Advertisement

Journal of Educational Change

, Volume 16, Issue 3, pp 251–280 | Cite as

Mathematics, PISA, and culture: An unpredictable relationship

  • Paul Andrews
Article
  • 519 Downloads

Abstract

Recent studies have indicated, particularly in the European context, that students’ mathematical successes on international tests of student achievement may not be attributable to the quality of classroom instruction, although, as is shown, this is unlikely to be the case in Flanders, the autonomous Dutch-speaking region of Belgium. Flemish students’ mathematics performance on such tests have placed them at the head of the European rankings, warranting Flanders as a site of research interest that has been largely ignored by the international community. In this paper, drawing on analyses of four sequences of five lessons, taught by teachers construed locally as competent, I explore the nature of Flemish mathematics teaching. Framed by anecdotal reports that it reflects the structuralism of the now largely abandoned Bourbakian new mathematics movement humanised by the Dutch tradition of realistic mathematics education, the analyses focus on examining not only the extent to which these traditions are manifested in Flemish classrooms but the ways in which they interact. The dominant tradition seems to be that of mathematical structuralism mediated by teachers’ use of realistic problems; a tradition not unlikely to underpin Flemish students’ repeated successes. The results are discussed in relation to research highlighting the significance on students’ achievement of the broader cultural milieu in which they and their teachers operate.

Keywords

Bourbaki Finland Flanders Mathematics instruction PISA Realistic mathematics education TIMSS 

