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Comparative studies of mathematics teaching: does the means of analysis determine the outcome?

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Abstract

This paper addresses four questions concerning the influence of culture on mathematics teachers’ professional practice. Firstly, drawing on categorical data yielded by the application of low inference coding schedule to video recordings of sequences of lessons taught by case study teachers on four common topics in England, Flanders, Hungary and Spain, we undertook an exploratory factor analysis to examine the ways in which such coded variables interact. This process yielded five factors, each of which was interpretable against the literature and highlighted the extent to which dichotomisations of mathematics teaching as reform or traditional are not necessarily helpful, not least because all project teachers exhibited characteristics of both. Secondly, factors scores were analysed by nationality to reveal culturally located practices resonant with the available literature. Thirdly, cluster analyses yielded four well-defined cross-cultural clusters of episodes, each indicative of particular didactical perspectives that appeared to challenge the exclusivity of these culturally located practices. Finally, the key methodological finding was that the manner in which data are analysed influences greatly the outcomes of comparative mathematics research.

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Notes

  1. For TIMSS, the Trends in International Mathematics and Science Study, see http://timss.bc.edu/ and for PISA, the Programme of International Student Assessment, see http://www.oecd.org/pisa/.

References

  • Anderson, L., Ryan, D., & Shapiro, B. (1989). The IEA classroom environment study. Oxford: Pergamon.

    Google Scholar 

  • Andrews, P. (2003). Opportunities to learn in the Budapest mathematics classroom. International Journal of Science and Mathematics Education, 1(2), 201–225.

    Article  Google Scholar 

  • Andrews, P. (2007). Negotiating meaning in cross-national studies of mathematics teaching: Kissing frogs to find princes. Comparative Education, 43(4), 489–509.

    Article  Google Scholar 

  • Andrews, P. (2011). The cultural location of teachers’ mathematical knowledge: Another hidden variable in mathematics education research? In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 99–118). New York: Springer.

    Chapter  Google Scholar 

  • Andrews, P., & Sayers, J. (2012). Teaching linear equations: Case studies from Finland, Flanders and Hungary. The Journal of Mathematical Behavior, 31(4), 476–488.

    Article  Google Scholar 

  • Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68.

    Article  Google Scholar 

  • Blanco, L. (2003). The mathematical education of primary teachers in Spain. International Journal of Mathematics Teaching and Learning. http://www.cimt.plymouth.ac.uk/journal/blanco1.pdf. Accessed 19 Sept 2012.

  • Cady, J., Meier, S., & Lubinski, C. (2007). The mathematical tale of two teachers: A longitudinal study relating mathematics instructional practices to level of intellectual development. Mathematics Education Research Journal, 18(1), 3–26.

    Article  Google Scholar 

  • Carver, F., Fuchs, A., Jantzen, K., & Kelso, J. (2002). Spatiotemporal analysis of the neuromagnetic response to rhythmic auditory stimulation: rate dependence and transient to steady-state transition. Clinical Neurophysiology, 113, 1921–1931.

    Article  Google Scholar 

  • Clarke, D. (2006). Using international research to contest prevalent oppositional dichotomies. ZDM The International Journal on Mathematics Education, 38(5), 376–387.

    Article  Google Scholar 

  • Clarke, D., Keitel, C., & Shimizu, Y. (2006). The learner’s perspective study. In D. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspectives (pp. 1–14). Rotterdam: Sense Publishers.

    Google Scholar 

  • Cogan, L., & Schmidt, W. (1999). An examination of instructional practices in six countries. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 68–85). London: Falmer.

    Google Scholar 

  • Di Stefano, C., Zhu, M., & Mîndrilă, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research & Evaluation, 14(20), 1–11.

    Google Scholar 

  • Evertson, C. M., Anderson, C. W., Anderson, L. M., & Brophy, J. E. (1980). Relationships between classroom behaviors and student outcomes in junior high mathematics and English classes. American Educational Research Journal, 17(1), 43–60.

    Google Scholar 

  • Fabrigar, L., Wegener, D., MacCallum, R., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299.

    Article  Google Scholar 

  • Givvin, K., Hiebert, J., Jacobs, J., Hollingsworth, H., & Gallimore, R. (2005). Are there national patterns of teaching? Evidence from the TIMSS 1999 video study. Comparative Education Review, 49(3), 311–343.

