Abstract
The main aim of the international Teacher Education and Development Study in Mathematics (TEDS-M), carried out under the auspices of the International Association for the Evaluation of Educational Achievement (IEA), was to understand how national policies and institutional practices influence the outcomes of mathematics teacher education. This paper reports on the definition of effective mathematics teacher education in TEDS-M, distinguishing between mathematics content knowledge and mathematics pedagogical content knowledge as essential cognitive components of mathematics teachers’ professional competencies. These competence facets were implemented as proficiency tests based on extensive coordination and validation processes by experts from all participating countries. International acceptance of the tests was accomplished whereas, by necessity, national specifications had to be left out, as is common in comparative large-scale assessments. In this paper, the nature of the TEDS-M tests for the primary study is analysed and commented on detail. The aims are to increase our understanding of mathematics content knowledge and mathematics pedagogical content knowledge, which are still fuzzy domains, to provide a substantive background for interpretations of the test results and to examine whether some educational traditions may be more accurately reflected in the test items than others. For this purpose, several items that have been released by the IEA are presented and elaborately analysed in order to substantiate the test design of TEDS-M. Our main conclusion is that the overall validity of the TEDS-M tests can be regarded as a given, but that readers have to be aware of limitations, amongst others from a continental European point of view.
Originally published in ZDM—The International Journal of Mathematics Education.
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Notes
- 1.
The international costs of TEDS-M were funded by the IEA, the National Science Foundation (REC 0514431) and the participating countries. In Germany, the German Research Foundation funded TEDS-M (DFG, BL 548/3-1). The instruments are copyrighted by the TEDS-M International Study Center at MSU (ISC). The views expressed in this paper are those of the authors and do not necessarily reflect the views of the IEA, the ISC, the participating countries or the funding agencies.
- 2.
The calculations of the percentage frequencies are based on the international TEDS-M data set version 3.0, provided by the IEA.
References
Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., & Pintrich, P. R. (Eds.) (2001). A taxonomy for learning, teaching and assessing: a revision of bloom’s taxonomy of educational objectives. New York: Longman.
Australian Council for Educational Research for the TEDS-M International Study Center (2011). Released items—future teacher mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK)—primary. IEA 2011.
Ball, D. L., & 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: Ablex.
Blömeke, S. (2002). Universität und Lehrerbildung. Bad Heilbrunn: Klinkhardt.
Blömeke, S., Kaiser, G., & Lehmann, R. (Eds.) (2008). Professionelle Kompetenz angehender Lehrerinnen und Lehrer. Wissen, Überzeugungen und Lerngelegenheiten deutscher Mathematikstudierender und -referendare—Erste Ergebnisse zur Wirksamkeit der Lehreraus-bildung. Münster: Waxmann.
Blömeke, S., Suhl, U., & Kaiser, G. (2011). Teacher education effectiveness: quality and equity of future primary teachers’ mathematics and mathematics pedagogical content knowledge. Journal of Teacher Education, 62(2), 154–171.
Blömeke, S., Suhl, U., Kaiser, G., & Döhrmann, M. (2012). Family background, entry selectivity and opportunities to learn: what matters in primary teacher education? An international comparison of fifteen countries. Teaching and Teacher Education, 28, 44–55.
Blum, W., & Kirsch, A. (1991). Preformal proving: examples and reflections. Educational Studies in Mathematics, 22, 183–202.
Bromme, R. (1992). Der Lehrer als Experte. Zur Psychologie des professionellen Wissens. Bern: Huber.
Fan, L., & Cheong, N. P. C. (2002). Investigating the sources of Singaporean mathematics teachers’ pedagogical knowledge. In D. Edge & B. H. Yap (Eds.), Mathematics education for a knowledge-based era (Vol. 2, pp. 224–231). Singapore: AME.
Ferrini-Mundy, J., Floden, R., McCrory, R., Burill, G., & Sandow, D. (2005). A conceptual framework for knowledge for teaching school algebra. East Lansing: Authors.
Gruber, H., & Renkl, A. (2000). Die Kluft zwischen Wissen und Handeln: Das Problem des trägen Wissens. In G. H. Neuweg (Ed.), Wissen—Können—Reflexion. Ausgewählte Verhältnisbestimmungen (pp. 155–174). Innsbruck: Studienverlag.
Healy, L., & Hoyles, C. (1998). Justifying and proving in school mathematics. Technical Report on the Nationwide Survey. London: University of Education.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., et al. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: an exploratory study. Cognition and Instruction, 26(4), 430–511.
Hsieh, F.-J., Lin, P.-J., & Wang, T.-Y. (2012). Mathematics related teaching competence of Taiwanese primary future teachers: evidence from TEDS-M. ZDM—The International Journal on Mathematics Education, 44(3), 277–292.
Hudson, B. & Meyer, M. A. (Eds.) (2011). Beyond fragmentation: didactics, learning and teaching in Europe. Opladen, Farmington Hills: Barbara Budrich Publishers.
Kaiser, G. (1999). Unterrichtswirklichkeit in England und Deutschland. Vergleichende Untersuchungen am Beispiel des Mathematikunterrichts. Weinheim: Deutscher Studien Verlag.
Kaiser, G. (2002). Educational philosophies and their influences on mathematics education—an ethnographic study in English and German classrooms. Zentralblatt für Didaktik der Mathematik, 34(6), 241–256.
Kaiser, G., Hino, K., & Knipping, C. (2006). Proposal for a framework to analyse mathematics education in Eastern and Western traditions. In K. D. Graf, F. Leung, & F. Lopez-Real (Eds.), New ICMI studies series: Vol. 9. Mathematics education in different cultural traditions—a comparative study of East Asia and the West (pp. 319–351). New York: Springer.
