies in mathematical thinking and learning. The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1–33). Mahwah, NJ, US: Lawrence Erlbaum Associates Publishers.
  • DesJardins, S.L., & Toutkoushian, R.K. (2005). Are Students Really Rational? The Development of Rational Thought and its Application to Student Choice. In: Smart J.C. (eds) Higher Education: Handbook of Theory and Research. Higher Education: Handbook of Theory and Research, vol 20. Dordrecht, Netherlands:Springer.
  • Harwell, M., Rubinstein, E., Hayes, W., & Olds, C. (1992). Summarizing Monte Carlo Results in Methodological Research: The One- and Two-Factor Fixed Effects ANOVA Cases. Journal of Educational Statistics, 17(4), 315-339.
  • Heinze, A., Star, J.R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535–540.
  • Kerlinger, F.N., & Lee, H.B. (2000). Foundations of behavioral research. 4th Ed. Orlando, FL, Harcourt college publishers.
  • Maxwell, S.E., & Delaney, H.D. (2003). Designing experiments and analyzing data: A model comparison perspective. Routledge: Abingdon, United Kingdom.
  • McMullen, J., Brezovszky, B., Hannula-Sormunen, M.M., Veermans, K., Rodríguez-Aflecht, G., Pongsakdi, N., & Lehtinen, E. (2017). Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge. Learning and Instruction, 49, 178–187.
  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, D.C.: Authors.
  • Opetushallitus (2015). Lukion opetussuunnitelman perusteet. Helsinki, Finland: Authors.
  • Rittle-Johnson, B., & Star, J.R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561–574.
  • Rittle-Johnson, B., Star, J.R., & Durkin, K. (2012). Developing procedural flexibility: Are novices prepared to learn from comparing procedures? British Journal of Educational Psychology, 82(3), 436–455.
  • Schneider, M., Rittle-Johnson, B., & Star, J.R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525–1538.
  • Star, J.R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and instruction, 18(6), 565–579.
  • Verschaffel, L., Luwel, K., Torbeyns, J. & Van Dooren, W. (2007). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education, European Journal of Psychology of Education, 24: 335–359.
  • Wright, D.B. (2006). Comparing groups in a before–after design: When t test and ANCOVA produce different results. British Journal of Educational Psychology, 76(3), 663–675.
  • Xu, L., Liu, R., Star, J.R., Wang, J., Liu, Y., Zhen, R. (2017). Measures of potential flexibility and practical flexibility in equation solving. Frontiers in Psychology, 8, 1368.