Email this article Student teachers’ conceptualizations of mathematical problem solving and the nature of their warrants
Zakaria Ndemo(1*), David K. J. Mtetwa(2)(1) Bindura University of Science Education
(2) University of Zimbabwe
(*) Corresponding Author
Abstract
Absence of inquiry about meaning of mathematical objects learners deal with has permeated the school mathematics curriculum. Deep learning through questioning situations can be achieved if learners are helped to embrace the argumentation discourse in their problem solving efforts. This paper reports on a study that investigated linkages between the kinds of mathematical arguments constructed by students and the students’ grasp of the concept of problem solving. With the overall goal of teasing out such linkages a questionnaire that elicited likert-style and textual data was administered to 30 undergraduate and 5 postgraduate mathematics education students. The two data sources were triangulated with reflective interviews guided by students’ written responses and their validations on likert items. Descriptive statistics were applied to likert data and directed content analysis was used to analyze and interpret the qualitative data. The study concluded that students lacked appropriate conceptions of the notion of problem solving and in particular their thinking as reflected in their arguments that contradicted current understandings on the construct. The fragile grasp of the idea of mathematical problem solving uncovered by this study has the potential to inform mathematics instruction
Keywords
References
References
Bleiler, S.K.,Thompson, D.R., & Krajc ̌evski, M. (2014). Providing feedback on students’
mathematical arguments: Validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17, 105-127.
Carlson, M.P., Bloom, I. (2005). The cyclic nature of problem solving: an emergent multidimensional
problem-solving-framework. Educational Studies in Mathematics, 58, 58-75.
Charmaz, K. (2014). Constructing grounded theory: A practical guide through qualitative analysis.
London: Sage.
Creswell, J.W. (2014). Research design: Qualitative, quantitative and mixed methods approaches.
London: Sage.
Dede, A.T. (2019). Arguments constructed within the mathematical modelling cycle. International
Journal of Mathematics Education in Science and Technology, 50(2), 292-314.
Driver, R., Newton, P., & Osborne, J. (2000). Establishingthe norms of scientific argumentation in
classrooms. Science Education, 84, 287-312.
Furingheti, F., & Morselli, F. (2011). Beliefs and beyond: hows and whys in the teaching of proof.
Mathematics Education, 43, 587-599.
Greiff, S.,Holt, V., & Funke, J. (2013). Perspective on problem solving in education: Analytical,
interactive and collaboration problem solving. The Journal of Problem Solving, 5(2), 71-91.
Greiger, V., & Galbraith, P. (1998). Developing a diagnostic framework for evaluating students’
approaches to applied mathematics. International Journal of Mathematics Education, Science and Technology, 29, 533-559.
Housman, D. & Porter, M. (2003). Proof schemes and learning strategies of above-average
mathematics students. Educational Studies in Mathematics, 53, 139-158.
Jonassen, D.H, & Kim, B. (2010). Arguing to learn and learning to argue: Design justifications and
guidelines. Educational Technology Research and Development, 58 (4), 439-457.
Kuhn, D. (1991). The skills argument. Cambridge: Cambridge University Press.
Lewis, J. (2009). Redefining qualitative methods: Believability of the fifth moment. International
Journal of Qualitative Methods, 8(2), 1-13.
Lawson, T. (2009). Cambridge sociology: an interview with Tony Lawson. Erasmus Journal of
Philosophy and Economics, 2(1), 100-122.
Liljedahl, P. , Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics
education. ICME-13 Topical surveys. Hambury: Hamburg University.
Lovett, M.C. (2002). Memory and cognitive processes. In D. Medin (Ed), Stevens handbook of
experimental psychology, 317-362.
Mamona-Downs, J., & Downs, M. (2013). Problem solving and its elements in forming proof. The
Mathematics Enthusiast, 1(1), 136-160.
Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Harlow: Pearson Prentice Hall.
Maxwell, J.A., & Mittapalli, K. (2010). Realism as a stance for mixed methods research. In A.
Tashakkori and T. Teddlie (Eds), Sage handbook of mixed methods in social behavioural research (pp.145-166). Washington DC: Sage Publications.
Maya, R., & Sumarmo, U. (2011). Mathematical understanding and proving abilities: Experiment
with undergraduate student by using modified Moore learning approach. IndoMS, Journal of Mathematics Education, 2(2), 231-250.
Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27,
-266.
Perkins, D.N., Farady, M., & Bushey, B. (1991). Everyday reasoning and the roots of intelligence. In
J.F. Voss, D.N.Perkins, & J.W. Segal (Eds.), Informal reasoning and education (pp. 83-106), Hillsdale, NJ: Erlbaum.
Punch, K.F.(2005). Introduction to social science research: Quantitative and qualitative approaches.
London: Sage.
Puri, B.K. (1996). Statistics in practice: An illustrated guide to SPSS. New York: Oxford University
Press.
Schoenfeld, A.H.(1992). Learning to think mathematically: Problem solving, metacognitionand sense-
making in mathematics. In D.A. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning, Macmillan Publishing Company, New York, pp.334-370.
Schoenfeld, A.H. (1982). Some thoughts on problem solving research and mathematics education. In
F.K. Lester & J. Garofalo (Eds.), Mathematical problem solving: Issues in Research. Franklin Institute Press, Philademia, pp. 27-37.
Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell
whether an argument proves a theorem? Journal for Research in Mathematics Education, 34, 4–36.
Stylianides, A.J., & Stylianides, G.J. (2009). Proof constructions and evaluations. Educational
Studies in Mathematics, 72(3), 237-253.
Toulmin, S. E. (2003). The uses of argument. Cambridge, UK: Cambridge University Press.
Ubuz, B., Dincer, S., & Bu ̈bu ̈l, A. (2013). Argumentation in undergraduate math courses: A study on
definition construction. In A.M. Lindmeier, & A. Heinze (Eds.), Proceedings of the 37th Conference of International Group for the Psychology of Mathematics Education: Vol. 4. (pp. 313-320). Kiel University: PME.
van Eemeren, F., Grootendorst, R., & Henkemans, F.S. (1996). Fundamentals of argumentation
theory: A handbook of historical backgrounds and contemporary developments. Mahwah. NJ: Erlbaum.
Varghese, T. (2009). Secondary-level teachers’ conceptions of mathematical proof. Issues in the
Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, 1-13.
Vinner, S. (1997). The pseudo-conceptual and pseudo-analytical thought processes in mathematics
learning. Educational Studies in Mathematics, 34, 97-129.
Walton, D.N. (1996). Argumentation schemes for presumptive reasoning. Mahwah NJ: Erlbaum
Associates.
Weber, K. (2001). Student difficulty in constructing proofs. The need for strategic knowledge.
Educational Studies in Mathematics, 48, 101-119.
Weber, K., & Mejia-Ramos, J.P. (2015). On relative and absolute conviction in mathematics. For the
Learning of Mathematics, 35(2), 3-18.
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