Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics
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From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater depth through case study of two teachers each teaching two lessons of this type. The practitioner model developed in earlier research (Ruthven & Hennessy, Educational Studies in Mathematics 49(1):47–88, 2002; Micromath 19(2):20–24, 2003) provided a framework for synthesising teacher thinking about the contribution of graphing software. Further analysis highlighted the crucial part played by teacher prestructuring and shaping of technology-and-task-mediated student activity in realising the ideals of the practitioner model. Although teachers consider graphing software very accessible, successful classroom use still depends on their inducting students into using it for mathematical purposes, providing suitably prestructured lesson tasks, prompting strategic use of the software by students and supporting mathematical interpretation of the results. Accordingly, this study has illustrated how, in the course of appropriating the technology, teachers adapt their classroom practice and develop their craft knowledge: particularly by establishing a coherent resource system that effectively incorporates the software; by adapting activity formats to exploit new interactive possibilities; by extending curriculum scripts to provide for proactive structuring and responsive shaping of activity; and by reworking lesson agendas to take advantage of the new time economy.
KeywordsClassroom teaching practice Computer graphing software Secondary-school mathematics Teacher knowledge and thinking Technology use and integration
Particular thanks are due to the teacher colleagues featured in the case studies; to Theresa Daly our project secretary; and to the UK Economic and Social Research Council which funded the Eliciting Situated Expertise in ICT-integrated Mathematics and Science Teaching project (R000239823). An earlier report of this study was presented at the November 2008 day-conference of the British Society for Research in Learning Mathematics: we are grateful to the BSRLM audience as well as to the ESM editor and reviewers for their helpful comments and suggestions.
- Brown, S., & McIntyre, D. (1993). Making sense of teaching. Buckingham: Open University Press.Google Scholar
- Burns, R. B., & Lash, A. A. (1986). A comparison of activity structures during basic skills and problem-solving instruction in seventh-grade mathematics. American Educational Research Journal, 23(3), 393–414.Google Scholar
- Caliskan-Dedeoglu, N. (2006). Usages de la géométrie dynamique par des enseignants de collège. Des potentialités à la mise en oeuvre: quelles motivations, quelles pratiques. Unpublished doctoral thesis, University of Paris 7.Google Scholar
- Department for Education and Employment [DfEE] (2001). Key stage 3 national strategy: framework for teaching mathematics. London: DfEE.Google Scholar
- Department for Education and Skills [DfES] (2003). Integrating ICT into mathematics at key stage 3. London: DfES.Google Scholar
- Guin, D., Ruthven, K., & Trouche, L. (Eds.) (2005). The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument. New York: Springer.Google Scholar
- Jenson, J., & Rose, C. B. (2006). Finding space for technology: pedagogical observations on the organization of computers in school environments. Canadian Journal of Learning and Technology, 32(1). Accessed at http://www.cjlt.ca/content/vol32.1/jenson.html
- Lagrange, J.-B., & Caliskan-Dedeoglu, N. (2009). Usages de la technologie dans des conditions ordinaires: le cas de la géométrie dynamique au collège: Potentialités, attentes, pratiques. Recherches en Didactique des Mathématiques, in press.Google Scholar
- Leinhardt, G. (1988). Situated knowledge and expertise in teaching. In J. Calderhead (Ed.), Teachers’ professional learning (pp. 146–168). London: Falmer.Google Scholar
- Leinhardt, G., Putnam, T., Stein, M. K., & Baxter, J. (1991). Where subject knowledge matters. Advances in Research in Teaching, 2, 87–113.Google Scholar
- Office for Standards in Education [OfStEd] (2004). ICT in schools—the impact of government initiatives: secondary mathematics. London: OfStEd.Google Scholar
- Ruthven, K. (2007). Teachers, technologies and the structures of schooling. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, pp. 52–67.Google Scholar
- Ruthven, K. (2008). Towards a naturalistic conceptualisation of technology integration in classroom practice: the example of school mathematics. Education & Didactique. http://www.educ.cam.ac.uk/people/staff/ruthven.
- Ruthven, K., & Hennessy, S. (2003). Successful ICT use in secondary mathematics—a teacher perspective. Micromath, 19(2), 20–24.Google Scholar
- Ruthven, K., Hennessy, S., & Deaney, R. (2005). Incorporating dynamic geometry systems into secondary mathematics education: didactical perspectives and practices of teachers. In D. Wright (Ed.), Moving on with dynamic geometry (pp. 138–158). Association of Teachers of Mathematics: Derby.Google Scholar
- Simmt, E. (1997). Graphing calculators in high school mathematics. Journal of Computers in Mathematics and Science Teaching, 16(2/3), 269–289.Google Scholar
- Strauss, A., & Corbin, J. (1994). Grounded theory methodology: an overview. In N. K. Denzin, & Y. S. Lincoln (Eds.), Handbook of qualitative research. London: Sage.Google Scholar
- Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). ‘150 different ways’ of knowing: representations of knowledge in teaching. In J. Calderhead (Ed.),Exploring teachers’ thinking (pp. 104–124). London: Cassell.Google Scholar