Skip to main content

Knowledge of Future Primary Teachers for Teaching Mathematics: An International Comparative Study

  • Chapter
International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

This article reports the results of the Teacher Education and Development Study in Mathematics (TEDS-M) that are related to prospective primary teachers’ knowledge for teaching mathematics. TEDS-M was conducted under the auspices of the International Association for the Evaluation of Educational Achievement with additional support from the US National Science Foundation and the participating countries. In 2008 more than 15,000 future primary teachers, enrolled in about 450 institutions that prepare future primary teachers, were surveyed. Two domains of knowledge for teaching mathematics were assessed using items that had been developed and validated in a cross-national field trial. Large differences in the structure of teacher preparation programs are reported. Differences in mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) were also observed both within and between programs and countries. Anchor points on the MCK and MPCK scales are used to describe qualitative characteristics of knowledge for teaching mathematics.

Originally published in ZDM—The International Journal on Mathematics Education.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    NSF grant number REC 0514431. The views expressed in this article are those of the authors and do not necessarily reflect the views of the NSF or the IEA.

  2. 2.

    TEDS-M is directed by a Joint Management Committee consisting of Maria Teresa Tatto (chair), John Schwille and Sharon L. Senk of Michigan State University; Lawrence Ingvarson, Ray Peck, and Glenn Rowley of the Australian Council for Educational Research; and ex-officio members from the IEA and Statistics Canada.

  3. 3.

    Canada was unable to satisfy the minimum sample size requirements set by the study and consequently results for Canada do not appear in Sect. 5.

  4. 4.

    For Oman, only future secondary teachers participated in the TEDS-M study.

  5. 5.

    The software package WinW3S was provided by the IEA and used in each National Research Center to select the samples of future teachers. This software also allows reliable documentation of the whole sampling process. Sampling errors were computed using a well-established re-sampling method, specifically BRR (balanced half-sample repeated replication).

References

  • American Educational Research Association (2004). English language learners: boosting academic achievement (Vol. 2, Issue 1). Issue researcher: C. E. Snow; Issue reviewers: D. August, R. Gersten, and L. Siegel. Retrieved from American Educational Research Association Research Points website. http://www.aera.net/ResearchPoints.htm.

  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7, 145–172.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: the unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed.). New York: Macmillan Co.

    Google Scholar 

  • Ball, D. L., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching: who knows mathematics well enough to teach third grade. American Educator, Fall, 2005.

    Google Scholar 

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y.-M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.

    Article  Google Scholar 

  • Blömeke, S., Felbrich, A., MĂĽller, C., Kaiser, G., & Lehmann, R. (2008a). Effectiveness of teacher education: state of research, measurement issues and consequences for future studies. ZDM—The International Journal on Mathematics Education, 40(5), 719–734.

    Article  Google Scholar 

  • Blömeke, S., Kaiser, G., Lehmann, R., & Schmidt, W. H. (2008b). Introduction to the issue on empirical research on mathematics teachers and their education. ZDM—The International Journal on Mathematics Education, 40(5), 715–717.

    Article  Google Scholar 

  • Blömeke, S., Suhl, U., & Kaiser, G. (2011a). 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., Lehmann, R., & Döhrmann, M. (2011b). 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(1), 44–55.

    Article  Google Scholar 

  • Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. E. (1999). Children’s mathematics: cognitively guided instruction. Westport: Heinemann.

    Google Scholar 

  • Even, R. & Ball, D. L. (Eds.) (2009). New ICMI study series: Vol. 11. The professional education and development of teachers of mathematics: the 15th ICMI study. New York: Springer.

    Google Scholar 

  • Garden, R., Lie, S., Robitaille, D. F., Angell, C., Martin, M. O., Mullis, I. V. S., et al. (2006). TIMSS advanced 2008 assessment frameworks. Boston College: Chestnut Hill.

    Google Scholar 

  • Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: results from California’s Mathematics Professional Development Institutes. Journal for Research in Mathematics Education, 35, 330–351.

    Article  Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Hill, H. C., Sleep, L., Lewis, J., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: what knowledge matters. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111–156). Charlotte: Information Age.

    Google Scholar 

  • Hsieh, F.-J., Law, C.-K., Shy, H.-Y., Wang, T.-Y., Hsieh, C.-J., & Tang, S.-J. (2011). Mathematics teacher education quality in TEDS-M: globalizing the views of future teachers and teacher educators. Journal of Teacher Education, 62(2), 172–187.

    Article  Google Scholar 

  • Husen, T. (1967). International study of achievement in mathematics: a comparison of twelve countries. New York: Wiley (2 vols.).

    Google Scholar 

  • Krauss, S., Baumert, J., & Blum, W. (2008a). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs. ZDM—The International Journal on Mathematics Education, 40(5), 873–892.

    Article  Google Scholar 

  • Krauss, S., Neubrand, M., Blum, W., & Baumert, J. (2008b). The professional knowledge of German secondary mathematics teachers: investigations in the context of the COACTIV project. Prepared for Topic Study Group 27 (Mathematical knowledge for teaching) of the 11th international congress on mathematical education. http://tsg.icme11.org/tsg/show/30.

  • Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Erlbaum.

    Google Scholar 

  • Masters, G. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.

    Article  Google Scholar 

  • Mazzeo, J., Lazer, S., & Zieky, M. J. (2006). Monitoring educational progress with group-score assessments. In R. L. Brennan (Ed.), Educational measurement (4th ed.). Westport: Praeger.

    Google Scholar 

  • Mullis, I. V. S., Martin, M. O., Ruddock, G. J., O’Sullivan, C. Y., Arora, A., & Erberber, E. (2007). TIMSS 2007 assessment frameworks. Chestnut Hill: Boston College.

    Google Scholar 

  • National Research Council (2010). Preparing teachers: building evidence for sound policy. Washington: National Academies Press. Committee on the Study of Teacher Preparation Programs in the United States.

    Google Scholar 

  • OECD (2005). Attracting, developing and retaining effective teachers—final report: teachers matter. Paris.

    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.), TNTEE publications: Vol. 2(1). Didaktik/Fachdidaktik as science(s) of the teaching profession? (pp. 49–66). Umea.

    Google Scholar 

  • Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press.

    Google Scholar 

  • Schmidt, W. H., Blömeke, S., & Tatto, M. T. (Eds.) (2011a). Teacher education matters: a study of middle school mathematics teacher preparation in six countries. New York: Teachers College Press.

    Google Scholar 

  • Schmidt, W. H., Houang, R., & Cogan, L. (2011b). The role of opportunity to learn in teacher preparation: an international context. Journal of Teacher Education, 62(2), 138–153.

    Article  Google Scholar 

  • Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H. C., Wiley, D. E., Cogan, L. S., & Wolfe, R. C. (2001). Why schools matter: a cross-national comparison of curriculum and learning. New York: Jossey-Bass.

    Google Scholar 

  • Schmidt, W., Tatto, M. T., Bankov, K., Blömeke, S., Cedillo, T., Cogan, L., Han, S. I., Houang, R., Hsieh, F. J., Paine, L., Santillan, M., & Schwille, J. (2007). The preparation gap: teacher education for middle school mathematics in six countries (MT21 report). East Lansing, MI: Michigan State University (NSF REC 0231886/January 2003). http://usteds.msu.edu/MT21Report.pdf.

  • Senk, S. L., Peck, R., Bankov, K., & Tatto, M. T. Conceptualizing and measuring mathematical knowledge for teaching: issues from TEDS-M, an IEA cross-national study. Prepared for Topic Study Group 27 (Mathematical knowledge for teaching) of the 11th international congress on mathematical education. http://tsg.icme11.org/document/get/746.

  • Shulman, L. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57, 1–22.

    Google Scholar 

  • Son, J., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117–142.

    Article  Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap—best ideas from the world’s teachers for improving education in the classroom. New York: Free Press.

    Google Scholar 

  • Tatto, M. T. (Ed.), (2013, in press). Teacher Education Study in Mathematics (TEDS-M): technical report. Amsterdam: International Association for the Evaluation of Student Achievement.

    Google Scholar 

  • Tatto, M. T., Schwille, J., Senk, S. L., Bankov, K., Rodriguez, M., Reckase, M., Ingvarson, L., Rowley, G., & Peck, R. (2013, in press). The Teacher Education Study in Mathematics (TEDS-M), Findings from the IEA study of the mathematics preparation of future teachers. Amsterdam: International Association for the Evaluation of Student Achievement.

    Google Scholar 

  • Tatto, M. T., Schwille, J., Senk, S. L., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education Study in Mathematics (TEDS-M), conceptual framework. Amsterdam: International Association for the Evaluation of Student Achievement.

    Google Scholar 

  • Wu, M. L., Adams, R. J., Wilson, M. R., & Haldane, S. A. (2007). ACER ConQuest version 2: generalised item response modelling software [computer program]. Camberwell: Australian Council for Educational Research.

    Google Scholar 

Download references

Acknowledgements

The authors of this article gratefully acknowledge Michael Rodriguez, University of Minnesota; Jean Dumais, Statistics Canada; Falk Brese, Ralph Carstens, Barbara Malak, Sabine Meinck, and Hans Wagemaker of the IEA; and our colleagues from the National Research Centers in the 17 participating countries.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Sharon L. Senk or Ray Peck .

Editor information

Editors and Affiliations

Appendix

Appendix

This appendix shows the coding guides for the five constructed response sample items reproduced in this article. The items can be identified by their item IDs.

Correct Responses (Code 20)

Picture:

1

figure a
Picture:

2

figure b
Picture:

3

figure c
Picture:

4

figure d
Picture:

5 (Code 10)

figure e
Picture:

6 (Code 11)

figure f
Picture 7:

(Code 12)

figure g

Incorrect response (Code 70)

Picture:

8

figure h

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Senk, S.L., Tatto, M.T., Reckase, M., Rowley, G., Peck, R., Bankov, K. (2014). Knowledge of Future Primary Teachers for Teaching Mathematics: An International Comparative Study. 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_4

Download citation

Publish with us

Policies and ethics