Abstract
Using mathematics to solve or make sense of real-world problem situations and examining how mathematics has been used in context is of growing interest and importance in research within Australasia. Simultaneously curricula writers are increasingly recognising the importance of educating mathematically literate citizens of the world who can solve real-world problems. This chapter considers the different perspectives on teaching through mathematical modelling and applications and briefly reviews exemplary literature focusing on the teaching of mathematical modelling and applications. Not surprisingly, clear differences emerge in classroom practices engaged in applications, using known mathematics, versus modelling—where the mathematics that might be useful needs to be determined by the student. Theoretical developments in the field are reviewed. Recently, the research field has expanded from being mainly school focused to include pre-service and in-service teacher education. Methodological tools used in modelling and applications research that are being adopted or adapted in the region are then reviewed. Finally, the current positive state of Australasian modelling and applications research and its progress since last being reviewed in 2008 is discussed with an eye to possible future developments.
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References
Ang, K. C. (2013). Real life modelling within a traditional curriculum: Lessons from a Singapore experience. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 131–140). Dordrecht, The Netherlands: Springer.
Ang, K. C. (2015). Mathematical modelling in Singapore schools: A framework for instruction. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 57–72). Singapore: World Scientific.
Ang, K. C., & Tan, L. S. (2014). Professional development for teaching in mathematical modelling. Proceedings of the 19th Asian Technology Conference in Mathematics (pp. 33–42). Yogyakarta, Indonesia: ATCM.
Australian Curriculum, Assessment and Reporting Authority. (2014). The Australian Curriculum: Mathematical Methods v5.2. Retrieved January 26 2014 from http://www.australiancurriculum.edu.au/SeniorSecondary/Mathematics/Mathematical-Methods/.
Bennison, A. (2015a). Developing an analytic lens for investigating identity as an embedder-of-numeracy. Mathematics Education Research Journal, 27(1), 1–19.
Bennison, A. (2015b). Supporting teachers to embed numeracy across the curriculum: A sociocultural approach. ZDM, 47(4), 561–573.
Bhaskar, R. (1975). A realistic theory of science. Brighton: Harvester.
Bills, T., & Hunter, R. (2015). The role of cultural capital in creating equity for Pãsifika learners in mathematics. In M. Marshman, V. Geiger, & A. Bennison (Eds.), Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 109–116). Sunshine Coast, QLD: MERGA.
Brown, J. P. (2013). Inducting year 6 students into “A culture of mathematising as a practice”. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 295–305). Dordrecht, The Netherlands: Springer.
Brown, J. P. (2015a). Complexities of digital technology use and the teaching and learning of function. Computers & Education, 87, 112–122.
Brown, J. P. (2015b). Visualisation tactics for solving real world tasks. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 431–442). Cham, Switzerland: Springer.
Brown, R., Redmond, T., Sheehy, J., & Lang, D. (2015). Mathematical modelling—An example from an inter-school modelling challenge. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 143–160). Singapore: World Scientific.
Chan, E. (2013). Initial perspectives of teacher professional development on mathematical modelling in Singapore: Conceptions of mathematical modelling. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 405–415). Dordrecht, The Netherlands: Springer.
Chan, E. (2014). Exploring group dynamics of Primary 6 students engaged in mathematical modelling activities. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 127–132). Sydney: MERGA.
Chan, E., Ng, D., Widjaja, W., & Seto, C. (2012). Assessment of primary 5 students’ mathematical modelling competencies. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 146–178.
Choy, B. H. (2013). Productive mathematical noticing: What it is and why it matters. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 186–193). Melbourne: MERGA.
Downton, A. (2013). Problem posing: A possible pathway to mathematical modelling. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 527–536). Dordrecht, The Netherlands: Springer.
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.
English, L. D. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81(1), 15–30.
English, L. D. (2013). Complex modelling in the primary and middle school years: An interdisciplinary approach. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 491–505). Dordrecht, The Netherlands: Springer.
English, L. D., & Gainsburg, J. (2016). Problem solving in a 21st-century mathematics curriculum. In L. D. English & D. Kirschner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 313–335). New York: Routledge.
English, L. D., Hudson, P. B., & Dawes, L. (2012). Engineering design processes in seventh-grade classrooms: Bridging the engineering education gap. European Journal of Engineering Education, 37(5), 436–447.
English, L. D., & Watson, J. M. (2015). Statistical literacy in the elementary school: Opportunities for problem posing. In F. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 241–256). Dordrecht, The Netherlands: Springer.
