Developing prospective mathematics teachers’ knowledge of the modelling approach
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How to Cite

Shahbari, J. A., & Tabach, M. (2018). Developing prospective mathematics teachers’ knowledge of the modelling approach. Scientia in Educatione, 9(2), 146-158. https://doi.org/10.14712/18047106.1183

Abstract

Modelling is considered an important approach that requires prospective teachers to be qualified both in modelling competencies and in pedagogical knowledge. In order to investigate the development of these competencies, we examined 49 prospective mathematics teachers studying in a course that included a sequence of modelling activities. During the course, groups of 5–6 participants engaged in these modelling activities as learners. The data include two sets of reports by the prospective teachers on their observations of a recorded modelling activity carried out by a group of five 6th grade students. The first set of reports was collected before the prospective teachers worked on any modelling activities, while the second set was collected after they had engaged in the modelling activities. The findings indicate that, prior to working on modelling activities, most of the prospective teachers described the students’ modelling activity as a linear process and focused on the final mathematical model and the mathematical results. After the prospective
teachers engaged in the activities, most of their reports identified cyclical processes as the mathematical models progressed.

https://doi.org/10.14712/18047106.1183
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References

Blum, W. & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of mathematical modelling and application, 1(1), 45–58.

Blum, W. & Leib, D. (2005). “Filling Up” – the problem of independence – preserving teacher interventions in lessons with demanding modelling tasks. In M. Bosch (Ed.), CERME 4 – Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (1623–1633). Sant Feliu de Guíxols, Spain: ERME.

Borromeo Ferri, R. & Blum, W. (2010). Mathematical modelling in teacher education – experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), CERME 6, Proceedings of the sixth congress of the European Society for Research in Mathematics Education (2046–2055). Lyon: Institut national de recherche pédagogique.

Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modelling problems. Teaching Mathematics and its Applications: An International Journal of the IMA, 30(1), 19–36.

Cetinkaya, B., Kertil, M., Erbas, A.K., Korkmaz, H., Alacaci, C. & Cakiroglu, E. (2016). Pre-service teachers’ developing conceptions about the nature and pedagogy of mathematical modeling in the context of a mathematical modeling course. Mathematics Thinking Learning, 18(4), 287–314.

Ciltas, A. & Isik, A. (2013). The effect of instruction through mathematical modelling on modelling skills of prospective elementary mathematics teachers. Educational Sciences: Theory and Practice, 13(2), 1187–1192.

Doerr, H. M. & English, L. D. (2006). Middle grade teachers’ learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education, 9(1), 5–32.

Doerr, H. & English, L. (2003). A modelling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.

English, L. D. & Fox, J. L. (2005). Seventh-graders’ mathematical modelling on completion of a three-year program. In P. Clarkson et al. (Eds.), Building connections: Theory, research and practice (Vol. 1, 321–328). Melbourne: Deakin University Press.

English, L. D. & Watters, J. J. (2005). Mathematical modelling in the early school years. Mathematics education research journal, 16(3), 58–79.

English, L. & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (263–290). Berlin/Heidelberg: Springer Science and Business.

Geiger, V. (2011). Factors affecting teachers’ adoption of innovative practices with technology and mathematical modeling. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modeling, (ICTMA 14) (305–314). New York: Springer.

Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38(2), 196–208.

Kuntze, S., Siller, H.-S. & Vogl, C. (2013). Teachers’ self-perceptions of their pedagogical content knowledge related to modelling – an empirical study with Austrian teachers. In G. Stillman, G. Kaiser, W. Blum & J.P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (317–326). Dordrecht, The Netherlands: Springer.

Lesh, R.A. & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives in mathematics teaching, learning, and problem Ssolving. Mahawah, N.J.: Lawrence Erlbaum.

Lesh, R., Hoover, M., Hole, B., Kelly, A. & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (591–644). Mahwah, NJ: Lawrence Erlbaum.

Lesh, R. & Lehrer, R. (2003). Models and modelling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129.

Lingefjard, T. & Holmquist, M. (2001). Mathematical modelling and technology in teacher education – visions and reality. In J. Matos, S. K. Houston, W. Blum, & S. Carreira (Eds.), Modelling and mathematics education: Applications in science and technology (205–215). Chichester: Horwood Publishing.

Maaß, K. (2006). What are modelling competencies? ZDM, 38(2), 113–142.

Maaß, K. & Gurlitt, J. (2011). LEMA-Professional development of teachers in relation to mathematical modeling. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling: ICTMA 14 (629–639). New York: Springer.

Mischo, C. & Maaß, K. (2013). The effect of teacher beliefs on student competence in mathematical modeling – an intervention study. Journal of Education and Training Studies, 1(1), 19–38.

Shahbari, J. A. & Tabach, M. (2016a). Different generality levels in the product of a modelling activity. In C. Csikos, A. Rausch & J. Szitanyi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, 179–186). Szeged, Hungary: PME.

Shahbari, J. A. & Tabach, M. (2016b). Developing modelling lenses among practicing teachers. International Journal of Mathematical Education in Science and Technology, 47(5), 717–732.

Shahbari, J. A. & Tabach, M. (2017). The commognitive framework lens to identify the development of modelling routines. In B. Kaur, W. Kin Ho, B. Heng Choy (Eds.), Proceedings of the 41th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, 185–192). Singapore, Singapore: PME.

Stender, P. & Kaiser, G. (2015). Scaffolding in complex modelling situations. ZDM, 47(7), 1255–1267.

Stillman, G., Galbraith, P., Brown, J. & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick (Eds.), Proceedings of the 30th Mathematics Education Research Group of Australasia conference Mathematics: Essential research, essential practice (Vol. 2, 688–707). Adelaide: MERGA.

Stohlmann, M., DeVaul, L., Allen, C., Adkins, A., Ito, T., Lockett, D. & Wong, N. (2016). What is known about secondary grades mathematical modelling – A Review. Journal of Mathematics Research, 8(5), 12.

Tan, L. S. & Ang, K.C. (2013). Pre-service secondary school teachers knowledge in mathematical modelling – A case study. In G. Stillman, G. Kaiser, W. Blum & J. Brown (Eds.), Teaching mathematical modelling: Connecting research to practice (373–384). New York: Springer.

Vorhölter, K., Kaiser, G. & Borromeo Ferri, R. (2014). Modelling in mathematics classroom instruction: An innovative approach for transforming mathematics education. In Y. Li, E.A. Silver & S. Li (Eds.), Transforming Mathematics Instruction (21–36). Cham, Switzerland: Springer.