Teacher education and the professional development of practicing teachers need to provide a sound basis of knowledge for teaching, theoretically but also with strong ties to issues of practice. Although this seems like a common-sense statement, it is harder to make a reality than expected. At least three factors could account for this difficulty: the sheer complexity of the knowledge required for teaching, the interconnectedness of knowledge, and the fact that teachers’ knowledge comes from different and in certain cases even contradictory sources.
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Keywords
- Professional Development
- Content Knowledge
- Mathematics Teacher
- Pedagogical Content Knowledge
- Mathematical Knowledge
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References
Agudelo-Valderrama, C. (2004a). Explanations of attitudes to change: Colombian mathematics teachers’ conceptions of their own teaching practices of beginning algebra. Ph.D. dissertation, Monash University, Melbourne.
Agudelo-Valderrama, C. (2004b). A novice teacher’s conception of the crucial determinants of his teaching of beginning algebra. In I. Putt, R. Faragher, & M. McLean (Eds.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 1 (pp. 31–38). Townsville, Australia: MERGA.
Agudelo-Valderrama, C., & Clarke, B. (2005). The challenges of mathematics teacher change in the Colombian context: The power of institutional practices. Paper presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil.
Agudelo-Valderrama, C., Clarke, B., & Bishop, A. (2007). Explanations of attitudes to change: Colombian mathematics teachers’ conceptions of the crucial determinants of their teaching practices of beginning algebra. Journal of Mathematics Teacher Education, 10, 69–93.
Atkinson, T., & Claxton, G. (Eds.). (2000). The intuitive practitioner: On the value of not always knowing what one is doing. Philadelphia: Open University Press.
Ball, D., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.
Ball, D., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2001 Annual Meeting of the Canadian Mathematics Education Study Group, (p. 3014). Edmonton, CA: CMESG/GCEDM.
Ball, D., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 14–46.
Baumert, J., Blum, W., & Neubrand, M. (2004). Drawing the lessons from PISA-2000: Long term research implications: Gaining a better understanding of the relationship between system inputs and learning outcomes by assessing instructional and learning processes as mediating factors. In D. Lenzen, J. Baumert, R. Watermann, & U. Trautwein (Eds.), PISA und die Konsequenzen für die erziehungswissenschaftliche Forschung Zeitschrift für Erziehungswissenschaft, Special Issue, 3, 143–158.
Blum, W., Baumert, J., Neubrand, M., Krauss, S., Brunner, M., Jordan, A., et al. (2005, May). COACTIV—A Project for Measuring and Improving the Professional Expertise ofMathematics Teachers. Paper presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil.
Brousseau, G. (1986). Fondements et méthodes de la didactique des mathématiques. Recherches en didactique des mathématique, 7(2). 33–115.
Brunner, M., Kunter, M., Krauss, St., Klusmann, U., Baumert, J., Blum, W., et al. (2006). Die professionelle kompetenz von Mathematiklehrkräften: Konzeptualisierung, erfassung und bedeutung für den unterricht. Eine zwischenbilanz des COACTIV-Projekts. In M. Prenzel & L. Allolio-Näcke (Eds.), Untersuchungen zur Bildungsqualität von Schule. Abschlussbericht des DFG-Schwerpunktprogramms (pp. 54–83). Münster: Waxmann.
Cooney, T., & Shealy, B. (1997). On understanding the structure of teachers’ beliefs and their relationship to change. In E. Fennema & B.S. Nelson (Eds.), Mathematics teachers in transition (pp. 87–109). Mahwah, N.J.: Lawrence Erlbaum Associates.
DeBlois, L. (1996). Une analyse conceptuelle de la numération positionnelle. Recherches en didactique des mathématique. Les Éditions La pensée sauvage, 16(1), 71–128.
DeBlois, L. (1997a). Trois élèves en difficulté devant des situations de réunion et de complément d’ensembles. Educational Studies in Mathematics, 34(1), 67–96.
DeBlois, L. (1997b). Quand additionner ou soustraire implique comparer. Éducation et Francophonie, XXV(1), 102–120. Québec: Association Canadienne d’éducation en Langue Française (http://ACELF.CA/revue).
