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STRENGTHENING THE CONCEPTUALIZATION OF MATHEMATICS PEDAGOGICAL CONTENT KNOWLEDGE FOR INTERNATIONAL STUDIES: A TAIWANESE PERSPECTIVE

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Abstract

This paper discusses different conceptual frameworks for measuring mathematics pedagogical content knowledge (MPCK) in international comparison studies. Two large-scale international comparative studies, Mathematics Teaching in the Twenty-First Century (MT21; Schmidt et al., 2011) and the Teacher Education and Development Study in Mathematics (TEDS-M; Tatto et al., 2012), were used for analysis. The challenges faced by these studies included the lack of elaborate conceptual frameworks for MPCK developed by non-Western scholars and the corresponding test items that were tied to the frameworks. In this paper, I introduce a conceptual framework developed by Hsieh (Secondary Education, 63(3), 30–47, (2012) in Taiwan relating to MPCK. The items of the 2 international comparison studies were reexamined according to Hsieh’s model. A study based on Hsieh’s model is introduced to manifest the existence of distinct or probably conflicting ideas between Taiwanese and Western countries regarding the scope and substance of different types of mathematics teachers’ knowledge. Hsieh’s model is a start toward searching for an East Asian identity in MPCK.

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References

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

    Article  Google Scholar 

  • Arkar, H., Sorias, O., Tunca, Z., Şafak, C., Alkin, T., Binnur Akdede, B. & Cimilli, C. (2005). Factorial structure, validity and reliability of the Turkish temperament and character inventory. Turkish Journal of Psychiatry, 16(3), 1–14.

    Google Scholar 

  • Ball, D. L. & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Edmonton, Alberta, Canada: Canadian Mathematics Education Study Group/Groupe Canadien d’e´tude En Didactique des Mathe´matiques.

    Google Scholar 

  • Ball, D. L., Hill, H. C. & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29, 14–22.

    Google Scholar 

  • Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  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 

  • Bond, T. G. & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.

    Article  Google Scholar 

  • Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G. & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171–197.

    Article  Google Scholar 

  • ETS (2010). Elementary education: Content knowledge (0014/5014). Princeton, NJ: Educational Testing Service. Retrieved 29 July 2011 from http://www.ets.org/Media/Tests/PRAXIS/taag/0014/glance.htm.

  • Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching: International Research and Pedagogy, 15(1), 13–33.

    Article  Google Scholar 

  • Grossman, P. L. & McDonald, M. (2008). Back to the future: Directions for research in teaching and teacher education. American Educational Research Journal, 45(1), 184–205.

    Article  Google Scholar 

  • Hill, H. C., Ball, D. L. & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.

    Google Scholar 

  • Hill, H. C., Schilling, S. G. & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11–30.

    Article  Google Scholar 

  • Hsieh, F.-J. (2006). Research on the development of the professional ability for teaching mathematics in the secondary school level (1/3) (Rep. No. NSC 94-2522-S-003-009). Taiwan: National Science Council (in Chinese).

    Google Scholar 

  • Hsieh, F.-J. (2009). Research on the development of the professional ability for teaching mathematics in the secondary school level (3/3) (Rep. No. NSC 96-2522-S-003-008). Taiwan: National Science Council (in Chinese).

    Google Scholar 

  • Hsieh, C.-J. (2011). [Concept images of mathematics teaching of secondary mathematics pre-service teachers]. Unpublished doctoral dissertation, National Taiwan Normal University, Taipei.

  • Hsieh, F.-J. (2012). 國高中數學教學專業知能指標 [Indicators of professional mathematics teaching competence at the secondary school level]. Secondary Education, 63(3), 30–47.

    Google Scholar 

  • Hsieh, F.-J., Lin, P.-J. & Wang, T.-Y. (2012). Mathematics related teaching competence of Taiwanese primary future teachers: Evidence from the TEDS-M. ZDM—The International Journal on Mathematics Education, 44(3), 277–292. doi:10.1007/s11858-011-0377-7.

    Article  Google Scholar 

  • Huang, R., & Leung, F. K. S. (2002). Is there a Chinese approach? A comparison on the ways of teaching the Pythagoras theorem among Australia, Czech Republic, Hong Kong and Shanghai. Proceedings of 2nd EARCOME, Singapore, vol. 2, pp. 247–252.

