Abstract
Based on theoretical considerations, a possible means of gaining a resolution of the long standing issues of problem formulation and specification and their successful mathematisation by relatively naïve modellers is proposed. This is based on empirical evidence having been provided for paradigmatic cases of the construct of implemented anticipation as proposed by Niss, that is, foreshadowing of future action projected back onto decisions about current action during ideal mathematisation. A Foreshadowing and Feedback Framework to Engage Beginning Modellers in Implemented Anticipation and its theoretical underpinnings are outlined and illustrated using empirical data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Student names used throughout this chapter are pseudonyms.
References
Brown, J. (2013). Perceiving and enacting the affordances of Technology-Rich Teaching and Learning Environments (TRTLE’s) for student understanding of function. Unpublished doctor of philosophy thesis, University of Melbourne.
Dewey, J. (1916). Democracy and education. New York: Macmillan.
Dewey, J. (1917). The need for a recovery of philosophy. In J. Dewey (Ed.), Creative intelligence: Essays in the pragmatic attitude (pp. 3–69). New York: Holt.
Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies in Mathematics, 12(2), 133–150.
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 143–162.
Galbraith, P., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 130–140). Chichester: Horwood Press.
Geiger, V. (2009). The master, servant, partner, extension-of-self framework in individual, small group and whole class contexts. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (pp. 201–208). Adelaide: MERGA.
Getzels, J. W. (1979). Problem finding: A theoretical note. Cognitive Science, 3(2), 167–179.
Holzman, L. (1997). Schools for growth: Radical alternatives to current educational models. Mahwah: Lawrence Erlbaum.
Huang, C.-H. (2012). Investigating engineering students’ mathematical modelling competency. World Transactions on Engineering and Technology Education, 10(2), 99–104.
Hunter, R. (2012). Coming to “know’ mathematics through being scaffolded to ‘talk and do’ mathematics. International Journal for Mathematics Teaching and Learning, 14. http://www.cimt.plymouth.ac.uk/journal/hunter2.pdf
Maaβ, K. (2006). What are modelling competencies? ZDM, 38(2), 113–142.
Mercer, N. (2000). Words & minds. London: Routledge.
Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modelling students’ mathematical competencies (pp. 43–59). New York: Springer.
Stillman, G. (2015). Problem finding and problem posing for mathematical modelling. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 41–56). Singapore: World Scientific.
Stillman, G., & Brown, J. (2012). Empirical evidence for Niss’ implemented anticipation in mathematizing realistic situations. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: Expanding horizons (Vol. 2, pp. 682–689). Adelaide: MERGA.
Stillman, G., & Brown, J. (2014). Evidence of Implemented Anticipation in mathematising by beginning modellers. Mathematics Education Research Journal, 26(4), 763–789.
Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at year 9. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical competencies (pp. 385–398). New York: Springer.
Stillman, G., Brown, J., & Galbraith, P. (2013). Challenges in modelling challenges: Intents and purposes. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 217–227). Dordrecht: Springer.
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom in mathematics. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Vol. 2, pp. 688–707). Adelaide: MERGA.
Treilibs, V. (1979). Formulation processes in mathematical modelling. Unpublished Master of Philosophy, University of Nottingham.
Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: MIT Press.
Willemain, T. R., & Powell, S. G. (2007). How novices formulate models. Part II: A quantitative description of behaviour. Journal of the Operational Research Society, 58, 1271–1283.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Stillman, G.A., Brown, J.P., Geiger, V. (2015). Facilitating Mathematisation in Modelling by Beginning Modellers in Secondary School. In: Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-18272-8_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18271-1
Online ISBN: 978-3-319-18272-8
eBook Packages: Humanities, Social Sciences and LawEducation (R0)