Complex Modelling in the Primary and Middle School Years: An Interdisciplinary Approach

International Perspectives on the Teaching and Learning of Mathematical Modelling

Volumn , Issue , 2013, Pages 491-505

  English, Lyn D ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Bridge Design; Engineering Design Process; Interdisciplinary Problem; Scientific Thinking; Suspension Bridge

Indexed keywords

EID: 84941276085     PISSN: 22114920     EISSN: 22114939     Source Type: Book Series    
DOI: 10.1007/978-94-007-6540-5_42     Document Type: Chapter

References (57)

1. Australian Academy of Science. (2006). Critical skills for Australia’s future. www.review.ms. unimelb.edu.au. Accessed June 2011.
2. Australian Academy of Science. (2010). Academy 2010 election statement: Empower science, power the future. http://www.science.org.au/reports/election-statement.html. Accessed June 2011.
3. Bar-Yam, Y. (2004). Making things work: Solving complex problems in a complex world. Cambridge, MA: NECSJ, Knowledge Press.
4. Beckmann, A., Michelsen, C., & Sriraman, B. (2005). Proceedings of the 1st international symposium of mathematics and its connections to the arts and sciences. Schwöbisch Gmund: The University of Education.
5. Bereiter, C., & Scardamalia, M. (2006). Education for the knowledge age: Design-centered models of teaching and instruction. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (pp. 695–714). Mahwah, NJ: Lawrence Erlbaum.
6. Bethel, E. (2008). Michael recycle. Sydney: Koala Books.
7. Bethel, E. (2009). Litterbug Doug. Sydney: Koala Books.
8. Business Council of Australia (2007, April 26). Action required to make education Australia’s advantage. http://www.bca.com.au/Content.aspx?ContentID=101154. Accessed 10 July 2010.
9. Clayton, M. (1999). What skills does mathematics education need to provide? In C. Hoyles, C. Morgan, & G. Woodhouse (Eds.), Rethinking the mathematics curriculum (pp. 22–28). London: Falmer Press.
10. Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: Social class, sex and problem solving. Buckingham: Open University Press.
11. Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Upper Saddle River: Merrill Prentice Hall.
12. di Sessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. Cognition and Instruction, 22(3), 291–292.
13. Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.
14. English, L. D. (2008). Setting an agenda for international research in mathematics education. In L. D. English (Ed.), Handbook of international research in mathematics education: Directions for the 21st century (Vol. 2, pp. 3–19). New York: Routledge.
15. English, L. D. (2010a). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24–47.
16. English, L. D. (2010b). Interdisciplinary modelling. Mediterranean Journal for Research in Mathematics Education, 9(1), 73–90 (Special Issue).
17. English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. Mahwah: Lawrence Erlbaum.
18. English, L. D., & Mousoulides, N. (2011). Engineering-based modelling experiences in the elementary classroom. In M. S. Khine & I. M. Saleh (Eds.), Dynamic modeling: Cognitive tool for scientific enquiry. New York: Springer.
19. English, L. D., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. D. English (Eds.), Theories of mathematics education: Seeking new frontiers (Advances in mathematics education series, pp. 263–285). New York: Springer.
20. English, L. D., Jones, G. A., Bartolini Bussi, M. G., Lesh, R., Sriraman, B., & Tirosh, D. (2008). Moving forward in international mathematics education research. In L. D. English (Ed.), Handbook of international research in mathematics education: Directions for the 21st century (2nd ed., pp. 872–905). New York: Routledge.
21. English, L. D., Hudson, P. B., & Dawes, L. (2010, November 26–27). Middle school students’ perception of engineering. Paper presented at the STEM in education conference, Brisbane. http://stem.ed.qut.edu.au/index.php/conference-proceedings.html#m. Accessed 2 Aug 2012.
22. Erickson, F. (1998). Qualitative research methods for science education. In B. J. Fraser & K. G. Tobin (Eds.), International handbook of science education Part 2 (pp. 1155–1173). Dordrecht: Kluwer.
23. Gainsburg, J. (2006). The mathematical modeling of structural engineers. Mathematical Thinking and Learning, 8(1), 3–36.
24. Gravemeijer, K. (1999). How emergent models may foster the construction of formal mathematics. Mathematical Thinking and Learning, 1, 155–177.
25. Greer, B., & Mukhopadhyay, S. (2003). What is mathematics education for? The Mathematics Educator, 13(2), 2–6.
26. Greer, B., & Mukhopadhyay, S. (2012). The hegemony of mathematics. In O. Skovsmose & B. Greer (Eds.), Opening the cage: Critique and politics of mathematics education (pp. 229–248). Rotterdam: Sense Publishers.