Galbraith, P. (2012). Models of modelling: genres, purposes or perspectives. Journal of Mathematical Modelling and Application, 1(5), 3–16.
Galbraith, P. (2013). From conference to community: An ICTMA journey. In G. A. Stillman, G., Kaiser, W., Blum, & J. P. Brown (Eds.). Mathematical modelling: Connecting to practice (pp. 27–45). Dordrecht, The Netherlands: Springer.
Galbraith, P. (2015a). Modelling, education and the epistemic fallacy. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 339–349). Cham, Switzerland: Springer.
Galbraith, P. (2015b). “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, Germany: Springer.
Gatabi, A. R., Stacey, K., & Gooya, Z. (2012). Investigating grade nine textbook problems for characteristics related to mathematical literacy. Mathematics Education Research Journal, 24(4), 403–421.
Geiger, V. (2013). Strässer’s didactic tetrahedron as a basis for theorising mathematical modelling activity within social contexts. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 107–118). Dordrecht, The Netherlands: Springer.
Geiger, V., & Frejd, (2015). A reflection on mathematical modelling and applications as a field of research: Theoretical orientation and diversity. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 161–172). Cham, Switzerland: Springer.
Geiger, V., Forgasz, H., & Goos, M. (2015). A critical orientation to numeracy across the curriculum. ZDM, 47(4), 611–624.
Geiger, V., Goos, M., & Dole, S. (2013). Taking advantage of incidental school events to engage with the applications of mathematics: The case of surviving the reconstruction. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 175–194). Dordrecht, The Netherlands: Springer.
Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM, 47(4), 531–548.
Goos, M., Geiger, V., & Dole, S. (2013). Designing rich numeracy tasks. In C. Margolinas (Ed.), Proceedings of International Commission on Mathematical Instruction Study 22 (Vol. 1, pp. 591–599). Oxford: ICMI.
Jacobs, V. R., Lamb, L. L. C., & Phillipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
Jennings, M., & Adams, P. (2013). Mathematics and the pharmacokinetics of alcohol. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 597–606). Dordrecht, The Netherlands: Springer.
Julie, C., & Mudalay, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 503–510). New York: Springer.
Kaiser, G., Blum, W., Borromeo Ferri, R., & Stillman, G. (Eds.). (2011). Trends in teaching and learning of mathematical modelling. New York: Springer.
Lamb, J., Kawakami, T., Saeki, A., & Matsuzaki, A. (2014). Leading a new pedagogical approach to Australian Curriculum Mathematics: Using the dual modelling cycle framework. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 357–364). Sydney: MERGA.
Lamb, J., & Visnovska, J. (2013). On comparing mathematical models and pedagogical learning. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 457–466). Dordrecht, The Netherlands: Springer.
Lamb, J., & Visnovska, J. (2015). Developing statistical numeracy: The model must make sense. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 363–373). Cham, Switzerland: Springer.
Lesh, R., & Doerr, H. (Eds.). (2003). Beyond constructivism: Models and modelling perspectives on mathematics teaching, learning and problem solving. Mahwah, NJ: Erlbaum.
Makar, K. (2011). Learning over time: Pedagogical change in teaching mathematical inquiry. In J. Clarke, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.), Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 27–37). Alice Springs, NT: MERGA.
Mousoulides, N., & English, L. D. (2012). Modelling as a bridge between real world problems and school mathematics. Paper presented at Topic Study Group 17, 12th International Congress on Mathematical Education, Seoul, Korea.
Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). (2008). Melbourne declaration on educational goals for young Australians. Melbourne: MCEETYA.
Ministry of Education. (2006). Secondary mathematics syllabus. Singapore: Author. Retrieved from http://www.moe.edu.sg/education/syllabuses/sciences/.
Ministry of Education. (2014). 21st century competencies. Singapore: Author. Retrieved from http://www.moe.gov.sg/education/21cc/.
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.
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 3–32). New York: Springer.
Ng, D., Widjaja, W., Chan, E., & Seto, C. (2015). Developing teaching competencies through for facilitation of mathematical modelling in Singapore primary schools. In S. F. Ng (Ed.), The contributions of video and audio technology towards professional development of mathematics teachers (pp. 15–38). New York: Springer.
Nolan, C., & Herbert, S. (2015). Introducing linear functions: An alternative statistical approach. Mathematics Education Research Journal, 27(4), 401–421.
