# From Acorns to Oak Trees: Charting Innovation Within Technology in Mathematics Education

## Abstract

Technology has created an expectation in all levels of education that requires us to understand how we can harness its potential for improving the depth and quality of mathematical learning. It is highly unlikely that there is a universal recipe or formula for how technology should be used that would satisfy every context or culture, but there have been recurring trends in the process of designing and implementing such innovative environments. By considering the papers included in proceedings of the past International Conferences on Technology in Mathematics Teaching (ICTMT), this chapter aims to highlight how a few key innovations have been seeded and taken root within this community. We begin by describing the ways in which innovation has been presented at ICTMT conferences with a view to exploring this from the perspectives of technology designers, researchers and teachers/lecturers from all levels of education. Given the extensive literature on this topic, it is not feasible to carry out a comprehensive survey of the complete literature base, however it is anticipated that the analysis of key ICTMT papers will be sufficient to present an informative and insightful picture and highlight some important knowledge and experience that has been elicited and disseminated.

## References

- Adu-Gyamfi, K. (1993).
*External multiple representations in mathematics teaching*. A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science.Google Scholar - Amado, N., & Carreira, S. (Eds.). (2015).
*Proceedings of the 12th International Conference on Technology in Mathematics Teaching*. Faro, Portugal: University of Algarve.Google Scholar - Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work.
*International Journal of Computers for Mathematical Learning,**7*(3), 245–274. doi: 10.1023/A:1022103903080 CrossRefGoogle Scholar - Bardini, C. Fortin, P. Oldknow, A., & Vagost D. (Eds.). (2009).
*Proceedings of the 9th International Conference on Technology in Mathematics Teaching*. Metz, France.Google Scholar - Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.),
*Handbook of International Research in Mathematics Education*(2nd ed., pp. 746–805). Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Borba, M. C., & Confrey, J. (1996). A student’s construction of transformation of functions in a multiple representational environment.
*Educational Studies in Mathematics,**31*(3), 319–397.CrossRefGoogle Scholar - Borovcnik, M, & Kautschlitsch, H (Eds.). (2002a).
*5th International Conference on Technology in Mathematics Teaching: Plenary lectures and strands*. Klagenfurt, Austria.Google Scholar - Borovcnik, M., & Kautschlitsch, H. (Eds.). (2002b).
*5th International Conference on Technology in Mathematics Teaching: Special groups and working groups*. Klagenfurt, Austria.Google Scholar - de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: The body in/of mathematics.
*Educational Studies in Mathematics,**83*(3), 453–470.CrossRefGoogle Scholar - diSessa, A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments.
*Journal of the Learning Sciences,**13*(1), 77–103.CrossRefGoogle Scholar - Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. In F. Furinghetti (Ed.),
*Proceedings of the 15th Conference of the International Group for the Psychology of Mathematics Education*(Vol. 1, pp. 33–48). Genova, Italy: University of Genova.Google Scholar - Faggiano, E., & Montone, A. (Eds.). (2013).
*Proceedings of the 11th International Conference on Technology in Mathematics Teaching*. Bari, Italy: University of Bari.Google Scholar - Fey, J. T. (1989). Technology and mathematics education: A survey of recent developments and important problems.
*Educational Studies in Mathematics,**20*(3), 237–272.CrossRefGoogle Scholar - Fischer, G. (2001). External and shareable artifacts as opportunities for social creativity in communities of interest. In J. S. Gero and M. L. Maher (Eds.),
*Proceedings of the Fifth International Conference on Computational and Cognitive Models of Creative Design*(pp. 67–89). Sydney: University of Sydney.Google Scholar - Fraunholz, W. (Ed.). (1997).
*Proceedings of the 3rd International Conference on Technology in Mathematics Teaching*. Koblenz, Germany: University of Koblenz.Google Scholar - Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators.
*International Journal of Computers for Mathematical Learning,**3*(3), 195–227.CrossRefGoogle Scholar - Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In L. Puig & A. Gutiérrez (Eds.),
*Proceedings of the 20th conference of the international group for the psychology of mathematics education*(Vol. 1, pp. 3–19). Valencia: Universidad de Valencia.Google Scholar - Hoyles, C., & Lagrange, J.-B. (Eds.). (2009).
