Abstract
Many affordances useful in facilitating the solution of real world tasks are available in Technology-Rich Teaching and Learning Environments (TRTLE’s). Of particular use are those allowing visual image generation by technology. Whilst the TRTLE provides additional opportunities and approaches to engaging with the real world, additional complexities also exist. One of the transformational powers of the technology is to produce technology-generated images to clarify and refine students’ mental models of the situation, but is this power being realised? Following a grounded theory approach, this study showed that students often did not take up the opportunities, such as the usefulness of the data plot informing their choice of function model or comparing models with data or each other, even though they had the technological and mathematical knowledge to do so.
Data were collected in an ARC funded Linkage Project – LP0453701 at The University of Melbourne.
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See Brown and Edwards (2011) for further details of the task.
References
Borba, M. (2005). Humans-with-media: Transforming communication in the classroom. In A. Chronaki & I. M. Christiansen (Eds.), Challenging perspectives on mathematics classroom communication (pp. 51–77). Greenwich: Information Age.
Borba, M. (2012). Humans-with-media and continuing education for mathematics teachers in online environments. ZDM_The International Journal on Mathematics Education, 44(6), 801–814.
Brown, J. (2013). Perceiving and enacting the affordances of technology-rich teaching and learning environments (TRTLE’s) for student understanding of function. Unpublished doctor of philosophy thesis, University of Melbourne, Melbourne.
Brown, J., & Edwards, I. (2011). Modelling tasks: Insights into mathematical understanding. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 187–197). New York: Springer.
Doerr, H., & Zangor, R. (2000). Creating meaning for and with a graphing calculator. Educational Studies in Mathematics, 41(2), 143–163.
Galbraith, P., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 130–140). Chichester: Horwood Press.
Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin.
Gibson, J. J. (1977). The theory of affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, acting and knowing: Toward an ecological psychology (pp. 67–82). Hillsdale: Erlbaum.
Johnson-Laird, P. N. (1988). The computer and the mind. Cambridge, MA: Harvard University Press.
Pead, D., & Ralph, B. (2007). Uses of technologies in learning mathematics through modelling. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (14th ICMI Study) (pp. 309–318). New York: Springer.
Pollak, H. O. (1986). The effects of technology on the mathematics curriculum. In M. Carss (Ed.), Proceedings of the fifth international congress on mathematical education (pp. 346–351). Boston: Birkhäuser.
Powell, A., Francisco, J., & Maher, C. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22(4), 405–435.
Scarantino, A. (2003). Affordances explained. Philosophy of Science, 70, 949–961.
Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications tasks. Mathematics Education Research Journal, 16(1), 41–76.
Stillman, G., Edwards, I., & Brown, J. (2004). Mediating the cognitive demand of lessons in real-world settings. In B. Tadich et al. (Eds.), Towards excellence in mathematics (pp. 489–500). Melbourne: MAV.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks: Sage.
Tikhomirov, O. K. (1981). The psychological consequences of computerization. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 256–278). Armonk: M. E. Sharpe.
Waisel, L. B., Wallace, W. A., & Willemain, T. R. (1999). Visualizing modelling heuristics: An exploratory study. In ICIS 1999, proceedings of the 20th international conference on information systems (ICIS), Paper 16. http://aisel.aisnet.org/icis1999/16
Waisel, L. B., Wallace, W. A., & Willemain, T. R. (2008). Visualization and model formulation: An analysis of the sketches of expert modelers. Journal of the Operational Research Society, 59(3), 353–361.
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Brown, J.P. (2015). Visualisation Tactics for Solving Real World Tasks. In: Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_36
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