DeBlois, L. (2000). Un modèle d’interprétation des activités cognitives pour des élèves qui éprouvent des difficultés d’apprentissage en mathématiques. Dans Actes du colloque “Constructivismes: Usages et perspectives en éducation”, 2 (CD Rom). Genève: SRED, 565–573.
DeBlois, L. (2003a). Préparer à intervenir auprès des élèves en interprétant leurs productions: Une piste. Éducation et Francophonie, XXXI(2).
DeBlois, L. (2003b). Les enjeux d’une formation continue chez les orthopédagogue. 20th Congrès de l’Association Internationale pour la Pédagogie Universitaire (AIPU). Sherbrooke, Québec.
DeBlois, L. (2006). Influence des interprétations des productions des élèves sur les stratégies d’intervention en classe de mathématiques. Educational Studies in Mathematics, 62(3),307–329.
DeBlois, L., & Maheux, J. (2005, May). (Laval University, Canada) When things don’t go exactly as planned: Leveraging from student teachers’ insights to adapted interventions and professional practice. Paper presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil.
DeBlois L., & Squalli, H. (2002). Une modélisation des savoirs d’expérience des orthopédagogues intervenant en mathématiques. Difficultés d’apprentissage et enseignement: Évaluation et intervention (pp. 155–178). Sherbrooke: Éditions du CRP.
Desgagné S, (1997). Le concept de recherche collaborative: L’idée d’un rapprochement entre chercheurs universitaires et praticients enseignants. Revue des sciences de l’éducation, XXIII (2), 371–394.
Driscoll, M., Zawojewski, J., Humez, A., Nikula, J., Goldsmith, L., & Hammerman, J. (2001). Fostering algebraic thinking toolkit. Portsmouth, N.H,: Heinemann.
Erikson, G. (1989). A constructivist approach to the learning of science: Collaborative research with science teachers. Montreal: Université du Québec à Montréal.
Erikson, G. (1991). Collaborative inquiry and the professional development of science teachers, Journal of Educational Thought, 25(3), 228–245.
Fauvel, J., & van Maanen, J. (Eds.). (2000). History in mathematics education: The 10th ICMI Study (New ICMI Study Series, Vol. 6). Dordrecht: Kluwer Academic.
Ferrini-Mundy, J., Floden, R., McCrory, R., Burrill, G., & Sandow, D. (2004). A conceptual framework for knowledge for teaching school algebra. Unpublished manuscript. East Lansing, MI: Michigan State University.
Gates, P. (2001). Mathematics teachers’ beliefs systems: Exploring the social foundations. In M. van den Heuvel-Panuizen (Ed.), Proceedings of the 25th International Conference of Psychology of Mathematics Education, Vol. 3 (pp. 17–24). Utrecht University, The Netherlands: Psychology of Mathematics Education.
Goldsmith, L. T., Seago, N., Driscoll, M., Nikula, J., & Blasi, Z. (2006). Turning to the evidence: Examining the impact of two practice-based professional development programs. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
Goldsmith, L. T., & Seago, N. (2008). Using video cases to unpack the mathematics in students’ mathematical thinking. In Smith M.S. (Ed.) Monographs of the Association of Mathematics Teacher Educators.
Hanna, G. (1983). Rigorous proof in mathematics education. Toronto: OISE-Press.
Hanna, G., & Jahnke, H. (1993). Proof and application. Educational Studies in Mathematics, 24, 421–438.
Heck, D. J. (2003). Measuring teacher knowledge in mathematics professional development using embedded assessments. Paper presented at the annual meeting of the American Educational Research Association, Chicago.
Hill, H., & Ball, D. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35, 330–351.
Hill, H., & Collopy, R. (2002). What might teachers learn: An evaluation of the potential opportunities to learn in Videocase. An evaluation report to VCMPD, University of Michigan, Ann Arbor, MI.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, D.C.: National Academy Press.
