# Mathematical modelling in teacher education: dealing with institutional constraints

- 80 Downloads

## Abstract

Considering the general problem of integrating mathematical modelling into current educational systems, this paper focuses on the *ecological dimension* of this problem—the institutional constraints that hinder the development of mathematical modelling as a normalised teaching activity—and the inevitable step of the professional development of teachers. Within the framework of the Anthropological Theory of the Didactic, this step is approached using the *study and research paths for teacher education* (SRP-TE), an inquiry-based process combining practical and theoretical questioning of school mathematical activities. We present a research study focusing on the design and analysis of an online and distance-learning course for in-service mathematics teachers based on the SRP-TE methodology. This course starts from the initial question of how to analyse, adapt and integrate a learning process related to mathematical modelling and how to sustain its long-term development. Our analysis is based on a case study consisting in four successive editions of a course for Latin American in-service mathematics teachers held at the Centre for Applied Research in Advanced Science and Technology in Mexico. The starting point is a modelling activity about forecasting the number of Facebook users, which includes functional modelling and regression. The results show how the course represents a valuable instrument to help teachers progress in the critical issue of identifying institutional constraints—most of them beyond the scope of action of teachers and students and not approached by previous research—hindering the integration of mathematical modelling in current secondary schools.

### Keywords

Mathematical modelling Study and research path Teacher education Anthropological theory of the didactic Institutional constraints Ecology Functions## Notes

### Acknowledgements

The research leading to these results has received funding from the Spanish R&D Projects: EDU2015-64646-P and EDU2015-69865-C3-1-R (MINECO/FEDER, UE).