    Article  Google Scholar 

  • Hair, J., Black, W., Babin, B., Anderson, R., & Tatham, R. (2006). Multivariate data analysis (6th ed.). New York: Prentice Hall.

    Google Scholar 

  • Henson, R., & Roberts, J. (2006). Use of exploratory factor analysis in published research: Common errors and some comment on improved practice. Educational and Psychological Measurement, 66(3), 393–416.

    Article  Google Scholar 

  • Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30(1), 3–19.

    Article  Google Scholar 

  • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K., Hollingsworth, H., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington: National Center for Educational Statistics.

    Google Scholar 

  • Hiebert, J., Stigler, J., Jacobs, J., Givvin, K., Garnier, H., et al. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111–132.

    Article  Google Scholar 

  • Hufton, N., & Elliott, J. (2000). Motivation to learn: The pedagogical nexus in the Russian school: Some implications for transnational research and policy borrowing. Educational Studies, 26(1), 115–136.

    Article  Google Scholar 

  • Janssen, R., De Corte, E., Verschaffel, L., Knoors, E., & Colemont, A. (2002). National assessment of new standards for mathematics in elementary education in Flanders. Educational Research and Evaluation, 8(2), 197–225.

    Article  Google Scholar 

  • Jennings, S., & Dunne, R. (1996). A critical appraisal of the National Curriculum by comparison with the French experience. Teaching Mathematics and its Applications, 15(2), 49–55.

    Article  Google Scholar 

  • Jeon, H.-J., Langill, C., Peterson, C., Luze, G., Carta, J., & Atwater, J. (2010). Children’s individual experiences in early care and education: Relations with overall classroom quality and children’s school readiness. Early Education & Development, 21(6), 912–939.

    Article  Google Scholar 

  • Kaiser, G., Hino, K., & Knipping, C. (2006). Proposal for a framework to analyse mathematics education traditions in eastern and western traditions. In F. Leung, K.-D. Graf, & F. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West, the 13th ICMI study (pp. 319–351). New York: Springer.

    Chapter  Google Scholar 

  • Kawanaka, T., Stigler, J., & Hiebert, J. (1999). Studying mathematics classrooms in Germany, Japan and the United States: Lessons from the TIMSS videotape study. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 86–103). London: Falmer.

    Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: The National Academies Press.

    Google Scholar 

  • La Paro, K., Pianta, R., & Stuhlman, M. (2004). The Classroom Assessment Scoring System: Findings from the prekindergarten year. The Elementary School Journal, 104(5), 409–426.

    Article  Google Scholar 

  • Lambert, M., Williams, S., Morrison, J., Samms-Vaughan, M., Mayfield, W., et al. (2008). Are the indicators for the language and reasoning subscale of the early childhood environment rating scale-revised psychometrically appropriate for Caribbean classrooms? International Journal of Early Years Education, 16(1), 41–60.

    Article  Google Scholar 

  • LeTendre, G., Baker, D., Akiba, M., Goesling, B., & Wiseman, A. (2001). Teachers’ work: Institutional isomorphism and cultural variation in the U.S. Germany, and Japan. Educational Researcher, 30(6), 3–15.

    Article  Google Scholar 

  • Leu, Y.-C. (2005). The enactment and perception of mathematics pedagogical values in an elementary classroom: Buddhism, Confucianism, and curriculum reform. International Journal of Science and Mathematics Education, 3(2), 175–212.

    Article  Google Scholar 

  • Leung, F. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51.

    Article  Google Scholar 

  • Ma, Y., Zhao, D., & Tuo, Z. (2004). Differences within communities: How is mathematics taught in rural and urban regions in mainland China? In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 413–442). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Malmberg, L.-E., Hagger, H., Burn, K., Mutton, T., & Colls, H. (2010). Observed classroom quality during teacher education and two years of professional practice. Journal of Educational Psychology, 102(4), 916–932.

    Article  Google Scholar 

  • Maxwell, B., Pryor, F., & Smith, C. (2002). Cluster analysis in cross-cultural research. World Cultures, 13(1), 22–38.

    Google Scholar 

  • Osborn, M. (2004). New methodologies for comparative research? Establishing ‘constants’ and ‘contexts’ in educational experience. Oxford Review of Education, 30(2), 265–285.

