# Exploring Techno-Pedagogic Task Design in the Mathematics Classroom

Chapter

First Online:

## Abstract

This chapter explores task design in Dynamic and Interactive Mathematics Learning Environments. Teacher knowledge and pedagogical digital tool are discussed under the ideas of Mathematics Digital Task Design Knowledge and Mathematical Digital Boundary Object. Leung’s (*ZDM-The International Journal on Mathematics Education, 43*, 325–336, 2011) techno-pedagogic task design is revisited and refined with respect to these two ideas. A GeoGebra applet on exploring the meaning of convergent sequence is used to illustrated features of techno-pedagogic task design.

## Keywords

Task design Digital-based task Boundary object Teacher knowledge## References

- Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English (Ed.),
*Handbook of international research in mathematics education*(2nd ed., pp. 746–783). New York: Routledge.Google Scholar - Cheng, K., & Leung, A. (2015). A dynamic applet for the exploration of the concept of the limit of a sequence.
*International Journal of Mathematics Education in Science and Technology, 46*(2),187–204.Google Scholar - Crisan, C., Lerman, S., & Winbourne, P. (2007). Mathematics and ICT: A framework for conceptualising secondary school mathematics teachers’ classroom practices.
*Technology, Pedagogy and Education,**16*(1), 21–39.CrossRefGoogle Scholar - Fischbein, E. (1993). The theory of figural concepts.
*Educational Studies in Mathematics,**24*, 139–162.CrossRefGoogle Scholar - Hoyle, C., & Noss, R. (2009). The technological mediation of mathematics and its learning.
*Human Development,**52*, 129–147.CrossRefGoogle Scholar - Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge?
*Contemporary Issues in Technology and Teacher Education,**9*(1), 60–70.Google Scholar - Laborde, C. (2007). The role and uses of technologies in mathematics classrooms: Between challenge and modus Vivendi.
*Canadian Journal of Science, Mathematics and Technology Education,**7*(1), 68–92.CrossRefGoogle Scholar - Leung, A. (2011). An epistemic model of task design in dynamic geometry environment.
*ZDM—The International Journal on Mathematics Education,**43*, 325–336.CrossRefGoogle Scholar - Leung, A., & Bolite-Frant, J. (2015). Designing mathematics tasks: The role of tools. In A. Watson & M. Ohtani (Eds.),
*Task design in mathematics education: The 22nd ICMI study. New ICMI study series*(pp. 191–225). New York: Springer.Google Scholar - Marton, F. (2015).
*Necessary conditions of learning*. New York: Routledge.Google Scholar - Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A new framework for teacher knowledge.
*Teachers College Record,**108*(6), 1017–1054.CrossRefGoogle Scholar - Noss, R., & Hoyle, C. (1996).
*Windows on mathematical meanings*. Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar - Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction.
*International Journal of Computers for Mathematical Learning,**15*, 81–97.CrossRefGoogle Scholar - Star, L. S., & Griesemer, J. R. (1989). Institutional ecology, ‘translations’ and boundary objects: Amateurs and professional in Berkeley’s museum of vertebrate zoology, 1907–1930.
*Social Studies of Science,**19*(3), 387–420.CrossRefGoogle Scholar - Shulman, L. (1986). Those who understand: Knowledge growth in teaching.
*Educational Researcher,**15*(2), 4–14.CrossRefGoogle Scholar - Tapan, S. (2003, February–March).
*Integration of ICT in the teaching of mathematics in situations for treatment of difficulties in proving*. Paper presented to 3rd Conference of the European Society for Research in Mathematics Education (CERME 3), Bellaria, Italy.Google Scholar - Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.),
*The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument*(pp. 197–230). New York: Springer.CrossRefGoogle Scholar

## Copyright information

© Springer International Publishing Switzerland 2017