*Mathematics education and technology—Rethinking the terrain: The 17th ICMI study*. Berlin: Springer.Google Scholar - Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. Bishop, M. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.),
*Second international handbook of mathematics education*. Dordrecht: Kluwer Academic.Google Scholar - Jaworski, B. (Ed.). (1993). A bridge between teaching and learning.
*Proceedings of the International Conference on Technology in Mathematics Teaching*. University of Birmingham, UK, LG Davis.Google Scholar - Joubert, M., Clark-Wilson, A., & McCabe, M. (Eds.). (2011). Enhancing mathematics education through technology. In
*Proceedings of the 10th International Conference on Technology in Mathematics Teaching*. Portsmouth, UK: University of Portsmouth.Google Scholar - Kafai, Y. B., & Resnick, M. (1996).
*Constructionism in practice: Designing, thinking, and learning in a digital world*. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Kaput, J. (1999). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows.
*Journal of Mathematical Behavior (special issue),**17*(2), 265–281.Google Scholar - Laborde, C., & Sträßer, R. (2010). Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years.
*ZDM—The International Journal on Mathematics Education*,*42*(1), 121–133.Google Scholar - Linn, M. C., & Peterson, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis.
*Child Development,**56,*1479–1498.CrossRefGoogle Scholar - Maull, W., & Sharp, J. (Eds.). (1999).
*Proceedings of the 4th International Conference on Technology in Mathematics Teaching*. Plymouth, UK: University of Plymouth.Google Scholar - Milkova, E. (Ed.). (2007).
*Proceedings of the 8th International Conference on Technology in Mathematics Teaching*. (CD-Rom) and online at http://fim.uhk.cz/ictmt8/seznam/?nazev=&autor=&typ=&v=1&Submit=Search (abstracts only). - Moreno-Armella, L., Hegedus, S., & Kaput, J. (2008). From static to dynamic mathematics: Historical and representational perspectives.
*Educational Studies in Mathematics,**68,*99–111.CrossRefGoogle Scholar - National Council of Teachers of Mathematics. (1989).
*Curriculum and evaluation standards for school mathematics*. Reston, VA: Author.Google Scholar - National Research Council. (1989).
*Everybody counts*. Washington, DC: National Academy Press.Google Scholar - Noss, R., & Hoyles, C. (1996).
*Windows on mathematical meanings: Learning cultures and computers*. Dordrecht: Kluwer Academic.Google Scholar - Olivero, F., & Sutherland, R. (Eds.). (2005).
*Proceedings of the 7th International Conference on Technology in Mathematics Teaching*(Vols. 1 and 2). Bristol, UK: Bristol University.Google Scholar - Ozgun-Koca, S. A. (1998).
*Students’ use of representations in mathematics education*. In S. B. Berenson, et al. (Eds.),*Procedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*, (Vol. 2, p. 812) Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.Google Scholar - Papert, S. (1980).
*Mindstorms: Children, computers, and powerful ideas*. New York: Basic Books.Google Scholar - Park, D., Lee, J.-H., & Kim, S. (2011). Investigating the affective quality of interactivity by motion feedback in mobile touchscreen user interfaces.
*International Journal of Human-Computer Studies,**69*(12), 839–853.CrossRefGoogle Scholar - Ruthven, K., & Hennessy, S. (2002). A practitioner model for the use of computer-based tools and resources to support mathematics teaching and learning.
*Educational Studies in Mathematics,**49,*47–88.CrossRefGoogle Scholar - Schwarz, B., Dreyfus, T., & Bruckheimer, M. (1990). A model of the function concept in a three-fold representation.
*Computers & Education,**14*(3), 249–262.CrossRefGoogle Scholar - Shaffer, D., & Kaput, J. (1999). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education.
*Educational Studies in Mathematics,**37,*97–119.CrossRefGoogle Scholar - Skemp, R. (1978). Relational understanding and instrumental understanding.
*Arithmetic Teacher,**26,*9–15.Google Scholar - Tartre, L. A. (1990). Spatial orientation skill and mathematical problem solving.
*Journal for Research in Mathematics Education,**21*(3), 216–229.CrossRefGoogle Scholar - Triandafillidis, T., & Hatzikiriakou, K. (Eds.). (2003).
*Proceedings of the 6th International Conference on Technology in Mathematics Teaching*. Volos, Greece: University of Thessally.Google Scholar - Verillon, P., & Rabardel, P. (1995). Cognition and artefacts: A contribution to the study of thought in relation to instrumented activity.
*European Journal of Psychology of Education,**10*(1), 77–102.CrossRefGoogle Scholar - Yeh, A., & Nason, R. (2004). Towards a semiotic framework for using technology in mathematics education: The case of learning 3D geometry. In
*Proceedings of the 12th International Conference on Computers in Education*. Melbourne, Australia.Google Scholar - Yook, H. (2009).
*A study on the types of interactive motions in Mobile touch interface (Doctoral dissertation)*. Korea, HK: Hongik University.Google Scholar