    Article  Google Scholar 

  • Pakarinen, E., Lerkkanen, M.-K., Poikkeus, A.-M., Kiuru, N., Siekkinen, M., et al. (2010). A validation of the Classroom Assessment Scoring System in Finnish kindergartens. Early Education & Development, 21(1), 95–124.

    Article  Google Scholar 

  • Peterson, P., Fennema, E., Carpenter, T., & Loef, M. (1989). Teachers’ pedagogical content beliefs in mathematics. Cognition and Instruction, 6(1), 1–40.

    Article  Google Scholar 

  • Schmidt, W., Jorde, D., Cogan, L., Barrier, E., Gonzalo, I., et al. (1996). Characterizing pedagogical flow: An investigation of mathematics and science teaching in six countries. Dordrecht: Kluwer.

    Google Scholar 

  • Sharpe, K. (1997). The Protestant ethic and the spirit of Catholicism: Ideological and institutional constraints on system change in English and French primary schooling. Comparative Education, 33(3), 329–348.

    Article  Google Scholar 

  • Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.

    Google Scholar 

  • Spillane, J., & Zeuli, J. (1999). Reform and teaching: Exploring patterns of practice in the context of national and state mathematics reforms. Educational Evaluation and Policy Analysis, 21(1), 1–27.

    Google Scholar 

  • Stigler, J., Gallimore, R., & Hiebert, J. (2000). Using video surveys to compare classrooms and teaching across cultures: Examples and lessons from the TIMSS video studies. Educational Psychologist, 35(2), 87–100.

    Article  Google Scholar 

  • Stigler, J., Gonzales, P., Kawanaka, T., Knoll, S., & Serrano, A. (1999). The TIMSS videotape classroom study. Washington, DC: National Center for Educational Statistics.

    Google Scholar 

  • Stigler, J., & Perry, M. (1988). Cross cultural studies of mathematics teaching and learning: Recent findings and new directions. In D. A. Grouws, T. J. Cooney, & D. Jones (Eds.), Perspectives on research on effective mathematics teaching. Reston, VA: NCTM.

    Google Scholar 

  • Stipek, D., Givvin, K., Salmon, J., & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226.

    Article  Google Scholar 

  • Szalontai, T. (2000). Some facts and tendencies in Hungarian mathematics teaching. International Journal of Mathematics Teaching and Learning. http://www.cimt.plymouth.ac.uk/journal/tshungmt.pdf. Accessed 4 Dec 2012.

  • Szendrei, J., & Török, J. (2007). The tradition and role of proof in mathematics education in Hungary. In P. Boero (Ed.), Theorems in school (pp. 117–134). Rotterdam: Sense Publishers.

    Google Scholar 

  • Trawick-Smith, J., Russell, H., & Swaminathan, S. (2011). Measuring the effects of toys on the problem-solving, creative and social behaviours of preschool children. Early Child Development and Care, 181(7), 909–927.

    Article  Google Scholar 

  • Waeytens, K., Lens, W., & Vandenberghe, R. (1997). Learning to learn: How do teachers differ? Paper presented at the annual meeting of the American Educational Research Association, Chicago.

  • Watters, P. (2002). Discriminating English word senses using cluster analysis. Journal of Quantitative Linguistics, 9(1), 77–86.

    Article  Google Scholar 

  • Wong, N.-Y. (2008). Confucian heritage culture learner’s phenomenon: From “exploring the middle zone” to “constructing a bridge”. ZDM The International Journal on Mathematics Education, 40(6), 973–981.

    Article  Google Scholar 

  • Wong, N.-Y. (2009). Exemplary mathematics lessons: What lessons we can learn from them? ZDM The International Journal on Mathematics Education, 41(3), 379–384.

    Article  Google Scholar 

  • Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning and Instruction, 7(4), 329–338.

    Article  Google Scholar 

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Acknowledgments

The Mathematics Education Traditions of Europe (METE) project team acknowledges the financial support of the European Union, Socrates Action 6.1 programme, project code 2002-5048.

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Correspondence to Paul Andrews.

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Andrews, P., Sayers, J. Comparative studies of mathematics teaching: does the means of analysis determine the outcome?. ZDM Mathematics Education 45, 133–144 (2013). https://doi.org/10.1007/s11858-012-0481-3

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