Thematic problem solving: a case study on an approach to teaching problem solving in undergraduate mathematics
DOI:
https://doi.org/10.21100/msor.v17i2.978Keywords:
Problem solving, mathematics education, realistic mathematics education, cognitive process.Abstract
Specialist mathematics, statistics and operational research (MSOR) programmes are recognised as intellectually demanding, and require students to formulate, abstract, and solve mathematical problems in a rigorous way. The process of developing the skills to do this well and communicate results can be challenging for learners as it requires a deep understanding of themes in mathematics as well as methods for solving problems. In this article we demonstrate how elements of Freudenthal’s Realistic Mathematics Education can be applied to teaching problem solving in undergraduate mathematics programmes. We describe an approach that moves away from standard practices and goes beyond problem solving methods to develop an understanding of common themes in mathematics.References
Bransford, J.D., and Stein, B.S., 1993. The IDEAL Problem Solver: Guide for Improving Thinking, Learning and Creativity. W.H. Freeman & Co.
Freudenthal, H., 1968. Why to teach mathematics as to be useful? Educational Studies in Mathematics, 1 (1), pp.3–8. Available at: https://www.jstor.org/stable/3481973 [Accessed 11 March 2019].
Freudenthal, H., 1973. Mathematics as an Educational Task. Springer.
Freudenthal, H., 1991. Revisiting Mathematics Education: China Lectures. Springer.
Gravemeijer, K., 1994. Developing Realistic Mathematics Education. Doctoral dissertation, Utrecht University. Utrecht: CdBeta Press.
Gravemeijer, K., and Terwel, J., 2000. Hans Freudenthal: A mathematician on didactics and curriculum theory. Journal of Curriculum Studies, Vol. 32, no. 6, pp.777–796.
Jones, F.B., 1977. The Moore Method. The American Mathematical Monthly, 84:4, pp.273-278.
Kintsch, W., and Greeno, J.G., 1985. Understanding and solving word arithmetic problems. Psychological Review, 92(1), pp.109–129.
Lakatos, I., 1976. Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
Mason, J., Burton, L., and Stacey, K., 2010. Thinking Mathematically (2nd Ed.). London: Prentice Hall.
Mayer, R., 1992. Mathematical problem solving: Thinking as based on domain specific knowledge. In R. Mayer [ed.], Thinking, problem solving, and cognition, pp.455–489. W.H. Freeman & Co.
Polya, G., 1957. How to Solve It. Princeton: Princeton University Press.
Resusser, K., 1996. From cognitive modelling to the design of pedagogical tools. In S. Vosniadou, E. De Corte, R. Glaser, and H. Mandl [eds.], International perspectives on the design of technology-supported learning environments, pp.81–103. Mahwah, NJ: Lawrence Erlbaum.
