Inconsistency Among Beliefs, Knowledge, and Teaching Practice in Mathematical Problem Solving: A Case Study of a Primary Teacher

Tatag Yuli Eko Siswono, Ahmad Wachidul Kohar, Ika Kurniasari, Sugi Hartono

Abstract


This is a case study investigating a primary teacher’s beliefs, knowledge, and teaching practice in mathematical problem solving. Data was collected through interview of one primary teacher regarding his beliefs on the nature of mathematics, mathematics teaching, and mathematics learning as well as knowledge about content and pedagogy of problem solving. His teaching practice was also observed which focused on the way he helped his students solve several different mathematics problems in class based on Polya’s problem
solving process: understand the problem, devising a plan, carrying out the plan, and looking back. Findings of this study point out that while the teacher’s beliefs, which are closely related to his problem solving view, are consistent with his knowledge of problem solving, there is a gap between such beliefs and knowledge around his teaching practice. The gap appeared primarily around the directive teaching which corresponds to instrumental view he held in most of Polya’s process during his teaching practice, which is not consistent with beliefs and knowledge he professed during the interview. Some possible causes related to several associate factors such as immediate classroom situation and teaching practice experience are discussed to explain such inconsistency. The results of this study are encouraging, however, further studies still need to be conducted.


Keywords


inconsistency; problem solving; teacher beliefs; teacher knowledge; teaching practice

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References


Anderson, J., White, P., & Sullivan, P. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem-solving beliefs and practices. Mathematics Education Research Journal, 17(2), 9-38. https://doi.org/10.1007/BF03217414

Antonius, S., Haines, C., Jensen, T. H., Niss, M., & Burkhardt, H. (2007). Classroom activities and the teacher. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 295-308). New York: Springer.

Beswick, K. (2005). The belief/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39-68.

Blum, W., & Ferri, R. B. (2009). Mathematical modeling: can it be taught and learned? Journal of Mathematical Modelling and Application, 1(1), 45-58.

Bray, W. S. (2011). A collective case study of the influence of teachers' beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics Education, 42(1), 2-38.

Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT, 3, 19-36

Empson, S. B., & Junk, D. L. (2004). Teachers’ knowledge of children’s mathematics after implementing a student-centered curriculum. Journal of Mathematics Teacher Education, 7, 121-144

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Eds.), Mathematics teaching: The state of the art (pp. 249-253). New York: Falmer.

Fennema, E., Carpenter, T. P., & Peterson, P. (1989). Teachers' decision making and cognitively guided instruction: A new paradigm for curriculum development. In N. F. Ellerton, & M. A. Clements (Eds.), School mathematics: The challenge to change (pp.174-187). Geelong: Deakin University Press.

ranke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F.K. Lester Jr. (Eds.), Second handbook of research on mathematics teaching and learning (pp. 225-256). Charlotte, NC: Information Age.

FHollingsworth, H., Lokan, J., & McCrae, B. (2003). Teaching mathematics in Australia:Results from the TIMSS 1999 video study. Melbourne: Australian Council of Educational Research.

Miles & Huberman (1994). Qualitative data analysis: An exposed sourcebook (2nd Ed.). London: SAGE Publication Ltd.

Ontario Ministry of Education. (2008). A guide to effective instruction in mathematics, kindergarten to grade 6 – Volume two. Toronto: Author.

Pehkonen, E., & Pietilä, A. (2003). On relationships between beliefs and knowledge in mathematics education. Proceedings of the CERME-3 (Bellaria) …, 1–8. Retrieved from http://www.cimm.ucr.ac.cr/ciaemIngles/articulos/universitario/concepciones/On Relationships Between Beliefs and Knowledge in Mathematics Education.*Pehkonen, Erkki; Pietil?, Anu. *Pehkonen, E. Relationships between Beliefs ... 2003.pdf

Purnomo, Y. W., Suryadi, D., & Darwis, S. (2016). Examining pre-service elementary school teacher beliefs and instructional practices in mathematics class. International Electronic Journal of Elementary Education, 8(4), 629-642.

Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-76.

Siswono, T.Y.E., Kohar, A. W., Kurniasari, I., & Astuti, Y. P. (2016). An investigation of secondary teachers’ understanding and belief on mathematical problem solving. Journal of Physics: Conference Series, 693(1), p. 012015. IOP Publishing. https://doi.org/10.1088/1742-6596/693/1/012015

Siswono, T.Y.E, Kohar, A.W., & Hartono, S. (2017). Secondary teachers’ mathematicsrelated beliefs and knowledge about mathematical problem solving. Journal of Physics: Conference series, 812(1), p. 012046. IOP Publishing. https://doi.org/10.1088/1742-6596/812/1/012046

Viholainen, A., Asikainen, M., & Hirvonen, P. E. (2014). Mathematics student teachers’ epistemological beliefs about the nature of mathematics and the goals of mathematics teaching and learning in the beginning of their studies. Eurasia Journal of Mathematics, Science and Technology Education, 10(2), 159-171. https://doi.org/10.12973/eurasia.2014.1028a




DOI: https://doi.org/10.46517/seamej.v7i2.51

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