  • König, J., Blömeke, J., Paine, L., Schmidt, W. H. & Hsieh, F.-J. (2011). General pedagogical knowledge of future middle school teachers: On the complex ecology of teacher education in United States, Germany, and Taiwan. Journal of Teacher Education, 62(2), 188–201. doi:10.1177/0022487110388664.

    Article  Google Scholar 

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

    Google Scholar 

  • Lee, Y.-S., Lin, F.-L., Leu, Y.-C. & Chen, M.-F. (2008). 小學教師數學教學發展標準之探究:學者的觀點 [The standards for development in elementary mathematics teaching: Perspectives of elementary mathematics educators]. Chinese Journal of Science Education, 16(6), 627–650.

    Google Scholar 

  • Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47, 35–51.

    Article  Google Scholar 

  • Li, C.-L. & Chung, J. (2007). 數學種子教師專業知能內涵之探討 [Professional knowledge and abilities of a mathematics teacher leader]. Journal of Taiwan Normal University: Mathematics & Science Education, 52, 23–47.

    Google Scholar 

  • Linacre, J. M. (2009). WINSTEPS Rasch measurement computer program (version 3.69.0), Beaverton, Oregon. Winsteps.com.

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

    Google Scholar 

  • Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.

    Article  Google Scholar 

  • Mickovska, A. (2009). A comparative analysis of Macedonian and English teachers’ implicit theories of pupils’ intelligence and motivation. Journal of European Psychology Students, 1(1), 1–10.

    Google Scholar 

  • Ministry of Education (1999). 九年一貫課程概要內涵 [Essentials of nine year sequential curriculum]. Retrieved 5 July 2002 from http://teach.eje.edu.tw/9CC/brief/brief8.php.

  • National Board for Professional Teaching Standards (2001). NBPTS early childhood generalist standards (2nd ed.). Arlington, VA: National Board for Professional Teaching Standards.

    Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Park, K. (2005). Mathematics teacher education in East Asian countries—From the perspective of pedagogical content knowledge. Proceedings of the Third International ICMI East Asia Regional Conference on Mathematics Education, 7–12 August 2005, Shanghai.

  • Pepin, B. (1999). Existing models of knowledge in teaching: Developing an understanding of the Anglo/American, the French and the German scene. TNTEE Publications, 2(1), 49–66.

    Google Scholar 

  • Putnam, R. T. & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning. Educational Researcher, 29, 4–15.

    Article  Google Scholar 

  • Schmidt, W. H., Blömeke, S., Tatto, M. T., Hsieh, F.-J., Cogan, L., Houang, R. T., et al (2011). Teacher education matters: A study of middle school mathematics teacher preparation in six countries. New York, NY: Teacher College Press.

    Google Scholar 

  • Schön, D. A. (1983). The reflective practitioner: How professionals think in action. New York, NY: Basic Books.

    Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

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

    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 

  • Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Rowley, G., Peck, R., et al (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Amsterdam: Multicopy.

    Google Scholar 

  • Viadero, D. (2004). Teaching mathematics requires special set of skills. Education Week, p. 8.

  • Wang, T.-Y., Hsieh, F.-J., & Schmidt, W. H. (2012). Comparison of mathematical language-related teaching competence of future teachers from Taiwan and the United States. Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education, Taiwan, vol. 4, pp. 211–218.

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  1. National Taiwan Normal University, 88, Sec. 4, Ting Chou Road, Taipei, 116, Taiwan, Republic of China

    Feng-Jui Hsieh

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  1. Feng-Jui Hsieh
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Correspondence to Feng-Jui Hsieh.

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Hsieh, FJ. STRENGTHENING THE CONCEPTUALIZATION OF MATHEMATICS PEDAGOGICAL CONTENT KNOWLEDGE FOR INTERNATIONAL STUDIES: A TAIWANESE PERSPECTIVE. Int J of Sci and Math Educ 11, 923–947 (2013). https://doi.org/10.1007/s10763-013-9425-9

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  • DOI: https://doi.org/10.1007/s10763-013-9425-9

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