# Designing Technology that Enables Task Design

## Abstract

Although there is considerable interest in the use of technology in mathematics teaching and learning, there has been little focus within mathematics education on the design of the technology itself, or on how technology design might facilitate task design. In this chapter, we address the question of how technology has been designed to enable task design through interviews with four developers of technology environments designed to facilitate the learning of mathematics. Questions ranged from more general ones concerning the purposes and challenges faced in designing the environments to more specific aspects concerned with task design, such as the management of instrumental genesis and the provision of feedback. We found that all designers are facing technical challenges due to rapid hardware and software changes which make it important to identify the crucial aspects of the technology to conserve and develop. Such aspects include maintaining an appropriate balance between flexibility and constraint as well as addressing issues such as the way in which the environment responds to student actions.

## Keywords

Task Design Designers## References

- Beeson, M. (1998). Design principles of Mathpert: Software to support education in algebra and calculus. In N. Kajler (Ed.),
*Computer-human interaction in symbolic computation*(pp. 89–116). New York: Springer.Google Scholar - Bokhove, C., & Drijvers, P. (2010). Digital tools for algebra education: Criteria and evaluation.
*International Journal of Computers for Mathematical Learning,**15*(1), 45–62.CrossRefGoogle Scholar - Bokhove, C., Koolstra, G., Heck, A., & Boon, P. (2006). Using SCORM to monitor student performance: experiences from secondary school practice. In
*LTSN MSOR CAA Series.*Retrieved April 2006 from http://mathstore.ac.uk/articles/maths-caa-series/apr2006/. - Brousseau, G., & Warfield, V. (1999). The case of Gaël.
*Journal of Mathematical Behavior,**18*(1), 7–52.CrossRefGoogle Scholar - Butler, D., Jackiw, N., Laborde, J., Lagrange, J., & Yerushalmy, M. (2009). Design for transformative practices. In C. Hoyles & J.-B. Lagrange (Eds.),
*Mathematics education and technology—rethinking the terrain: The 17th ICMI study*(pp. 425–438). New York: Springer.Google Scholar - Hegedus, S. (2010). Accommodating the instrumental genesis framework within dynamic technological environments.
*For the Learning of Mathematics,**30*(1), 26–31.Google Scholar - Ladel, S., & Kortenkamp, U. (2014). Number concepts—processes of internalization and externalization by the use of multi-touch technology. In U. Kortenkamp, B. Brandt. C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.),
*Early Mathematics Learning: Selected Papers of the POEM 2012 Conference*(pp. 237–253). Dordrecht: Springer.Google Scholar - Leung, F. (2013). Introduction to section C: Technology in the mathematics curriculum. In M. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.),
*Third international handbook of mathematics education*(pp. 517–524). New York: Springer.Google Scholar - Mackrell, K. (2011). Design decisions in interactive geometry software.
*ZDM: The International Journal on Mathematics Education,**43*(3), 373–387.CrossRefGoogle Scholar - Mackrell, K. (2012). Introducing algebra with interactive geometry software.
*Electronic Journal of Mathematics & Technology,**6*(1), 96–114.Google Scholar - Mackrell, K. (2015, February). Feedback and formative assessment with Cabri. Paper presented at CERME 9, Prague, Czech Republic.Google Scholar
- Mavrikis, M., & Gutierrez-Santos, S. (2010). Not all wizards are from Oz: Iterative design of intelligent learning environments by communication capacity tapering.
*Computers & Education,**54*(3), 641–651.CrossRefGoogle Scholar - Mor, Y., & Winters, N. (2007). Design approaches in technology-enhanced learning.
*Interactive Learning Environments,**15*(1), 61–75.CrossRefGoogle Scholar - Rabardel, P. (2002).
*People and technology: A cognitive approach to contemporary instruments*. Retrieved from https://hal.archives-ouvertes.fr/hal-01020705. - Sangwin, C., & Grove, M. (2006). STACK: Addressing the needs of the neglected learners. In M. Seppalal, S. Xambo, & O. Caprotti (Eds.),
*WebALT 2006 Proceedings*(pp. 81–96). Eindhoven, Netherlands: Technical University of Eindhoven.Google Scholar - Sedig, K., & Sumner, M. (2006). Characterizing interaction with visual mathematical representations.
*International Journal of Computers for Mathematical Learning,**11*(1), 1–55.CrossRefGoogle Scholar - Sinclair, N., & Heyd-Metzuyanim, E. (2014). Learning number with TouchCounts: The role of emotions and the body in mathematical communication.
*Technology, Knowledge and Learning,**19*(1), 81–99.CrossRefGoogle Scholar - Stacey, K., & Wiliam, D. (2013). Technology and assessment in mathematics. In M. A. Clements, et al. (Eds.),
*Third international handbook of mathematics education*(pp. 721–751). New York: Springer.Google Scholar

## Software

- Autograph [Computer software] (2015). Retrieved from http://www.autograph-maths.com/.
- Cabri [Computer software].Google Scholar
- Fathom [Computer software].Google Scholar
- Geometer’s Sketchpad [Computer software].Google Scholar
- Data Workshop [Computer software].Google Scholar
- Digital Mathematics Environment [Computer software].Google Scholar
- Tinkerplots [Computer software].Google Scholar