Saeki, A., & Matsuzaki, A. (2013). Dual modelling cycle framework for responding to the diversities of modellers. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 89–99). Dordrecht, The Netherlands: Springer.
Sarantakos, S. (1998). Social research. Melbourne: Macmillan.
Schoenfeld, A. H. (2015). How we think: A theory of human decision-making, with a focus on teaching. In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 229–243). Cham, Switzerland: Springer.
Sfard, A. (2008). Thinking as communication: Human development, the growth of discourses, and mathematising. Cambridge, UK: Cambridge University Press.
Stacey, K. (2015). The international assessment of mathematical literacy: PISA 2012 framework and items. In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 771–790). Cham, Switzerland: Springer.
Shimizu, Y., & Williams, G. (2013). Studying learners in intercultural contexts. In K. Clements, A. Bishop, J. Kilpatrick, F. Leung, & C. Keitel (Eds.), Third international handbook in mathematics education (pp. 145–168). New York: Springer.
Stillman, G. (2002). Assessing higher order mathematical thinking through applications (Unpublished doctoral dissertation). Brisbane: University of Queensland.
Stillman, G. (2015). Applications and modelling research in secondary classrooms: What have we learnt? In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 791–805). Cham, Switzerland: Springer.
Stillman, G. A., Blum, W., & Biembengut, M. S. (2015). Mathematical modelling in education research and practice: Cultural, social and cognitive influences. Cham, Switzerland: Springer.
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. (2008). Research into the teaching and learning of applications and modelling in Australasia. In H. Forgasz, et al. (Eds.), Research in mathematics education in Australasia 2004-2007 (pp. 141–164). Rotterdam, The Nethelands: Sense.
Stillman, G., Brown, J., & Geiger, V. (2015). Facilitating mathematisation in modelling by beginning modellers in secondary school. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 93–104). Cham, Switzerland: Springer.
Stillman, G., Brown, J., Faragher, R., Geiger, V., & Galbraith, P. (2013). The role of textbooks in developing a socio-critical perspective on mathematical modelling in secondary classrooms. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Mathematical modelling: Connecting to research and practice (pp. 361–371). Dordrecht, the Netherlands: Springer.
Stillman, G., & Galbraith, P. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157–195.
Stillman, G., Kaiser, G., Blum, W., & Brown, J. (Eds.). (2013). Teaching mathematical modelling: Connecting to research and practice. Dordrecht, The Netherlands: Springer.
Stillman, G., & Ng, K. E. D. (2013). Embedding authentic real world tasks into secondary mathematics curricula. In A. Damlamian, J. F. Rodrigues, & R. Strasser (Eds.), Educational interfaces between mathematics and industry (pp. 299–307). Cham, Switzerland: Springer.
Tan, L. S., & Ang, K. C. (2012). Pedagogical content knowledge in mathematical modelling instruction. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 714–721). Singapore: MERGA.
Tan, L. S., & Ang, K. C. (2013a). Application of a proposed framework for mathematical modelling instruction. In M. Inprasitha (Ed.), Proceedings of the 6th East Asia Regional Conference on Mathematics Education (Vol. 3, pp. 248–257). Phuket: Center for Research in Mathematics Education, Khon Kaen University.
Tan, L. S., & Ang, K. C. (2013b). Pre-service secondary school teachers’ knowledge in mathematical modelling—A case study. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 405–415). Dordrecht, the Netherlands: Springer.
Valsiner, J. (1997). Culture and the development of children’s action: A theory for human development (2nd ed.) New York: Wiley.
Verschaffel, L., van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling. Journal of Mathematical Didaktics, 31, 9–29.
Visnovska, J., & Lamb, J. (2012). Planning for building models of situations: What is involved? Paper presented at topic study group 17, 12th International Congress on Mathematical Education, Seoul, Korea.
Wells, J. (2014). Developing argumentation in mathematics: The role of evidence and context (Unpublished doctoral dissertation). Brisbane: The University of Queensland.
Widjaja, W. (2013). Building awareness of mathematical modelling in teacher education: A case study in Indonesia. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 583–593). Dordrecht, The Netherlands: Springer.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
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Stillman, G., Brown, J., Galbraith, P., Ng, K.E.D. (2016). Research into Mathematical Applications and Modelling. In: Makar, K., Dole, S., Visnovska, J., Goos, M., Bennison, A., Fry, K. (eds) Research in Mathematics Education in Australasia 2012-2015. Springer, Singapore. https://doi.org/10.1007/978-981-10-1419-2_14
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