Kirsch, A. (2000). Aspects of simplification in mathematics teaching. In I. Westbury, St. Hopmann, & K. Riquarts (Eds.), Teaching as a reflective practice: The German Didaktik tradition (pp. 267–284). Mahwah, N.J.: Lawrence Erlbaum Associates.
Krauss, St., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand. M., & Jordan, A. (2004). COACTIV: Professionswissen von Lehrkräften, kognitiv aktivierender Mathematikunterricht und die Entwicklung von mathematischer Kompetenz. In J. Doll & M. Prenzel (Eds.), Bildungsqualität von Schule: Lehrerprofessionalisierung, Unterrichtsentwicklung und Schülerförderung als Strategien der Qualitätsverbesserung (pp. 31–53). Münster: Waxmann.
Krauss, St., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2007). Are Pedagogical Content Knowledge and Content Knowledge Two Empirically Separable Categories of Knowledge in Mathematics Teachers? Different Answere for Different Degrees of Teacher Expertise. Working paper. Max-Planck-Institute for Human Development, Berlin: Germany.
Krauss, St., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., et al. (in press). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology.
Kunter, M., Klusmann, U., Dubberke, Th., Baumert, J., Blum, W., Neubrand, M., et al. (2007). Linking aspects of teacher competence to their instruction: Results from the COACTIV Project. In M. Prenzel (Ed.), Studies on the educational quality of schools. The final report on the DFG Priority Programme. Münster: Waxmann.
Leikin, R. (2005). Teachers’ learning in teaching: Developing teachers’ mathematical knowledge through instructional interactions. Paper presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil.
Leikin, R. (2005a). Teachers’ learning in teaching: Developing teachers’ mathematical knowledge through instructional interactions. Paper presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil. http://stwww.weizmann.ac.il/G-math/ICMI/log_in.html
Leikin, R. (2005b). Qualities of professional dialog: Connecting graduate research on teaching and the undergraduate teachers’ program. International Journal of Mathematical Education in Science and Technology, 36(1–2), 237–256.
Leikin, R. (2006). Learning by teaching: The case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis & S. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects (pp. 115–140). Mahwah, N.J.: Lawrence Erlbaum Associates.
Leikin, R., & Dinur, S. (2003). Patterns of flexibility: Teachers’ behavior in mathematical discussion. In the Electronic Proceedings of the Third Conference of the European Society for Research in Mathematics Education. http://www.dm.unipi.it/∼didattica/CERME3/WG11.
Leikin, R., Levav-Waynberg, A., Gurevich, I., & Mednikov, L. (2006). Implementation of multiple solution connecting tasks: Do students’ attitudes support teachers’ reluctance? FOCUS on Learning Problems in Mathematics, 28, 1–22.
Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66, 349–371.
Leikin, R., & Zazkis, R. (2007). A view on the teachers’ opportunities to learn mathematics through teaching: Proceedings of the 31st International Group for the Psychology of Mathematics Education (p. 122). Seoul, Korea: University of Seoul Press.
Ma, L. (1999). Knowing and teaching elementary mathematics. Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, N.J.: Lawrence ErlbaumAssociates.
McEwan, H., & Bull, B. (1991). The pedagogic nature of subject matter knowledge’. American Educational Research Journal, 28, 316–334.
Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267.
Maturana H., & Varela, F. (1994). L’arbre de la connaissance. Paris: Addison-Wesley France.
Neubrand, J. (2006). The TIMSS 1995 and 1999 video studies: In search for appropriate units of analysis. In F.K. Leung, K-D. Graf & F.J. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West. The 13th ICMI Study (New ICMI Study Series, Vol. 9), pp. 291–318. New York: Springer.
Organization for Economic Cooperation and Development. (2004). Learning for tomorrow’s world: First results from PISA 2003. Paris: Author.
Piaget, J. (1977). Recherches sur l’abstraction réfléchissante, 1. L’abstraction de l’ordre des relations logico-mathématiques. Paris: Presses Universitaires de France.
René de Cotret, S. (1999). Quelques questions soulevées par l’adoption d’une perspective≪ bio-cognitive ≫ pour l’étude de relations du système didactique, Dans Séminaire DidaTech, Didactique et technologies cognitives en mathématiques, (Vol. 1997, 161–178). Grenoble: Laboratoire Leibniz-IMAG.
