A Model Eliciting Framework For Integrating Mathematics And Robotics Learning

David Nutchey

Abstract


Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile ground for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of
activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.


Keywords


mathematics; robotics; model eliciting; number line

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References


Australian Curriculum Assessment and Reporting Authority (ACARA). (2012). Australian Curriculum: Mathematics ver. 3.0.Canberra: Author

Bell, A. (1993). Principles for the design of teaching. Educational Studies in Mathematics, 24(1), 5-34.

Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dordrecht/Boston/London: Kluwer Academic Publishers.

Galbraith, P. (2011). Models of modelling: Is there a first among equals? Paper presented at the 34th Annual Conference of the Mathematics Education Research Group of Australasia.

Julie, C. (2002). Making relevance relevant in mathematics teacher education. Paper presented at the Proceedings of the Second International Conference on the Teaching of Mathematics (at the undergraduate level).

Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Model development sequences. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 35-58). Mahwah, NJ: Lawrence Erlbaum Associates.

Lesh, R., & English, L. (2005). Trends in the evolution of models and modeling perspectives on mathematical learning and problem solving. ZDM: The International Journal on Mathematics Education, 37(6), 487-489.

Lesh, R., & Kelly, A. (2000). Multitiered Teaching Experiments. In A. Kelly & R. Lesh (Eds.), Research Design in Mathematics and Science Education (pp. 197-230). Mahwah, NJ: Lawrence Erlbaum Associates.

Nutchey, D. (2011a). A Popperian consilience: Modelling mathematical knowledge and understanding. Paper presented at the 34th Annual Conference of the Australasian Mathematics Education Research Group, Alice Springs, Australia.

Nutchey, D. (2011b). Towards a model for the description and analysis of mathematical knowledge and understanding. (PhD), Queensland University of Technology, Brisbane, Australia.

Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. New York: Basic Books.

Papert, S. (1991). Situating constructionism. In I. Harel, S. Papert & Massachusetts Institute of Technology Epistemology and Learning Research Group (Eds.), Constructionism: Research reports and essays, 1985-1990 (pp. 1-12). Norwood, NJ: Ablex Publishing Corp.

Piaget, J. (2001). Studies in reflecting abstraction (R. Campbell, Trans.). Sussex, England: Psychology Press.

Popper, K. (1978). Three worlds. Retrieved from http://www.tannerlectures.utah.edu/lectures/documents/popper80.pdf.




DOI: https://doi.org/10.46517/seamej.v3i1.24

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