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Developing Mathematics Educators

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Third International Handbook of Mathematics Education

Part of the book series: Springer International Handbooks of Education ((SIHE,volume 27))

Abstract

This chapter addresses, from various perspectives, issues associated with teacher education and its development. Several categories of mathematics educators are characterized and their development and roles in the teaching/learning processes are summarized. Cooperation between teachers and researchers as well as the concept of teachers as researchers are discussed from different points of view. The crucial role that observations play at all levels is analyzed and illustrated by two different models of implementation of observations into teachers’ and researchers’ practice. Throughout the chapter the influence of the research of Guy Brousseau on mathematics education research is recognized.

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References

  • Adler, J., Ball, D., Krainer, K., Lin, F.-L., & Novotná, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educational Studies in Mathematics, 60(3), 359–381.

    Article  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 Mathematics Learning, 7, 245–274.

    Article  Google Scholar 

  • Breen, C. (2003). Mathematics teachers as researchers: Living on the edge? In A. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (pp. 523–544). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Brousseau, G. (1989). Utilité et intérêt de la didactique des mathématiques pour un professeur de collège. Petit x, 21, 47–68.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics 1970–1990. Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Brousseau, G. (2002). Cobayes et microbes (G. Warfield, Trans.). Electronic discussion.

    Google Scholar 

  • Brousseau, G., & Warfield, V. M. (1999). The Case of Gaël. The Journal of Mathematical Behavior, 18(1), 7–52.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2001). An experiment on the teaching of statistics and probability. The Journal of Mathematical Behavior, 20(3), 363–411.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, G. (2002). An experiment on the teaching of statistics and probability. Joumal of Mathematical Behavior, 23, 1–20.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2004a). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurement. Journal of Mathematical Behavior, 20, 363–411.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2004b). Rationals and decimals as required in the school curriculum: Part 1: Rationals as measurement. The Journal of Mathematical Behavior, 23(1), 1–20.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2007). Rationals and decimals as required in the school curriculum: Part 2: From rationals to decimals. The Journal of Mathematical Behavior, 26(4), 281–300.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2008). Rationals and decimals as required in the school curriculum: Part 3. Rationals and decimals as linear functions. The Journal of Mathematical Behavior, 27(3), 153–176.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2009). Rationals and decimals as required in the school curriculum: Part 4: Problem solving, composed mappings and division. The Journal of Mathematical Behavior, 28(2–3), 79–118.

    Google Scholar 

  • Brown, L., & Coles, A. (2000). Same/different: A “natural” way of learning mathematics. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 113–120). Hiroshima, Japan: Hiroshima University Press.

    Google Scholar 

  • Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20.

    Article  Google Scholar 

  • Carr, W. (1995). For education: Towards a critical educational inquiry. Buckingham, UK: Open University Press.

    Google Scholar 

  • Cavanagh, M., & Prescott, A. (2007). Professional experience in learning to teach secondary mathematics: Incorporating pre-service teachers into a community of practice. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (pp. 182–191). Adelaide, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Chapman, O. (2008). Mathematics teacher educators’ learning from research on their instructional practices: A cognitive perspective. In B. Jaworski & T. Wood (Eds.), International handbook of mathematics teacher education (Vol. 4, pp. 110–129). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Chevallard, Y. (1985). La transposition didactique. Grenoble, France: La Pensée Sauvage.

    Google Scholar 

  • Clarke, D. (1999). The Learner’s Perspective Study: Research design. Retrieved from http://extranet.edfac.unimelb.edu.au/DSME/lps/.

  • Clarke, D. (2001). Complementary accounts methodology. In D. Clarke (Ed.), Perspectives on practice and meaning in mathematics and science classrooms. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Clarke, D. J., Keitel, C., & Shimizu, Y. (Eds.). (2006). Mathematics classrooms in twelve countries: The insider’s perspective. Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Cochran-Smith, M., & Lytle, S. (1993). Research on teaching and teacher research: The issues that divide. Educational Researcher, 19(2), 2–11.

    Google Scholar 

  • Douady, R. (1991). Tool, object, setting, window elements for analysing and constructing didactical situations in mathematics. In A. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.), Knowledge: Its growth through teaching (pp. 109–130). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Feiman-Nemser, S. (2001). Helping novices learn to teach: Lessons from an exemplary support teacher. Journal of Teacher Education, 52(1), 17–30.

