Skip to main content

Advertisement

Log in

The conceptualisation of mathematics competencies in the international teacher education study TEDS-M

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

The main aim of the international teacher education study 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

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.

    Google Scholar 

  • Australian Council for Educational Research for the TEDS-M International Study Center. (2011). Released ItemsFuture 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, CT: Ablex.

    Google Scholar 

  • Blömeke, S. (2002). Universität und Lehrerbildung. Bad Heilbrunn: Klinkhardt.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Blum, W., & Kirsch, A. (1991). Preformal proving: Examples and reflections. Educational Studies in Mathematics, 22, 183–202.

    Article  Google Scholar 

  • Bromme, R. (1992). Der Lehrer als Experte. Zur Psychologie des professionellen Wissens. Bern: Huber.

    Google Scholar 

  • 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, MI: Authors.

    Google Scholar 

  • 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.

    Google Scholar 

  • Healy, L., & Hoyles, C. (1998). Justifying and proving in school mathematics. Technical Report on the Nationwide Survey. London: University of Education.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hsieh, F.-J., Lin, P.-J., & Wang, T.-Y. (2012). Mathematics Related Teaching Competence of Taiwanese Primary Future Teachers: Evidence from TEDS-M. ZDMThe International Journal on Mathematics Education, 44, 3 (this issue).

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.), Mathematics education in different cultural traditions—a comparative study of East Asia and the West (pp. 319–351)., New ICMI Studies Series No. 9 New York: Springer.

    Chapter  Google Scholar 

  • 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, No. 1, pp. 21–35). TNTEE Publications: Umea.

  • Knipping, C. (2008). A method for revealing structures of argumentation in classroom proving processes. Zentralblatt für Didaktik der Mathematik, 40(3), 427–441.

    Article  Google Scholar 

  • 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 (pp. 337–340), 4–11 July 2004. Roskilde, Roskilde University.

  • Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277–289.

    Article  Google Scholar 

  • 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, MA: 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.

    Google Scholar 

  • Padberg, F. (1997). Einführung in die Mathematikdidaktik. Heidelberg: Spektrum Akademischer Verlag.

    Google Scholar 

  • 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, No. 1, pp. 49–66). TNTEE Publication: Umea.

  • Radatz, H., & Schipper, W. (1983). Handbuch für den Mathematikunterricht an Grundschulen. Hannover: Schroedel.

    Google Scholar 

  • Reid, D., & Knipping, C. (2010). Proof in mathematics education. Rotterdam: Sense Publisher.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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. ZDMThe International Journal on Mathematics Education, 44, 3 (this issue).

    Google Scholar 

  • 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.

    Google Scholar 

  • 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, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martina Döhrmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Döhrmann, M., Kaiser, G. & Blömeke, S. The conceptualisation of mathematics competencies in the international teacher education study TEDS-M. ZDM Mathematics Education 44, 325–340 (2012). https://doi.org/10.1007/s11858-012-0432-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-012-0432-z

Keywords

Navigation