27. Greer, B., & Verschaffel, L. (2007). Modelling competencies—Overview. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: ICMI study 14 (pp. 219–224). New York: Springer.
28. Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children’s experience. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: ICMI study 14 (pp. 89–98). New York: Springer.
29. 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.
30. Hamilton, E., Lesh, R., Lester, F., & Brilleslyper, M. (2008). Model-eliciting activities (MEAs) as a bridge between engineering education research and mathematics education research. Advances in Engineering Education, 1(2), 1–25.
31. Hoyles, C., Wolf, A., Molyneux-Hodgson, S., & Kent, P. (2002). Mathematical skills in the workplace . London: Science, Technology and Mathematics Council. Retrieved May 24, 2006, from http://www.ioe.ac.uk/tlrp/technomaths/skills2002/
32. Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010). Improving mathematics at work: The need for techno-mathematical literacies. London: Routledge.
33. Jablonka, E., & Gellert, U. (2012). Potential, pitfalls, and discriminations: Curriculum conceptions revisited. In O. Skovsmose & B. Greer (Eds.), Opening the cage: Critique and politics of mathematics education (pp. 229–248). Rotterdam: Sense Publishers.
34. Jacobson, M., & Wilensky, U. (2006). Complex systems in education: Scientific and educational importance and implications for the learning sciences. The Journal of the Learning Sciences, 15(1), 11–34.
35. Jenkins, H., Clinton, K., Purushotma, R., Robinson, A. J., & Weigel, M. (2006). Confronting the challenges of participatory culture: Media education for the 21st century. Chicago: MacArthur Foundation.
36. Katehi, L., Pearson, G., & Feder, M. (2009). Engineering in K-12 education: Understanding the status and improving the prospects. Washington, DC: The National Academies Press.
37. Kelly, A. E., Lesh, R. A., & Baek, J. Y. (Eds.). (2008). Handbook of design research methods in education. New York: Routledge.
38. Konold, C., & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
39. Kuehner, J. P., & Mauch, E. K. (2006). Engineering applications for demonstrating mathematical problem-solving methods at the secondary education level. Teaching Mathematics and Its Applications, 25(4), 189–195.
40. Lehrer, R., & Lesh, R. (2003). Mathematical learning. In W. Reynolds & G. Miller (Eds.), Comprehensive handbook of psychology (Vol. 7, pp. 357–390). New York: Wiley.
41. Lehrer, R., & Schauble, L. (2006). Cultivating model-based reasoning in science education. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 371–386). New York: Cambridge University Press.
42. Lesh, R. (2006). Modeling students modeling abilities: The teaching and learning of complex systems in education. The Journal of the Learning Sciences, 15(1), 45–52.
43. Lesh, R., & Doerr, H. (2003). Foundation of a models and modeling perspective on mathematics teaching and learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving (pp. 9–34). Mahwah: Erlbaum.
44. Lesh, R., & Fennewald, T. (2010). Introduction to Part I modeling: What is it? Why do it? In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (ICTMA 13) (pp. 5–10). New York: Springer.
45. Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte, NC: Information Age Publishing.
46. Lombardi, J., & Lombardi, M. M. (2007, June 11–14). Croquet learning space and collaborative scalability. Paper presented at DLAC-II symposium, Singapore.
47. Office of the Chief Scientist. (2012). Mathematics, engineering & science in the national interest. Canberra: Author.
48. Pellegrino, J. W., & Hilton, M. L. (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. Washington, DC: The National Academies Press.
49. Pfannkuch, K. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13, 1–2.
50. 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.
51. Sabelli, N. H. (2006). Complexity, technology, science, and education. The Journal of the Learning Sciences, 15(1), 5–9.
52. Sriraman, B., & Steinthorsdottir, O. (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). Austin: Prufrock Press.
53. The National Academies. (2007). Rising above the storm: Energizing and employing America for a brighter economic future. www.national-academies.org. Accessed 24 Feb 2010.
54. The National Academies. (2009). Rising above the gathering storm: Two years later. http://www. nap.edu/catalog/12537.html. Accessed 24 Feb 2010.
55. Van den Heuvel-Panhuizen, M., & Van den Boogaard, S. (2008). Picture books as an impetus for kindergartners’ mathematical thinking. Mathematical Thinking and Learning: An International Journal, 10, 341–373.
56. Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah: Lawrence Erlbaum.
57. Yin, R. K. (2003). Applications of case study research. Thousand Oaks, CA: Sage.