Abstract
In the last years, several studies have investigated the role of technology in teaching and learning mathematics. However, the specific role of computer algebra systems (CAS) in early algebra in contrast to graphic calculators (GC) is still unclear. The CAYEN project is researching this field by comparing 13-year-old pupils—one GC class and two CAS classes have been observed while acquiring elementary algebraic competences with nearly the same teaching sequence. The field of algebraic competences is split into syntactic abilities and symbol sense. The results of this explorative case study show that the development of symbol sense is influenced by the adoption of CAS in the learning process. Especially when transitioning from arithmetic to algebra, the pupils’ views of algebra as well as their conceptions of algebraic objects seem to be affected by the availability of CAS.
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References
Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.
Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25(2), 50–55.
Barzel, B., Drijvers, P., Maschietto, M., & Trouche, L. (2005a). Tools and technologies in mathematical didactics. In M. Bosch (ed.), Proceedings of CERME 4.
Barzel, B., Hußmann, S., & Leuders, T. (2005b). Internet & Co im Mathematikunterricht Computer. Berlin: Cornelsen Scriptor.
Bell, A. (1996). Problem solving aspects to algebra. Two aspects. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra. Perspectives for Research and Teaching (pp. 167–185). Dordrecht: Kluwer.
Boers-van Oosterum, M. A. M. (1990). Understanding of variables and their uses acquired by students in traditional and computer-intensive algebra. Dissertation. MA: University of Maryland.
Brown, R. (1998). Using computer algebra systems to introduce algebra. The International Journal of Computer Algebra in Mathematics Education, 5, 147–160.
Buchberger, B. (1990). Should students learn integration rules? Sigsam Bulletin, 24(1), 10–17.
Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41, 143–163.
Drijvers, P. (2003). Learning algebra in a computer algebra environment. Utrecht: CD-ß Press.
Drijvers, P., & Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics (Vol. 2, pp. 363–392). Charlotte, NC: Information Age.
Fey, J. T. (1990). Quantity. In L. A. Steen (Ed.), On the shoulders of giants (pp. 61–94). Washington, DC: National Academy Press.
Fischer, R. (2007). Technology, mathematics and consciousness of society. In U. Gellert, E. Jablonka (Eds.), Mathematisation and demathematisation. Social, political and ramifications (pp. 67–80). Rotterdam: Sense Publishers.
Fuglestad, A. B. (2006). Students’ choice of tasks and tools in an ICT rich environment. In Contribution to the CERME4 conference.
Fujii, T. (2003). Probing students’ understanding of variables through cognitive conflict: Is the concept of a variable so difficult for students to understand? In N. A. Pateman, et al. (Eds.), Proceedings of the 27th annual meeting of the international group for the psychology of mathematics education (PME).
Hefendehl-Hebeker, L. (2008). Wege zur Formelsprache—Entwicklung algebraischen Denkens als didaktische Aufgabe. Unikate, 33, 66–71.
Heugl, H., Klinger, W., & Lechner, J. (1996). Mathematikunterricht mit Computeralgebrasystemen—Ein didaktisches Lehrerbuch mit Erfahrungen aus dem österreichischen Derive-Projekt. Bonn: Addison-Wesley.
Hoch, M. (2003). Structure sense. In Contribution to the CERME3 conference.
Irwin, K., & Britt, M. (2007). The development of algebraic thinking: Results of a three-year study. In Ministry of Education (Ed.), Findings from the New Zealand Numeracy Development Projects 2006 (pp. 33–43). Wellington: Learning Media Ltd.
Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). New York: Macmillan.
Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40, 173–196.
Malle, G. (1993). Didaktische Probleme der elementaren Algebra. Braunschweig/Wiesbaden: Vieweg.
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra, perspectives for research and teaching (pp. 65–86). Dordrecht: Kluwer.
Monaghan, J. (2005). Computer algebra, instrumentation and the anthropological approach. In Proceedings of CAME4.
Moser-Opitz, E. (2002). Zählen, Zahlbegriff, Rechnen. Bern: Haupt.
Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht: Kluwer.
Pierce, R. V., & Stacey, K. C. (2002). The algebra needed to use computer algebra systems. The Mathematics Teacher, 95, 622–627.
Prediger, S. (2005). Diversity as a chance in mathematics classrooms. International Journal for Mathematics Teaching and Learning.
Siebel, F. (2005). Elementare Algebra und ihre Fachsprache. Mühltal: Allgemeine Wissenschaft.
Strauss, A., & Corbin, J. (1996). Grounded theory—Grundlagen qualitativer Sozialforschung. Weinheim: Beltz, Psychologie Verlags Union.
Tall, D. (1997). Functions and calculus. In A. J. Bishop, et al. (Eds.), International handbook of mathematics education (pp. 289–325). Dordrecht: Kluwer.
Vollrath, H.-J. (1994). Algebra in der Sekundarstufe. Mannheim: BI Wissenschaftsverlag.
Wenger, R. H. (1987). Cognitive science and algebra learning. In A. Schoenfeld (Ed.), Cognitive science and mathematical education. Hillsdale, NJ: Lawrence Erlbaum Associates.
Zbiek, R., Heid, K., Blume, G., & Dick, Th. (2007). Research on technology in mathematics education—A perspective of constructs. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Charlotte, NC: Information Age.
Zorn, P. (2002). Algebra, computer algebra and mathematical thinking. In Contribution to the 2nd international conference on the teaching of mathematics.
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Zeller, M., Barzel, B. Influences of CAS and GC in early algebra. ZDM Mathematics Education 42, 775–788 (2010). https://doi.org/10.1007/s11858-010-0287-0
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DOI: https://doi.org/10.1007/s11858-010-0287-0