Promoting interdisciplinarity through mathematical modelling

Bar-Yam, Y. (2004). Making things work: Solving complex problems in a complex world. NECSI: Knowledge Press. Carmona, G. (2004). Designing an assessment tool to describe students’ mathematical knowledge. Ph.D. thesis. West Lafayette, IN: Purdue University. Cunningham, C. M., & Hester, K. (2007). Engineering is elementary: An engineering and technology curriculum for children. In Proceedings of the 2007 American Society for engineering education annual conference & exposition. Honolulu, Hawaii: American Society for Engineering Education. Davis, B., & Sumara, D. (2006). Complexity and education: Inquiries into learning, teaching, and research. Mahwah, NJ: Lawrence Erlbaum. Dawes, L., & Rasmussen, G. (2007). Activity and engagement—keys in connecting engineering with secondary school students. Australasian Journal of Engineering Education, 13(1), 13–20. Doerr, H. M, & English, L. D. (2001). A modelling perspective on students’ learning through data analysis. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th annual conference of the international group for the psychology of mathematics education (pp. 361–368). Utrecht: Utrecht University. Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–137. Doerr, H., & English, L. D. (2006). Middle-grade teachers’ learning through students’ engagement with modelling tasks. Journal for Research in Mathematics Teacher Education, 9(1), 5–32. Doerr, H. M., & Tripp, J. S. (1999). Understanding how students develop mathematical models. Mathematical Thinking and Learning, 1(3), 231–254. English, L. D. (2003). Reconciling theory, research, and practice: A models and modeling perspective. Educational Studies in Mathematics, 54(2/3), 225–248. English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 62(3), 303–323. English, L. D. (2008). Interdisciplinary problem solving: A focus on engineering experiences. In: Goos, M., Brown, R., & Makar, K., (Eds.). Navigating currents and Charting directions (pp. 187–194). University of Queensland: Mathematics Education Research Group of Australasia. English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. Mahwah: Lawrence Erlbaum. English, L. D., & Watters, J. J. (2005). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(3), 58–79. Freudenthal, H. (1973). Didactical phenomenology of mathematical structures. Boston: Kluwer. Gainsburg, J. (2006). The mathematical modeling of structural engineers. Mathematical Thinking and Learning, 8(1), 3–36. Gravemeijer, K. (1999). How emergent models may foster the construction of formal mathematics. Mathematical Thinking and Learning, 1, 155–177. Greer, B. (1997). Modeling reality in mathematics classroom: the case of word problems. Learning and Instruction, 7, 293–307. Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children’s experience. In W. Blum, W. Henne, & M. Niss (Eds.), Applications and modelling in mathematics education (ICMI study 14, pp. 89–98). Dordrecht: Kluwer. Hall, R. (1999). Case studies of math at work: Exploring design-oriented mathematical practices in school and work settings (NSF Rep. No. RED-9553648), Arlington: National Science Foundation. Hamilton, E. (2007). What changes are needed in the kind of problem solving situations where mathematical thinking is needed beyond school? In R. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 1–6). Mahwah: Lawrence Erlbaum. Jacobson, M., & Wilensky, U. (2006). Complex systems in education: Scientific and educational importance and implications for the learning sciences. Journal of the Learning Sciences, 15(1), 11–34. Lambert, M. Diefes-Dux, H., Beck, M., Duncan, D., Oware, E., & Nemeth, R. (2007). What is engineering?—An exploration of P-6 grade teachers’ perspectives. In Proceedings of the 37th ASEE/IEEE frontiers in education conference. Milwaukee, Wisconsin. Lesh, R. (2006). Modeling students modeling abilities: the teaching and learning of complex systems in education. Journal of the Learning Sciences, 15(1), 45–52. Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003a). Model development sequences. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematic problem solving, learning and teaching (pp. 35–58). Mahwah: Lawrence Erlbaum. Lesh, R., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematic problem solving, learning and teaching. Mahwah: Lawrence Erlbaum. Lesh, R., & Kelly, A. E. (2000). Multi-tiered teaching experiments. In R. A. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 197–230). Mahwah: Lawrence Erlbaum. Lesh, R., & Sriraman, B. (2005). John Dewey revisited—pragmatisim and the models-modeling perspective on mathematical learning. In A. Beckmann, C. Michelsen, & B. Sriraman (Eds.). Proceedings of the 1st international symposium of mathematics and its connections to the arts and sciences (pp. 7–31). The University of Education, Schwöbisch Gmund, Germany. Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning. Greenwich: Information Age Publishing. Lesh, R., Zawojewski, J. S., & Carmona, G. (2003b). What mathematical abilities are needed for success beyond school in a technology-based age of information? In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematic problem solving, learning and teaching (pp. 205–222). Mahwah: Lawrence Erlbaum. National Academy of Sciences. (2007). Rising above the gathering Storm: Energizing and employing America for a brighter economic future. Washington, DC: National Academics Press. Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, W. Henne, & M. Niss (Eds.), Applications and modelling in mathematics education (ICMI study 14, pp. 3–33). Dordrecht: Kluwer. Noss, R., Hoyles, C., & Pozzi, S. (2002). Abstraction in expertise: A study of nurses’ conceptions of concentration. Journal for Research in Mathematics Education, 33(3), 204–229. Romberg, T. A., Carpenter, T. P., & Kwako, J. (2005). Standards-based reform and teaching for understanding. In T. A. Romberg, T. P. Carpenter & F. Dremock (Eds.), Understanding mathematics and science matters. Mahwah: Lawrence Erlbaum. Sabelli, N. H. (2006). Complexity, technology, science, and education. Journal of the Learning Sciences, 15(1), 5–9. Sriraman, B., & Dhal, B. (2009). On bringing interdisciplinary ideas to gifted education. In L. V. Shavinina (Ed.), The international handbook of giftedness. Springer base: Springer Science & Business. Sriraman, B., & Steinthorsdottir (2007). Research into practice: Implications of research on mathematics gifted education for the secondary curriculum. In C. Callahan & J. Plucker (Eds.), Critical issues and practices in gifted education: What the research says (pp. 395–408). Waco, Texas: Prufrock Press. Stevens, R. (2000). Who counts what as mathematics: Emergent and assigned mathematics problems in a project-based classroom. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 105–144). Westport: Ablex Publishing. Taylor, P. (2008). Engineers Australia Media Release 29/01/2008. Fixing Australia’s engineering skills shortage. Van den Heuvel-Panhuzen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9–35. Zawojewski, J., & McCarthy, L. (2007). Numeracy in practice. Principal Leadership, 7(5), 32–38.