### References

- Artigue, M. (2014). Didactic engineering in mathematics education. In S. Lerman (Ed.),
*Encyclopedia of mathematics education*(pp. 159–162). New York: Springer.Google Scholar - Barquero, B., & Bosch, M. (2015). Didactic engineering as a research methodology: From fundamental situations to study and research paths. In A. Watson & M. Ohtani (Eds.),
*Task design in mathematics education. New ICMI study series*(pp. 249–272). Dordrecht: Springer.CrossRefGoogle Scholar - Barquero, B., Bosch, M., & Gascón, J. (2013). The ecological dimension in the teaching of mathematical modelling at university.
*Recherches en Didactique de Mathématiques, 33*(3), 307–338.Google Scholar - Barquero, B., Bosch, M., & Romo, A. (2015). A study and research path on mathematical modelling for teacher education. In K. Krainer, & N. Vondrová (Eds.),
*Proceedings of CERME 9*(pp. 809–815). Prague: CERME.Google Scholar - Barquero, B., Monreal, N., Ruiz-Munzón, N., & Serrano, L. (2017). Linking transmission with inquiry at university level through study and research paths: The case of forecasting Facebook user growth.
*International Journal of Research in Undergraduate Mathematics Education*. https://doi.org/10.1007/s40753-017-0067-0.Google Scholar - Blomhøj, M., & Kjeldsen, T. (2006). Teaching mathematical modelling through project work. Experiences from an in-service course for upper secondary teachers.
*ZDM, 38*(1), 163–177.CrossRefGoogle Scholar - Blum, W. (1996). Anwendungsbezüge im Mathematikunterricht—Trends und Perspektiven. In G. Kadunz, H. Kautschitsch, G. Ossimitz & E. Schneider (Eds.),
*Trends und Perspektiven*(pp. 15–38). Wien: Hölder-Pichler-Tempsky.Google Scholar - Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. BorromeoFerri & G. Stillman (Eds.),
*Trends in teaching and learning mathematical modelling*(pp. 15–30). Dordrecht: Springer.CrossRefGoogle Scholar - Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.),
*The Proceedings of the 12th International Congress on Mathematical Education*(pp. 73–96). Berlin: Springer.Google Scholar - Borba, M., & Llinares, S. (2012). Online mathematics teacher education: Overview of an emergent field of research.
*ZDM, 44*, 697–704.CrossRefGoogle 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.),
*Proceedings of CERME 6*(pp. 2046–2055). Lyon: Institut National de Recherche Pédagogique.Google Scholar - Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future.
*ZDM, 38*(2), 178–195.CrossRefGoogle Scholar - Cai, J., Cirillo, M., Pelesko, J. A., Ferri, B., Borba, R., Geiger, M., Stillman, V., English, G., Wake, L. D., Kaiser, G., G., & Kwon, O. N. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional and teacher education perspectives. In P. Liljedahl, C. Nicol, S. Oesterle & D. Allan (Eds.),
*Proceedings of the joint meeting of PME 38 and PME*-*NA 36, PME*-*NA*, Vancouver (pp. 145–172).Google Scholar - Chevallard, Y. (2015). Teaching mathematics in tomorrow’s society: A case for an oncoming counter paradigm. In S.J. Cho (Ed.),
*Proceedings of the 12th international congress on mathematical education*(pp. 173–187). Berlin: Springer.Google Scholar - De Oliveira, A. M. P., & Barbosa, J. (2013). Mathematical modeling, mathematical content and tensions in discourses. In G. A. Stillman, G. Kaiser, W. Blum & J. P. Brown (Eds.),
*Teaching mathematical modeling: Connecting to research and practice*(pp. 67–76). Dordrecht: Springer.CrossRefGoogle Scholar - Doerr, H., & Lesh, R. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.),
*Trends in teaching and learning of mathematical modelling*(pp. 247–268). Dordrecht: Springer.CrossRefGoogle Scholar - Doerr, H. D. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. L. Galbraith, H. Henn & M. Niss (Eds.),
*Modelling and applications in mathematics education: The 14th ICMI study*(pp. 69–78). New York: Springer.CrossRefGoogle Scholar - Dorier, J.-L., & García, F. J. (2013). Challenges and opportunities for the implementation of inquiry-based learning in day-to-day teaching.
*ZDM, 45*(6), 837–849.CrossRefGoogle Scholar - Galbraith, P. (2007). Beyond the low hanging fruit. In W. Blum, P. L. Galbraith, H. Henn & M. Niss (Eds.),
*Modelling and applications in mathematics education: The 14th ICMI Study*(pp. 79–88). New York: Springer.CrossRefGoogle Scholar - Goldsmith, L. T., Doerr, H. M., & Lewis, C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research.
*Journal of Mathematics Teacher Education, 17*, 5–36.CrossRefGoogle Scholar - Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling. Approaches and developments from German speaking countries. ICME 13-topical surveys.Google Scholar
- Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom—Problems and opportunities. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.),
*Modelling and applications in mathematics education: The 14th ICMI study*(pp. 99–108). New York: Springer.CrossRefGoogle Scholar - Kaiser, G., Schwarz, B., & Tiedemann, S. (2010). Future teachers’ professional knowledge on modeling. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.),
*Modeling students’ mathematical modeling competencies, ICTMA 13*(pp. 433–444). New York: Springer.CrossRefGoogle Scholar - Maaß, K., & Gurlitt, J. (2011). LEMA—professional development of teachers in relation to mathematical modelling. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. A. Stillman (Eds.),
*Trends in teaching and learning of mathematical modelling*(Vol. 1, pp. 629–639). Dordrecht: Springer, ICTMA14.CrossRefGoogle Scholar - Pepin, B., Gueudet, G., & Trouche, L. (2013). Re-sourcing teacher work and interaction: New perspectives on resource design, use and teacher collaboration.
*ZDM, 45*(7), 929–943.CrossRefGoogle Scholar - Schmidt, B. (2011). Modelling in the classroom: Obstacles from the teacher’s perspective. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. A. Stillman (Eds.),
*International perspectives on the teaching and learning of mathematical modelling, trends in teaching and learning of mathematical modelling*(Vol. 1, pp. 641–651). Dordrecht: Springer, ICTMA14.CrossRefGoogle Scholar - Serrano, L., Bosch, M., & Gascón, J. (2010). Fitting models to data. The mathematising step in the modelling process. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.),
*Proceedings of CERME 6*(pp. 2185–2196). Lyon: INRP.Google Scholar - Snyder, W. M., & Wenger, E. (2010). Our world as a learning system: A communities-of-practice approach. In C. Blackmore (Ed.), Social learning systems and communities of practice (pp. 107–124). UK: The Open University in Association with Springer London.CrossRefGoogle Scholar
- Stillman, G., Kaiser, G., Blum, W., & Brown, J. (Eds, 2013).
*Teaching mathematical modelling: Connecting to research and practice*. New York: Springer.Google Scholar - Swan, M., Pead, D., Doorman, M., & Mooldijk, A. (2013). Designing and using professional development resources for inquiry-based learning.
*ZDM, 45*(7), 945–957.CrossRefGoogle Scholar - Winsløw, C., Matheron, Y., & Mercier, A. (2013). Study and research courses as an epistemological model for didactics.
*Educational Studies in Mathematics, 83*(2), 267–284.CrossRefGoogle Scholar