Abstract
This chapter illustrates how, and to what extent, students (11–12-year olds) identified a straight-line graph (time–distance graph) as a mathematical model of average speed when making sense of walking situations in relation to technology. The results demonstrated the types of models that students identified explicitly, the phases of identifying such mathematical models, and essential actions needed for this identification. The approach of identifying mathematical models, through sense-making of embodied actions and technologies, can highlight students’ gradual mathematisation differentiating the phenomenal world, virtual technological world, and mathematical conceptual world.
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References
Ärlebäck, J. B., & Doerr, H. M. (2015). Moving beyond a single modelling activity. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 293–303). Cham: Springer.
Arzarello, F., Pezzi, G., & Robutti, O. (2007). Modelling body motion: An approach to function using measuring instruments. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 129–136). New York: Springer.
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 222–231). Chichester: Horwood.
Doerr, H. M., & Pratt, D. (2008). The learning of mathematics and mathematical modelling. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Vol. 1. Research syntheses (pp. 259–285). Charlotte, NC: Information Age.
Doerr, H. M., Ärlebäck, J. B., & Misfeldt, M. (2017). Representations of modelling in mathematics education. In G. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 421–432). Cham: Springer.
Geiger, V. (2011). Factors affecting teachers’ adoption of innovation practices with technology and mathematical modelling. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 305–314). Dordrecht: Springer.
Greefrath, G. (2011). Using technologies: New possibilities of teaching and learning modelling – Overview. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 301–304). Dordrecht: Springer.
Kaput, J., & Roschelle, J. (1999). The mathematics of change and variation from a millennial perspective: New content, new context. In C. Hoyles, C. Morgan, & G. Woodhouse (Eds.), Rethinking the mathematics curriculum (pp. 155–170). London: Springer.
Kawakami, T., Komeda S., Urago, A., Tateishi, K., & Ishii, G. (2015). Eliciting the concept of speed through walking: Utilizing a graph calculator and distance sensor. In Research report of Japan Society of Science Education (pp. 1–6). Saga: JSSE (in Japanese).
Komeda, S., Kawakami, T., Kaneko, M., & Yamaguchi, T. (2019). Deepening and expanding mathematical models of speed in relation to walking: The case of year 8 students. In G. A. Stillman, G. Kaiser, & E. Lampen (Eds.), Mathematical modelling education and sense making. Cham: Springer.
Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and graphing. Cognition and Instruction, 16(2), 119–172.
Núñez, R., Edwards, L. D., & Matos, J. F. (1999). Embodiment cognition as grounding for situatedness and context in mathematics education. Education Studies in Mathematics, 39, 45–65.
Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
Piaget, J. (1970). The child’s conception of movement and speed. New York: Basic Books.
Saeki, A., Ujiie, A., & Kuroki, N. (2004). Students’ analysis of the cooling rate of hot water in a mathematical modelling process. In H.-W. Henn & W. Blum (Eds.), ICMI Study 14: Applications and modelling in mathematics education: Pre-Conference volume (pp. 235–240). Dortmund: University of Dortmund.
Swan, M., Turner, R., Yoon, C., & Muller, E. (2007). The roles of modelling in learning mathematics. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 275–284). New York: Springer.
Thompson, P. W., & Thompson, A. G. (1992). Images of rate. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.
Acknowledgements
The authors thank Koichi Tateishi, Atsushi Urago, and Go Ishii for their cooperation in conducting classroom-teaching experiments. This work was supported by JSPS KAKENHI Grant Numbers JP17K14053.
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Kawakami, T., Komeda, S., Saeki, A. (2020). Year 6 Students’ Gradual Identification of Mathematical Models of Average Speed When Making Sense of ‘Walking’. In: Stillman, G.A., Kaiser, G., Lampen, C.E. (eds) Mathematical Modelling Education and Sense-making. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_14
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