Rozvoj znalostí o modelování u budoucích učitelů matematiky
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Jak citovat

Shahbari, J. A., & Tabach, M. (2018). Rozvoj znalostí o modelování u budoucích učitelů matematiky. Scientia in Educatione, 9(2), 146-158. https://doi.org/10.14712/18047106.1183

Abstrakt

Modelování je považováno za důležitý přístup k vyučování, jenž vyžaduje, aby byli budoucí
učitelé dostatečně kvalifikováni jak v samotném modelování, tak i v jeho didaktice.
Abychom prozkoumali možný rozvoj těchto kompetencí, provedli jsme výzkum u 49 budoucích
učitelů matematiky, kteří se účastnili kurzu, zahrnujícího sérii aktivit na modelování.
V průběhu kurzu se do těchto aktivit zapojovaly skupiny po 5 až 6 účastnících.
Výzkumná data zahrnují dvě zprávy, které vypracovali budoucí učitelé poté, co shlédli na záznamu skupinu pěti žáků 6. ročníku, jak se zabývají modelováním. První zpráva byla vypracována před tím, než se budoucí učitelé sami zapojili do modelovacích činností, druhá poté, co sami získali s modelováním zkušenosti. Výsledky ukazují, že před vlastním zapojením do modelovacích aktivit budoucí učitelé popisovali modelování u žáků jako lineární proces a zaměřovali se na výsledný matematický model a matematické výsledky. Po vlastním zapojení do modelovacích činností byla většina z budoucích učitelů schopna rozeznat cyklické procesy, pomocí nichž se matematické modely vyvíjely.

https://doi.org/10.14712/18047106.1183
PDF (English)

Reference

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.