The Effect of Problem Solving Course on Pre-Service Teachers’ Beliefs about Problem Solving in School Mathematics and Themselves as Problem Solvers
DOI:
https://doi.org/10.15291/magistra.1494Keywords:
pre-service teachers, explicit teaching, problem solving, beliefs and attitudesAbstract
Problem solving in schools begins with mathematics teachers. The degree to which mathematics teachers are prepared to teach for, about and through problem solving influences on their implementation of problem solving in school. We conducted a small scale study where we examined the effect of implementation of heuristic strategies and Polya’s steps in mathematics method course. We assessed pre-service teachers’ knowledge and attitudes about them as problem solvers before and after the course. Moreover we assessed their beliefs of problem solving in school mathematics. Those beliefs were assessed in two occasions: right after the course and after finished teaching practice. Although students’ knowledge on problem solving was improved, the results of students’ beliefs show that it is important that pre-service teachers, and consequently in-service teachers, are constantly reminded on the positive effect of constructivist and inquiry-based approach on teaching mathematics.References
Archer, A. L., & Hughes, C. A. (2011). Explicit instruction: Effective and efficient teaching. New York: Guilford Press.
Babakhani, N. (2011). The effect of teaching the cognitive and meta-cognitive strategies (self-instruction procedure) on verbal math problem-solving performance of primary school students with verbal problem solving difficulties. Procedia - Social and Behavioral Sciences, 15, 563–570.
Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT, 3(1), 19-36.
Eisenmann, P., Novotná, J., Přibyl, J., Břehovský, J. (2015). The development of a culture of problem solving with secondary students through heuristic strategies. Mathematics Education Research Journal, 27(4). 535–562, doi:10.1007/s13394-015-0150-2
Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41(5), 605–618.
Ellis, A. (2005). Research on educational innovations. Larchmont, NY: Eye On Education Inc.
Felbrich, A., Muller, C., & Blomeke, S. (2008). Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics. ZDM Mathematics Education, 40, 763-776.
Glasnović Gracin, D. (2011). Requirements in mathematics textbooks and PISA assessment. (Doctoral dissertation, University of Klagenfurt). Klagenfurt: University of Klagenfurt.
Hart, L. C. (2002). Preservice Teachers' Beliefs and Practice After Participating in an Integrated Content/Methods Course. School Science and Mathematics, 102, 4–14, doi:10.1111/j.1949-8594.2002.tb18191.x
Jonassen, D. H. (2011). Learning to solve problems: a handbook for designing problem-solving learning environments. New York: Routledge
Lortie, D. (1975). Schoolteacher: A sociological study. Chicago: University of Chicago Press.
MZOS [Ministarstvo znanosti, obrazovanja i športa] (2010). Nacionalni okvirni kurikulum. Zagreb: Ministarstvo znanosti, obrazovanja i športa Republike Hrvatske. In Croatian
NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Pajares, F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem solving. Contemporary Educational Psychology, 20(4), 426–443.
Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(1), 307-332.
Polya, G. (1945). How to solve it. New York: Doubleday.
Portnov-Neeman, Y., & Amit, M. (2015). Using an explicit teaching approach to develop strategic spirit: The case of the working backwards strategy. In A. Rogerson (ed.), Proceedings of the 13th International Conference Mathematics in a Connected World. Sicily, Italy.
Resnick, L. B. (1988). Treating mathematics as an ill-structured discipline. In R. I. Charles & E. A. Silver (Eds.), Research agenda for mathematics education: The teaching and assessing of mathematical problem solving (pp. 32-60). Reston, VA: National Council of Teachers of Mathematics.
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (pp.102-119). New York: Simon & Schuster.
Schoenfeld, A. H. (1985). Mathematical problem solving. London: Academic Press.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York, NY: Macmillan
Tetzlaff, T. (2009). Constructivist learning versus explicit teaching: A personal discovery of balance (Master's thesis). Retrieved from: http://www.cct.umb.edu/tetzlaff.pdf
Toh, P. C., Leong, Y. H., Toh, T. L., Dindyal, J., Quek, K. S., Tay, E. G., & Ho, F. H. (2014). The problem-solving approach in the teaching of number theory. International Journal of Mathematical Education in Science and Technology, 45(2), 241-255, doi: 10.1080/0020739X.2013.822580
Toh T. L., Quek, K. S., Tay, E. G. (2009). Mathematical problem solving – a new paradigm. In In J. Vincent, R. Pierce, & J. Dowsey (Eds.), Connected maths (pp. 356–365). Melbourne: Mathematical Association of Victoria
Toh T. L., Quek K. S., Tay, E. G., Leong, Y. H., Toh, P. C., Ho, F. H. & Dindyal, J. (2013). Infusing Problem Solving into Mathematics Content Course for Pre-service Secondary School Mathematics Teachers. The Mathematics Educator, 15(1), 98-120.
Yusof, Y. B. M., & Tall. D. (1994). Changing Attitudes to Mathematics through Problem Solving. In J. P. da Ponte & J. F. Matos (Eds.), Proceedings of 18th Psychology of Mathematics Education (Volume IV, pp. 401– 408), Lisbon, Portugal
Zollman, A., & Mason, E. (1992). The Standards’ Beliefs Instrument (SBI): Teachers’ beliefs about the NCTM Standards. School Science and Mathematics, 92(7), 359-364.
