Developing prospective mathematics teachers’ knowledge of the modelling approach

Juhaina Awawdeh Shahbari; Michal Tabach

doi:10.14712/18047106.1183

Vol. 9 No. 2 (2018): sciED Research Reports

Developing prospective mathematics teachers’ knowledge of the modelling approach

Juhaina Awawdeh Shahbari ¹ http://orcid.org/0000-0002-7361-8069 (unauthenticated)
Michal Tabach ² http://orcid.org/0000-0003-2869-3032 (unauthenticated)

College of Sakhnin for Teacher Education: Sakhnin
Tel-Aviv University

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

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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

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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.

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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
Doerr, H. & English, L. (2003). A modelling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. Search in Google Scholar
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. Search in Google Scholar
English, L. D. & Watters, J. J. (2005). Mathematical modelling in the early school years. Mathematics education research journal, 16(3), 58–79. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38(2), 196–208. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
Maaß, K. (2006). What are modelling competencies? ZDM, 38(2), 113–142. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
Stender, P. & Kaiser, G. (2015). Scaffolding in complex modelling situations. ZDM, 47(7), 1255–1267. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar

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

[2] 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. Search in Google Scholar

[3] 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. Search in Google Scholar

[4] 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. Search in Google Scholar

[5] 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. Search in Google Scholar

[6] 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. Search in Google Scholar

[7] 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. Search in Google Scholar

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

[9] 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. Search in Google Scholar

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

[11] 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. Search in Google Scholar

[12] 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. Search in Google Scholar

[13] Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38(2), 196–208. Search in Google Scholar

[14] 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. Search in Google Scholar

[15] 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. Search in Google Scholar

[16] 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. Search in Google Scholar

[17] 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. Search in Google Scholar

[18] 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. Search in Google Scholar

[19] Maaß, K. (2006). What are modelling competencies? ZDM, 38(2), 113–142. Search in Google Scholar

[20] 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. Search in Google Scholar

[21] 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. Search in Google Scholar

[22] 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. Search in Google Scholar

[23] 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. Search in Google Scholar

[24] 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. Search in Google Scholar

[25] Stender, P. & Kaiser, G. (2015). Scaffolding in complex modelling situations. ZDM, 47(7), 1255–1267. Search in Google Scholar

[26] 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. Search in Google Scholar

[27] 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. Search in Google Scholar

[28] 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. Search in Google Scholar

[29] 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. Search in Google Scholar

Scientia in educatione

Developing prospective mathematics teachers’ knowledge of the modelling approach

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