    Article  Google Scholar 

  • Fuglestad, A. B. (2011). Challenges teachers face with integrating ICT with an inquiry approach in mathematics. In CERME 7, Working Group 15. Retrieved April 9, 2011, from http://www.cerme7.univ.rzeszow.pl/WG/15a/CERME7-WG15A-Paper02_Fuglestad.pdf.

  • Goos, M. (2008). Critique and transformation in researcher-teacher relationships in mathematics education. Symposium on the Occasion of the 100th Anniversary of ICMI. Retrieved from http://www.unige.ch/math/EnsMath/Rome2008/partWG3.html.

  • Goos, M., Brown, L., Chapman, O., & Novotná, J. (2010). The learning and development of mathematics teacher educator-researchers. In M. Pinto & T. Kawasaki (Eds.), Proceedings of PME 34 (1st ed., p. 390). Belo Horizonte, Brazil: PME.

    Google Scholar 

  • Goos, M., Brown, L., Chapman, O., & Novotná, J. (2011). The learning and development of mathematics teacher educator-researchers. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (1st ed., p. 173). Ankara, Turkey: International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Jančařík, A., & Novotná, J. (2011). Potential of CAS for development of mathematical thinking. In M. Kováčová (Ed.), Aplimat 2011 (pp. 1375–1384). Bratislava, Slovakia: STU.

    Google Scholar 

  • Jaworski, B. (2003). Research practice into/influencing mathematics teaching and learning development: Towards a theoretical framework based on co-learning partnerships. Educational Studies in Mathematics, 54(2–3), 249–282.

    Article  Google Scholar 

  • Kinach, B. M. (2002). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18, 51–71.

    Article  Google Scholar 

  • Lagrange, J.-B. (2011). Working with teachers: Collaboration in a community around innovative software. In CERME 7, Working Group 15. Retrieved from http://www.cerme7.univ.rzeszow.pl/WG/15a/CERME7-WG15A-Paper24_Lagrange.pdf.

  • Llinares, S., & Krainer, K. (2006). Mathematics (student) teachers and teacher educators as learners. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 429–459). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Margolinas, C. (2002). Situations, milieux, connaissances: Analyse de l’activité du professeur. In J.-L. Dorier, M. Artaud, M. Artigue, R. Berthelot, & R. Floris (Eds.), Actes de la 11ème Ecole d’Eté de Didactique des Mathématiques (pp. 141–156). Grenoble: France La Pensée Sauvage.

    Google Scholar 

  • Margolinas, C., Coulange, L., & Bessot, A. (2005). What can the teacher learn in the classroom? Educational Studies in Mathematics, 59(1–3), 205–304.

    Article  Google Scholar 

  • Mishra, P., & Koehler, M. J. (2006). Technology pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108, 1017–1054.

    Article  Google Scholar 

  • Morin, E. (1999). La tête bien faite—Repenser la réforme, réformer la pensée. Paris, France: Ed. du Seuil.

    Google Scholar 

  • Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn? Journal for Research in Mathematics Education, 40(5), 491–529.

    Google Scholar 

  • Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905–928.

    Article  Google Scholar 

  • Nichols, S. I., & Berliner, D. C. (2005). Collateral damage: How high-stakes testing corrupts America’s schools. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Nieto, L. J. B. (1996). Learning to teach mathematics: Types of knowledge. In J. Giménez, S. Llinares, & V. Sánchez (Eds.), Becoming a primary teacher: Issues from mathematics education (pp. 159–177). Sevilla, Spain: Gracia Alvarez.

    Google Scholar 

  • Novotná, J., Lebethe, A., Rosen, G., & Zack, V. (2003). Navigating between theory and practice: Teachers who navigate between their research and their practice. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of PME 27/PME NA 25 (Vol. 1, pp. 69–99). Honolulu, HI: University of Hawai’i.

    Google Scholar 

  • Novotná, J., Zack, V., Rosen, G., Lebethe, A., Brown, L., & Breen, C. (2006). RF01: Teachers researching with university academics. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Annual Conference of the 30th International Group for the Psychology of Mathematics Education (Vol. 1, pp. 95–124). Praha: Univerzita Karlova v Praze.