Kansanen, P. (1999). The Deutsche Didaktik and the American research on teaching. In B. Hudson, F. Buchberger, P. Kansanen, & H. Seel (Eds.), Didaktik/Fachdidaktik as science(-s) of the teaching profession (Vol. 2, pp. 21–35). Umea: TNTEE Publications.
Knipping, C. (2008). A method for revealing structures of argumentation in classroom proving processes. Zentralblatt für Didaktik der Mathematik, 40(3), 427–441.
Kultusministerkonferenz (KMK) (2003). Bildungsstandards im Fach Mathematik für den Mittleren Schulabschluss. Köln: Luchterhand.
Kultusministerkonferenz (KMK) (2004a). Standards für die Lehrerbildung: Bildungswissenschaften. Beschluss vom 16.12.2004. http://www.kmk.org/fileadmin/veroeffentlichungen_beschluesse/2004/2004_12_16-Standards-Lehrerbildung.pdf. Accessed on 7 May 2012.
Kultusministerkonferenz (KMK) (2004b). Bildungsstandards im Fach Mathematik für den Primarbereich. Köln: Luchterhand.
Li, J., & Wisenbaker, J. M. (2008). Research and developments in the teaching and learning of probability and statistics. In M. Niss & E. Emborg (Eds.), Proceedings of the 10th international congress on mathematical education, 4–11 July 2004. Roskilde, Roskilde University. (pp. 337–340).
Mason, J., & Pimm, D. (1984). Generic examples: seeing the general in the particular. Educational Studies in Mathematics, 15, 277–289.
Mullis, I. V. S., Martin, M. O., & Foy, P. (2008). TIMSS 2007 international mathematics report. Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill: TIMSS & PIRLS International Study Center, Boston College.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston: NCTM.
NCATE (2008). Unit standards in effect 2008. http://www.ncate.org/Standards/NCATEUnitStandards/UnitStandardsinEffect2008/tabid/476/Default.aspx. Accessed on 7 May 2012.
Niss, M. (2003). Mathematical competencies and the learning of mathematics: the Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), 3rd Mediterranean conference on mathematical education, Athens, Hellas, 3–5 January 2003 (pp. 116–124). Athens: Hellenic Mathematical Society.
Padberg, F. (1997). Einführung in die Mathematikdidaktik. Heidelberg: Spektrum Akademischer Verlag.
Pepin, B. (1999). Existing models of knowledge in teaching: developing an understanding of the Anglo/American, the French and the German scene. In B. Hudson, F. Buchberger, P. Kansanen, & H. Seel (Eds.), Didaktik/Fachdidaktik as science(-s) of the teaching profession (Vol. 2, pp. 49–66). Umea: TNTEE Publication.
Radatz, H., & Schipper, W. (1983). Handbuch für den Mathematikunterricht an Grundschulen. Hannover: Schroedel.
Reid, D., & Knipping, C. (2010). Proof in mathematics education. Rotterdam: Sense Publisher.
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula, T. Buttery, & E. Guyton (Eds.), Handbook of research on teacher education (2nd ed., pp. 102–119). New York: Macmillan.
Schmidt, W. H., Blömeke, S., & Tatto, M. T. (2011). Teacher education matters. A study of middle school mathematics teacher preparation in six countries. New York: Teacher College Press.
Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many visions, many aims: a cross-national investigation of curricular intentions in school mathematics. Dordrecht: Kluwer.
Schneuwly, B. (2011). Subject didactics—an academic field related to the teacher profession and teacher education. In B. Hudson & M. A. Meyer (Eds.), Beyond fragmentation: didactics, learning and teaching in Europe (pp. 275–286). Opladen, Farmington Hills: Barbara Budrich Publishers.
Schwarz, B., Wissmach, B., & Kaiser, G. (2008). ‘Last curves not quite correct’: diagnostic competences of future teachers with regard to modelling and graphical representations. ZDM—The International Journal on Mathematics Education, 40(5), 777–790.
Senk, S., Tatto, M. T., Reckase, M., Rowley, G., Peck, R., & Bankov, K. (2012). Knowledge of future primary teachers for teaching mathematics: an international comparative study. ZDM—The International Journal on Mathematics Education, 44(3), 307–324.
Shulman, L. S. (1986). Paradigms and research programs in the study of teaching: a contemporary perspective. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 3–36). New York: Macmillan.
Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in mathematics (TEDS-M): policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing: Teacher Education and Development International Study Center, College of Education, Michigan State University.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: a synthesis of research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Weinert, F. E. (2001). Concept of competence: a conceptual clarification. In D. S. Rychen & L. H. Salgnik (Eds.), Defining and selecting key competencies (pp. 45–66). Göttingen: Hogrefe.
Westbury, I. (2000). Teaching as a reflective practice: what might Didaktik teach curriculum? In I. Westbury, S. Hopman, & K. Riquarts (Eds.), Teaching as a reflective practice: the German Didaktik tradition (pp. 15–40). Mahwah: Erlbaum.
Wittmann, E. C., & Müller, G. (1988). Wann ist ein Beweis ein Beweis? In P. Bender (Ed.), Mathematikdidaktik: Theorie und Praxis (pp. 237–257). Berlin: Cornelsen.
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Döhrmann, M., Kaiser, G., Blömeke, S. (2014). The Conceptualisation of Mathematics Competencies in the International Teacher Education Study TEDS-M. In: Blömeke, S., Hsieh, FJ., Kaiser, G., Schmidt, W. (eds) International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6437-8_20
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