Seago, N., & Goldsmith, L. (2006). Learning mathematics for teaching. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 5 (73–80). Charles University, Prague, Czech Republic.
Seago, N., Mumme, J., & Branca, N. (2004). Learning and teaching linear functions. Portsmouth, N.H.: Heinemann.
Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers’ ability to notice classroom interaction. Journal of Technology and Teacher Education, 13(3), 475–491.
Simon, M. (1997) Developing new models of mathematics teaching: An imperative for research on mathematics teacher development. In E. Fennema & B.S. Nelson (Eds.), Mathematics teachers in transition (pp. 55–86). Mahwah, N.J.: Lawrence Erlbaum Associates.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
Sullivan, P., & Mousley, J. (2001). Thinking teaching: Seeing mathematics teachers as active decision makers. In F.L. Lin & T.J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 147–163). Dordrecht, The Netherlands: Kluwer.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Wilson, M., & Lloyd, G. (2000). The challenge to share authority with students: High school teachers reforming classroom roles and activities through curriculum implementation. Journal of Curriculum and Supervision, 15(2), 146–169.
Wood, T. (2005). Developing a more complex form of mathematics practice in the early years of teaching. Paper presented at the International Commission for Mathematical Instruction (ICMI) 15 conference, The professional education and development of teachers of mathematics. Áquas de Lindóia, Brazil.
Orginal titles of papers submitted to ICMI15, Strand II, Theme 4. All papers presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil (available at http://stwww.weizmann.ac.il/G-math/ICMI/log_in.html).
Cecilia Agudelo-Valderrama & Barbara Clarke (2005). The challenges of mathematics teacher change in the Colombian context: The power of institutional practices.
Marcelo Bairral (University of FRualRJ, Brasil) & Joaquin Gimenez (University of Barcelona, Spain). Dialogic use of teleinteractions for distance geometry teacher training 12–16 years old) as an equity framework.
Marcelo Borba (UNESP–São Paulo State, Brazil). Internet-based continuing education programs.
Werner Blum, Jürgen Baumert, Michael Neubrand, Stefan Krauss, Martin Brunner, Alexander Jordan, Mareike Kunter. COACTIV: A project for measuring and improving the professional expertise of mathematics teachers.
Tenoch Cedillo & Marcela Santillan (National Pedagogical University, Mexico), Algebra as a language in use: A promising alternative as an agent of change in the conceptions and practices of the mathematics teachers.
K. C. Cheung & R. J. Huang (Faculty of Education, University of Macau, China). Contribution of realistic mathematics education and theory of multiple intelligences to mathematics practical and integrated applications: Experiences from Shanghai and Macao in China.
Douglas Clarke (Australian Catholic University, Australia) and Barbara Clarke (Monash University, Australia). Effective professional development for teachers of mathematics: Key principles from research and a program embodying these principles.
Lucie DeBlois & Jean-Francois Maheux (Laval University, Canada). When things don’t go exactly as planned: Leveraging from student teachers’ insights to adapted interventions and professional practice.
Roza Leikin (University of Haifa, Israel). Teachers’ learning in teaching: Developing teachers’ mathematical knowledge through instructional interactions.
Teresa Smart & Celia Hoyles (The Institute of Education, United Kingdom). A programme of sustainable professional development for mathematics teachers: Design and practice.
Olof Steinthorsdottir & Gundy Gunnarsdottir (Iceland University, Iceland). Analysis of professional development programs in Iceland.
Terry Wood (Purdue University, U.S.). Developing a more complex form of mathematics practice in the early years of teaching.
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Neubrand, M., Seago, N., Agudelo-Valderrama, C., DeBlois, L., Leikin, R., Wood, T. (2009). The Balance of Teacher Knowledge: Mathematics and Pedagogy. In: Even, R., Ball, D.L. (eds) The Professional Education and Development of Teachers of Mathematics. New ICMI Study Series, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09601-8_21
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