    Google Scholar 

  • Piaget, J. (1985). The equilibration of cognitive structures: The central problem of intellectual development. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Salin, M.-H., & Dreslard Nédélec, D. (1999). La collaboration entre chercheurs et enseignants dans un dispositif original d’observation de classes: Le centre d’observation et de recherche sur l’enseignement des mathématiques (COREM). In F. Jaquet (Ed.), Relations between classroom practice and research in mathematics education, Proceedings CIEAEM 50 (pp. 24–37). Neuchâtel, Switzerland: IRDP.

    Google Scholar 

  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123–140.

    Article  Google Scholar 

  • Sarrazy, B. (2002). Effects of variability on responsiveness to the didactic contract in problem-solving among pupils of 9–10 years. European Journal of Psychology of Education, 17(4), 321–341.

    Article  Google Scholar 

  • Sarrazy, B. (2009, December). Les évaluations internationales et leurs effets sur l’enseignement des mathématiques. Tangente Education [La didactique des mathématiques], 11, 9.

    Google Scholar 

  • Sarrazy, B., & Novotná, J. (2005). Didactical contract: Theoretical frame for the analysis of phenomena of teaching mathematics. In J. Novotná (Ed.), Proceedings SEMT 05 (pp. 33–44). Prague, Czech Republic: Charles University.

    Google Scholar 

  • Sherin, M. G. (2002). When teaching becomes learning. Cognition and Instruction, 20(2), 119–150.

    Article  Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.

    Google Scholar 

  • Stehlíková, N. (2007). Charakteristika kultury vyučování matematice. In A. Hošpesová, N. Stehlíková, & M. Tichá (Eds.) Cesty zdokonalování kultury vyučování matematice (pp. 13–48) [Characteristics of the culture of mathematics teaching, in Czech]. České Budějovice: JČU.

    Google Scholar 

  • Stengers, I. (1995). L’invention des sciences modernes. Paris, France: Flammarion.

    Google Scholar 

  • Vacc, N. N., & Bright, G. W. (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89–110.

    Article  Google Scholar 

  • Vygotsky, L. S. (1962). Thought and language. Cambridge, MA: MIT Press (Original work published 1934).

    Google Scholar 

  • Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. Review of Research in Education, 24, 173–209.

    Google Scholar 

  • Wittgenstein, L. (1980). Grammaire philosophique (A.-M. Lecourret, Trans.). Paris, France: Gallimard.

    Google Scholar 

  • Wittgenstein, L. (1983). Remarques sur les fondements des mathématiques. Paris, France: Gallimard.

    Google Scholar 

  • Zack, V., & Graves, B. (2001). Making mathematical meaning through dialogue: “Once you think of it, the z minus three seems pretty weird.” Educational Studies in Mathematics, 46(1–3), 229–271.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Charles University in Prague, Prague, Czech Republic

    Jarmila Novotná

  2. Laboratoire ACTé, Université Blaise Pascal, Clermont-Ferrand, France

    Claire Margolinas

  3. Université Victor Segalen Bordeaux, Bordeaux, France

    Bernard Sarrazy

Authors
  1. Jarmila Novotná
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  2. Claire Margolinas
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  3. Bernard Sarrazy
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Corresponding author

Correspondence to Jarmila Novotná .

Editor information

Editors and Affiliations

  1. Illinois State University, n/a, Normal, 61790-4520, Illinois, USA

    M.A. (Ken) Clements

  2. Fac. Education, Centre for Science, Mathematics &, Monash University, Clayton, 3800, Victoria, Australia

    Alan J. Bishop

  3. FB Erziehungswissenschaft und, Psychologie, FU Berlin, Habelschwerdter Allee 45, Berlin, 14195, Germany

    Christine Keitel

  4. Dept. Mathematics Education, University of Georgia, Aderhold Hall 105, Athens, 30602-7124, Georgia, USA

    Jeremy Kilpatrick

  5. Fac. Education, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong SAR

    Frederick K.S. Leung

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Novotná, J., Margolinas, C., Sarrazy, B. (2012). Developing Mathematics Educators. In: Clements, M., Bishop, A., Keitel, C., Kilpatrick, J., Leung, F. (eds) Third International Handbook of Mathematics Education. Springer International Handbooks of Education, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4684-2_14

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