Abstract
The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that “enable” year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of “enablers” within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students’ development as modellers.
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References
ACARA (2016). Australian Curriculum: Mathematics Aims Retrieved 27 Sept 2016 from http://www.australiancurriculum.edu.au/mathematics/aims.
Australian Industry Group (2015). Progressing STEM skills in Australia. Sydney: Author.
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.
Brown, J. (2015). Complexities of digital technology use and the teaching and learning of function. Computers & Education, 87, 112–122.
Burns, R. (2000). Introduction to research methods (4th ed.). Sydney: Longman.
Cai, J., & Melino, F. J. (2011). Metaphors: a powerful means for assessing students’ mathematical disposition. In D. J. Brahier & W. R. Speer (Eds.), Motivation and disposition: pathways to learning mathematics (pp. 147–156). Reston, VA: NCTM.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
English, L. D. (2016). Advancing mathematics education research within a STEM environment. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012–2015 (pp. 353–372). Singapore: Springer.
Flavell, J., Miller, P., & Miller, S. (2002). Cognitive development (4th ed.). Upper Saddle River, NJ: Prentice Hall.
Galbraith, P. (2015). “Noticing” in the practice of modelling as real world problem solving. In G. Kaiser & H.-W. Henn (Eds.), Werner Blum und seine Beiträge zum Modellieren im Mathematikunterricht: Realitätsbezüge im Mathematikunterricht (pp. 151–166). Wiesbaden: Springer.
Galbraith, P., Stillman, G., & Brown, J. (2010). Turning ideas into modeling problems. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’mathematical competencies (pp. 133–144). New York: Springer.
Geiger, V., Faragher, R., & Goos, M. (2010). CAS-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms. Mathematics Education Research Journal, 22(2), 48–68.
Geiger, V., Goos, M., & Dole, S. (2015a). The role of digital technologies in numeracy teaching and learning. International Journal of Science and Mathematics Education, 13(5), 1115–1137. doi:10.1007/s10763-014-9530-4.
Geiger, V., Goos, M., & Forgasz, H. (2015b). A rich interpretation of numeracy for the 21st century: a survey of the state of the field. ZDM–Mathematics Education, 47(4), 531–548. doi:10.1007/s11858-015-0708-1.
Gould, H., & Wasserman, N. H. (2014). Striking a balance: students’ tendencies to oversimplify or overcomplicate in mathematical modelling. Journal of Mathematics Education at Teachers’ College, 5(1), 27–34.
Jorgensen, R., & Lowrie, T. (2012). Digital games for learning mathematics: possibilities and limitations. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: expanding horizons (pp. 378–384). Adelaide: MERGA.
Kaiser, G., & Maaβ, K. (2007). Modelling in lower secondary mathematics classroom—problems and opportunities. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 99–108). New York: Springer.
Marginson, S., Tytler, R., Freeman, B. & Roberts, K. (2013). STEM country comparisons: international comparisons of science, technology, engineering and mathematics (STEM) education. Report for the Australian Council of Learned Academies. Retrieved from www.acola.org.au on 5 Feb 2017.
Maaß, K. (2006). What are modelling competencies? ZDM –Mathematics Education, 38(2), 113–142.
New York Academy of Sciences. (2015). The global STEM paradox. New York: Author.
Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical competencies (pp. 43–59). New York: Springer.
OECD. (2009). Mathematics framework. In OECD PISA 2009 assessment framework (pp. 83–123). Paris: OECD Publishing.
Office of the Chief Scientist. (2012). Mathematics, engineering and science in the national interest. Canberra: Commonwealth of Australia.
Paulos, J. A. (2000). Innumeracy: mathematical illiteracy and its consequences. London: Penguin.
Stacey, K., & Turner, R. (2015). PISA’s reporting of mathematical processes. In K. Beswick, T. Muir, & J. Wells (Eds.), Proceedings of the 39th conference of IGPME (Vol. 4, pp. 201–208). Hobart: PME.
STEM Task Force Report. (2014). Innovate: a blueprint for science, technology, engineering, and mathematics in California public education. Dublin, CA: Californians Dedicated to Education Foundation.
Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications task. Mathematics Education Research Journal, 16(1), 41–70.
Stillman, G. (2010). Implementing applications and modelling in secondary school: issues for teaching and learning. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modelling (pp. 300–322). Singapore: World Scientific.
Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borrromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 165–180). Dordrecht: Springer.
Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at year 9. In R. L. Lesh, P. L. Galbraith, C. L. Haines, & A. Hurford (Eds.), Modeling students mathematical modeling competencies (pp. 385–398). New York: Springer.
Stillman, G., & Brown, J. (2014). Evidence of “implemented anticipation” in mathematising by beginning modellers. Mathematics Education Research Journal, 26(4), 763–789. doi:10.1007/s13394-014-0119-6.
Stillman, G., Brown, J., & Geiger, V. (2015). Facilitating mathematisation in modelling by beginning modellers in secondary schools. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education, research and practice: cultural, social, and cognitive influences (pp. 93–103). Cham: Springer.
Thomson, S., De Bortoli, L., & Underwood, C. (2016a). PISA 2015: a first look at Australia’s results. Melbourne: ACER.
Thomson, S., Wernert, N., O’Grady, E., & Rodrigues, S. (2016b). TIMSS 2015: a first look at Australia’s results. Melbourne: ACER.
Treilibs, V. (1979). Formulation processes in mathematical modelling. – Thesis submitted to the University of Nottingham for the degree of Master of Philosophy.
Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context based PISA mathematics tasks: an analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584.
Witzel, A., & Reiter, H. (2012). The problem-centred interview. London: Sage.
Wood, L., Petocz, P., & Reid, A. (2012). Becoming a mathematician: an international perspective. Dordrecht: Springer.
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Geiger, V., Stillman, G., Brown, J. et al. Using mathematics to solve real world problems: the role of enablers. Math Ed Res J 30, 7–19 (2018). https://doi.org/10.1007/s13394-017-0217-3
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DOI: https://doi.org/10.1007/s13394-017-0217-3