Abstract
This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and their reflections on the nature of mathematics and mathematics teaching and learning with digital media. I discussed three different ways in which this media was used by the teachers; first, as a means to engage in technical-applied mathematics to engineer mathematical models; second, as a means to construct models for students to engage in experimental-constructivist activity; thirdly, as a means to engage in a discussion of a challenging mathematical problem.
Similar content being viewed by others
Notes
http://odysseia.cti.gr/English/ODYSSEIANEW.
“Preparation for Teacher Education for new practices with new tools in the classroom”. E42: Postgraduate course in the Educational Use of Computer and Information Technology in Secondary Education, Ministry of Education, EPEAEK, 1999–2000.
“Turtleworlds” is an E-slate Logo microworld combining turtle graphics with dynamic manipulation of variable values (Kynigos 2002). It can be downloaded from http://etl.ppp.uoa.gr.
References
Bartolini Bussi, M. G. (1999). Verbal interaction in mathematics classroom: A Vygotskian analysis. In A. Sierpinska et al. (Eds.), Language and communication in mathematics classroom (pp. 65–84). Reston, VA: NCTM.
Bowers, J., & Doerr, H. (2001). An analysis of prospective teachers’ dual roles in understanding the mathematics of change: Eliciting growth with technology. Journal of Mathematics Teacher Education, 4, 115–137.
Confrey, J. (1993). The role of technology in reconceptualizing functions and algebra. In J. Becker & B. Pence (Eds.), Proceedings of the 27th Annual Meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 47–74). California, USA.
Cooney, T. J. (1999). Conceptualizing teachers’ ways of knowing, Educational Studies in Mathematics, 38, 163–187.
Dewey, J. (1938). Education and experience. New York: Simon and Schuster.
DiSessa, A. (1997). Open toolsets: New ends and new means in learning mathematics and science with computers. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 47–62). Lahti, Finland.
Edwards, L. (1998). Embodying mathematics and science: Microworlds as representations. Journal of Mathematical Behavior, 17(1), 53–78.
Ernest, P. (1989). The knowledge beliefs and attitudes of the mathematics teacher: A Model. Journal of Education for Teaching, 15, 1.
Guin, D., & Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: necessity of instrumental orchestrations. Zentralblatt für Didaktik der Mathematik, 34(5), 204–211.
Hancock, C. (1995). The medium and the curriculum: Reflections on transparent tools and tacit mathematics. In A. diSessa, C. Hoyles, & R. Noss (Eds.), Computers and exploratory learning (pp. 221–241). Heidelberg: Springer-Verlag.
Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. J. Bishop, M. A. Clements, C. Keiterl, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 323–349). Dordrecht: Kluwer Academic Publishers.
Jackiw, N. (1991). The geometer’s sketchpad. Berkeley, CA: Key Curriculum Press.
Kafai Y., & Resnick M. (Eds.) (1996). Constructionism in practice. Designing, thinking and learning in a digital world. Mahwah, NJ: Lawrence Earlbaum Associates.
Kaput, J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Bieler, R. W. Scholz, R. Strasser, & B. Winkelman (Eds.), Mathematics didactics as a scientific discipline. Dordecht, Netherlands: Kluwer.
Krainer, K. (2003). Teams, communities and networks. Journal of Mathematics Teacher Education, 6(2), 93–105. Dordrecht: Kluwer Academic Publishers.
Kontogiannopoulou-Polidorides, G. (1996). Educational paradigms and models of computer use: Does technology change educational practice? In T. Plomp, R. E. Anderson, & G. Kontogiannopoulou-Polidorises (Eds.), Cross national policies and practices on computers in education (pp. 49–84). Dortrecht: Kluwer Academic Press.
Korthagen, F., & Kessels, J. (1999). Linking theory and practice: Changing the pedagogy of teacher education. Educational Researcher, 28(4), 4–17.
Kynigos, C. (2004). Α black and white box approach to user empowerment with component computing. Interactive Learning Environments, 12(1–2), 27–71.
Kynigos C., & Argyris, M. (2004) Teacher beliefs and practices formed during an innovation with computer-based exploratory mathematics in the classroom. Teachers And Teaching: Theory and Practice, 10(3), 247–273.
Kynigos, C. (2002). Generating cultures for mathematical microworld development in a multi-organisational context. Journal of Educational Computing Research, (1 & 2), 183–209.
Kynigos, C. (2001). New practices with new tools in the classroom: Educating teacher trainers in Greece, to generate a ‘school community’ use of new technologies. Themes in Education, 2.4, 381–399.
Kynigos, C., Koutlis, M., & Hadzilakos, Th. (1997). Mathematics with component-oriented exploratory software. International Journal of Computers for Mathematical Learning, 2, 229–250.
Laborde, C. (2000). Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Educational Studies In Mathematics, 44, 151–161. Netherlands: Kluwer Academic Publishers.
Laborde, C. (2001). The use of new technologies as a vehicle for restructuring teachers’ mathematics. In F. L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 87–109). Dordrecht: Kluwer Academic Publishers.
Laborde, C., Kynigos, C., Hollebrands, K., & Strasser, R. (2006) Teaching and learning geometry with technology. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275–304). Sense Publishers.
Mariotti, M. A. (2002). Influence of technology advances on students’ math learning. In L. English (Ed.), Handbook of international research in mathematics education, Mahwah, NJ: Lawrence Erlbaum.
Maritsas, M., Hatzilakos, Th., Kynigos, C., Koutlis, M., & Christodoulakis, D. (1992). “Astrolavos”: A Program to Utilize Computing Technologies to Support Education in the Hellenic Secondary Schools, Proposal submitted to the Ministry of Education under the supervision of D. Maritsas.
Nohda, N. (1996). From measurement to conjecture and proof in geometry problems—students use of measurements in the computer environment. In L. Puig & A. Gutierrez (Eds.), Proceedings of the 20th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 161–169). Valencia, Spain.
Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht/Boston/London: Kluwer Academic Publishers.
Oliveiro, F., & Robutti, O. (2001). Measures in Cabri as bridge between perception and theory. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th annual conference of the international group for the psychology of mathematics education (Vol. 4, pp. 9–16). The Netherlands: Utrecht.
Rabardel, P. (2001). Instrument mediated activity in situations. In A. Blandford, J. Vanderdonckt, & P. Gray (Eds.), People and computers XV—Interactions without frontiers (pp. 17–30). Berlin: Springer-Verlag.
Schön, D. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.
Sutherland, R., & Balacheff, N. (1999). Didactical complexity of computational environments for the learning of mathematics, International Journal of Computers for Mathematical Learning, 4, 1–26, Dordrecht: Kluwer Academic Publishers.
Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7, 5–32, Dordrecht: Kluwer Academic Publishers.
Acknowledgment
Thanks to Nikoleta Xenou and Kostas Gavrilis, my co-instructors who helped with the interviews and the reporting of the teacher education activity in the schools.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kynigos, C. Using half-baked microworlds to challenge teacher educators’ knowing. Int J Comput Math Learning 12, 87–111 (2007). https://doi.org/10.1007/s10758-007-9114-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10758-007-9114-2