## Appendix 1. The ICTMT Conference Series and Proceedings

- ICTMT1—Birmingham, 1993. Jaworski, B. (Ed.). (1993).
*A bridge between teaching and learning.*In*Proceedings of the International Conference on Technology in Mathematics Teaching*, University of Birmingham, UK, LG Davis.Google Scholar - ICTMT2—Edinburgh, 1995. Scott, T. (Ed.). (1995).
*Informal Proceedings of the Second International Conference on Technology in Mathematics Teaching*. Edinburgh: Napier University.Google Scholar - ICTMT3—Koblenz, 1997. Fraunholz, W. (Ed.). (1997).
*Proceedings of the 3rd International Conference on Technology in Mathematics Teaching*Koblenz, Germany: University of KoblenzGoogle Scholar - ICTMT4—Plymouth, 1999. Maull, W., & Sharp, J. (Eds.). (1999).
*Proceedings of the 4th International Conference on Technology in Mathematics Teaching.*Plymouth, UK: University of Plymouth.Google Scholar - ICTMT5—Klagenfurt, 2001. Borovcnik, M, & Kautschlitsch, H (Eds.). (2002).
*The 5th International Conference on Technology in Mathematics Teaching: Plenary lectures and strands*. Klagenfurt, Austria.Google Scholar - and Borovcnik, M, & Kautschlitsch, H (Eds.). (2002).
*The 5th International Conference on Technology in Mathematics Teaching: Special groups and working groups*. Klagenfurt, Austria.Google Scholar - ICTMT6—Volos, 2003. Triandafillidis, T, & Hatzikiriakou, K. (Eds.). (2003).
*Proceedings of the 6th International Conference on Technology in Mathematics Teaching*. Volos, Greece: University of Thessally.Google Scholar - ICTMT7—Bristol, 2005. Olivero, F., & Sutherland, R. (Eds.). (2005).
*Proceedings of the 7th International Conference on Technology in Mathematics Teaching*(Vols. 1 and 2). Bristol, UK: Bristol University.Google Scholar - ICTMT8—Hradec Králové, 2007. Milkova, E. (Eds). (2007).
*Proceedings of the 8th International Conference on Technology in Mathematics Teaching.*(CD-Rom) and online at http://fim.uhk.cz/ictmt8/seznam/?nazev=&autor=&typ=&v=1&Submit=Search (abstracts only). - ICTMT9—Metz, 2009. Bardini, C., Fortin, P., Oldknow, A., & Vagost D. (Eds.). (2009).
*Proceedings of the 9th International Conference on Technology in Mathematics Teaching*. Metz, France.Google Scholar - ICTMT10—Portsmouth, 2011. Joubert, M., Clark-Wilson, A., & McCabe, M. (Eds.). (2011).
*Enhancing mathematics education through technology.**Proceedings of the 10th International Conference on Technology in Mathematics Teaching*. Portsmouth, UK: University of Portsmouth.Google Scholar - ICTMT11—Bari, 2013. Faggiano, E. & Montone, A. (Eds.). (2013).
*Proceedings of the 11th International Conference on Technology in Mathematics Teaching*. Bari, Italy: University of Bari.Google Scholar - ICTMT12—Faro, 2015. Amado, N. & Carreira, S. (Eds.). (2015).
*Proceedings of the 12th International Conference on Technology in Mathematics Teaching*. Faro, Portugal: University of Algarve.Google Scholar