Abstract
This chapter argues for a future-oriented, interdisciplinary approach to mathematical problem solving in the elementary school—one that draws upon the engineering domain, using cognitive technological tools. New approaches in mathematics and science education and new forms of thinking and problem solving skills are needed as the world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges and demands. I consider complex problem solving within the mathematics and science curriculum and address how SimCalc MathWorlds® complements and enriches mathematical modeling in solving complex engineering-based problems. I report on a study in which a class of 9-year-olds created several different models for solving a complex problem on rocketry engineering. Results showed that young students, even before instruction, have the capacity to deal with complex interdisciplinary problems. Students created quite appropriate models that adequately solved the problem, by developing the necessary mathematical constructs and processes. I conclude with a discussion on the appropriateness of a technology-based modeling approach as a means for introducing complex, real-world problems to elementary school students.
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.
To obtain the software and curriculum documents for these activities, please contact kaputcenter@umassd.edu.
References
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modeling, applications, and links to other subjects: state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.
Curious minds (2008). The Hague: TalentenKracht.
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.
English, L. D. (Ed.) (2004). Mathematical and analogical reasoning of young learners. Mahwah: Erlbaum.
English, L. D. (2006). Mathematical modeling in the primary school: children’s construction of a consumer guide. Educational Studies in Mathematics, 6(3), 303–323.
English, L. D. (2011). Complex modeling in the primary/middle school years. Plenary talk at the international conference on modeling and applications. Melbourne, Australia.
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.
English, L., & 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 (pp. 173–194). New York: Springer.
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 (pp. 263–285). New York: Springer.
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 (pp. 89–98). Dordrecht, The Netherlands: Kluwer Academic.
Hegedus, S., & Penuel, W. (2008). Studying new forms of participation and classroom identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics, 68(2), 171–184.
Hegedus, S. & Roschelle, J. (Eds.) (2012). The SimCalc vision and contributions democratizing access to important mathematics. Berlin: Springer.
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.
Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), A handbook of research on mathematics teaching and learning (pp. 515–556). New York: Macmillan.
Kaput, J., & Blanton, M. (2002). Design principles for tasks that support algebraic thinking in elementary school classrooms. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th annual conference of the international group for the psychology of mathematics education (Vol. 2, pp. 105–112). Norwich: University of East Anglia.
Kaput, J., & Nemirovsky, R. (1995). Moving to the next level: a mathematics of change theme throughout the K–16 curriculum. UME Trends, 6(6), 20–21. Invited paper for a special issue on “The first decade of calculus reform”.
Lee, J. S., & Ginsburg, H. P. (2007). What is appropriate for mathematics education for four-year-olds? Journal of Early Childhood Research, 5(1), 2–31.
Lehrer, R., & Schauble, L. (2007). Contrasting emerging conceptions of distribution in contexts of error and natural variation. In M. C. Lovett & P. Shah (Eds.), Thinking with data (pp. 149–176). New York: Taylor & Francis.
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.
Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). 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: Erlbaum.
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.
Lesh, R., Hamilton, E., & Kaput, J. (Eds.) (2007). Foundations for the future in mathematics education. Mahwah: Erlbaum.
Miles, M., & Huberman, A. (1994). Qualitative data analysis (2nd ed.). London: Sage Publications.
Mousoulides, N. (2011). Geogebra as a cognitive tool for modelling engineering problems. In M. Hohenwarter (Ed.), Model centered learning with Geogebra (pp. 130–145). Rotterdam, The Netherlands: Sense Publishers.
Mousoulides, N., Christou, C., & Sriraman, B. (2008). A modeling perspective in mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293–304.
Mousoulides, N., & English, L. D. (2009). Integrating engineering experiences within the elementary mathematics curriculum. In L. Mann & R. Hadgraft (Eds.), Proceedings of the research in engineering education symposium 2009. Palm Core, Cairns: The University of Melbourne.
Mousoulides, N., & English, L. D. (2011). Engineering model eliciting activities for elementary school students. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 221–230). New York: Springer.
Mousoulides, N., Pittalis, M., Christou, C., Boytchev, P., Sriraman, B., & Pitta, D. (2007). Mathematical modelling using technology in elementary school. Paper presented at the 8th international conference on technology in mathematics teaching, University of Hradec Králové, Czech Republic.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
National Research Council (2001). J. Kilpatrick, J. Swafford, & B. Findell (Eds.) Adding it up: helping children learn mathematics Mathematics Learning Subcommittee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington: National Academy Press.
Perry, B., & Dockett, S. (2008). Young children’s access to powerful mathematical ideas. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 75–108). New York: Routledge.
Roschelle, J., & Kaput, J. (1996). Educational software architecture and systemic impact: the promise of component software. Journal of Educational Computing Research, 14(3), 217–228.
Roschelle, J., Kaput, J., & Stroup, W. (2000). SimCalc: accelerating students’ engagement with the mathematics of change. In M. J. Jacobson & R. B. Kozma (Eds.), Innovations in science and mathematics education (pp. 47–76). Mahwah: Erlbaum.
Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching mathematics for understanding: an analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46(2), 501–531.
Zawojewski, J., Hjalmarson, J. S., Bowman, K., & Lesh, R. (2008). A modeling perspective on learning and teaching in engineering education. In J. Zawojewski, H. Diefes-Dux, & K. Bowman (Eds.), Models and modeling in engineering education: designing experiences for all students (pp. 1–16). Rotterdam, The Netherlands: Sense Publishers.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Mousoulides, N.G. (2013). Mathematical Modeling with SimCalc: Enhancing Students’ Complex Problem Solving Skills Using a Modeling Approach. In: Hegedus, S., Roschelle, J. (eds) The SimCalc Vision and Contributions. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5696-0_20
Download citation
DOI: https://doi.org/10.1007/978-94-007-5696-0_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5695-3
Online ISBN: 978-94-007-5696-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)