Abbreviations

IEA

International Association for the Evaluation of Educational Achievement

OECD

Organisation for Economic Cooperation and Development

PIRLS

Progress in International Reading Literacy Study

PISA

Programme of International Student Assessment

RME

Realistic mathematics education

TIMSS

Trends in International Mathematics and Science Study

References

  1. Aelterman, A., Engels, N., Van Petegem, K., & Pierre Verhaeghe, J. (2007). The well-being of teachers in Flanders: The importance of a supportive school culture. Educational Studies, 33(3), 285–297.CrossRefGoogle Scholar
  2. Agirdag, O., Loobuyck, P., & Van Houtte, M. (2012a). Determinants of attitudes toward Muslim students among Flemish teachers: A research note. Journal for the Scientific Study of Religion, 51(2), 368–376.CrossRefGoogle Scholar
  3. Agirdag, O., Van Houtte, M., & Van Avermaet, P. (2012b). Why does the ethnic and socio-economic composition of schools influence math achievement? The role of sense of futility and futility culture. European Sociological Review, 28(3), 366–378.CrossRefGoogle Scholar
  4. Alexander, R. (2010). ‘World class schools’—noble aspiration or globalised hokum? Compare, 40(6), 801–817.Google Scholar
  5. Andrews, P. (2007). Negotiating meaning in cross-national studies of mathematics teaching: Kissing frogs to find princes. Comparative Education, 43(4), 489–509.CrossRefGoogle Scholar
  6. Andrews, P. (2013). Finnish mathematics teaching from a reform perspective: A video-based case study analysis. Comparative Education Review, 57(2), 189–211.CrossRefGoogle Scholar
  7. Andrews, P. (2014). The Emperor’s new clothes: PISA, TIMSS and Finnish mathematics. In A.-S. Röj-Lindberg, L. Burman, B. Kurtén-Finnäs, & K. Linnanmäki (Eds.), Spaces for learning: Past, present and future (pp. 43–65). Vasa: Åbo Akademi University.Google Scholar
  8. Andrews, P., Ryve, A., Hemmi, K., & Sayers, J. (2014). PISA, TIMSS and Finnish mathematics teaching: An enigma in search of an explanation. Educational Studies in Mathematics, 87(1), 7–26.CrossRefGoogle Scholar
  9. Andrews, P., & Sayers, J. (2013). Comparative studies of mathematics teaching: Does the means of analysis determine the outcome? ZDM: The International Journal on Mathematics Education, 45(1), 133–144.CrossRefGoogle Scholar
  10. Aubin, D. (1997). The withering immortality of Nicolas Bourbaki: A cultural connector at the confluence of mathematics, structuralism, and the Oulipo in France. Science in Context, 10(2), 297–342.CrossRefGoogle Scholar
  11. Ballet, K., & Kelchtermans, G. (2008). Workload and willingness to change: Disentangling the experience of intensification. Journal of Curriculum Studies, 40(1), 47–67.CrossRefGoogle Scholar
  12. Barnes, H. (2005). The theory of realistic mathematics education as a theoretical framework for teaching low attainers in mathematics. Pythagoras, 61(June), 42–57.Google Scholar
  13. Bray, M. (2010). Researching shadow education: Methodological challenges and directions. Asia Pacific Education Review, 11(1), 3–13.CrossRefGoogle Scholar
  14. Buchmann, C., & Park, H. (2009). Stratification and the formation of expectations in highly differentiated educational systems. Research in Social Stratification and Mobility, 27(4), 245–267.CrossRefGoogle Scholar
  15. Cai, J., Ding, M., & Wang, T. (2014). How do exemplary Chinese and U.S. mathematics teachers view instructional coherence? Educational Studies in Mathematics, 85(2), 265–280.CrossRefGoogle Scholar
  16. Cai, J., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context: Perspectives of teachers from China and the United States. Journal of Mathematics Teacher Education, 13(3), 265–287.CrossRefGoogle Scholar
  17. Cartan, H. (1980). Nicolas Bourbaki and contemporary mathematics. The Mathematical Intelligencer, 2(4), 175–180.CrossRefGoogle Scholar
  18. Cherchye, L., De Witte, K., Ooghe, E., & Nicaise, I. (2010). Efficiency and equity in private and public education: A nonparametric comparison. European Journal of Operational Research, 202(2), 563–573.CrossRefGoogle Scholar
  19. Clark, C. (2005). The author who never was: Nicolas Bourbaki. Science Editor, 28(3), 82–86.Google Scholar
  20. Clarke, D. (2006). Using international research to contest prevalent oppositional dichotomies. ZDM, 38(5), 376–387.CrossRefGoogle Scholar
  21. De Cooman, R., De Gieter, S., Pepermans, R., Du Bois, C., Caers, R., & Jegers, M. (2007). Graduate teacher motivation for choosing a job in education. International Journal for Educational and Vocational Guidance, 7(2), 123–136.CrossRefGoogle Scholar
  22. De Lange, J. (2002). Between end and beginning: Mathematics education for 12–16 year olds: 1987–2002. Educational Studies in Mathematics, 25(1/2), 137–160.Google Scholar
  23. De Meyer, I. (2008). Science competencies for the future in Flanders: The first results from PISA 2006. Gent: University of Gent and the Ministry of Education of the Flemish Community of Belgium.Google Scholar
  24. De Meyer, I., De Vos, H., & Van de Poele, L. (2002). Worldwide learning at age 15: First results from PISA 2000. Gent: University of Gent and Ministry of the Flemish Community Education Department.Google Scholar
  25. De Meyer, I., Pauly, J., & Van de Poele, L. (2005). Learning for tomorrow’s problems First Results from PISA2003. Gent: University of Gent and the Ministry of Education of the Flemish Community of Belgium.Google Scholar
  26. De Meyer, I., & Warlop, N. (2010). Leesvaardigheid van 15-jarigen in Vlaanderen: De eerste resultaten van PISA 2009. Gent: Universiteit Gent and Departement Onderwijs and Vorming.Google Scholar
  27. De Rynck, S. (2005). Regional autonomy and education policy in Belgium. Regional & Federal Studies, 15(4), 485–500.CrossRefGoogle Scholar
  28. Devos, G., Bouckenooghe, D., Engels, N., Hotton, G., & Aelterman, A. (2007). An assessment of well-being of principals in Flemish primary schools. Journal of Educational Administration, 45(1), 33–61.Google Scholar
  29. Dolk, M., den Hertog, J., & Gravemeijer, K. (2002). Using multimedia cases for educating the primary school mathematics teacher educator: A design study. International Journal of Educational Research, 37(2), 161–178.CrossRefGoogle Scholar
  30. Dronkers, J., & Van der Velden, R. (2013). Positive but also negative effects of ethnic diversity in schools on educational performance? An empirical test using PISA data. In M. Windzio (Ed.), Integration and inequality in educational institutions. Dordrecht: Springer.Google Scholar
  31. Dykstra, T. (2006). High performance and success in education in Flemish Belgium and the Netherlands. Washington DC: National Center on Education and the Economy.Google Scholar
  32. Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24(1), 8–40.CrossRefGoogle Scholar
  33. Elbers, E., & De Haan, M. (2005). The construction of word meaning in a multicultural classroom. Mediational tools in peer collaboration during mathematics lessons. European Journal of Psychology of Education, 20(1), 45–59.CrossRefGoogle Scholar
  34. Engels, N., Aelterman, A., Petegem, K. V., & Schepens, A. (2004). Factors which influence the well-being of pupils in Flemish secondary schools. Educational Studies, 30(2), 127–143.CrossRefGoogle Scholar
  35. Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1(1–2), 3–8.CrossRefGoogle Scholar
  36. Freudenthal, H. (1979). New math or new education? Prospects: Quarterly Review of Education, 9, 321–331.CrossRefGoogle Scholar
  37. Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer.Google Scholar
  38. Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3–20.CrossRefGoogle Scholar
  39. Furinghetti, F., Matos, J., & Menghini, M. (2013). From mathematics and education, to mathematics education. In M. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education (pp. 273–302). New York: Springer.Google Scholar
  40. Gispert, H., & Schubring, G. (2011). Societal, structural, and conceptual changes in mathematics teaching: Reform processes in France and Germany over the twentieth century and the international dynamics. Science in Context, 24(1), 73–106.CrossRefGoogle Scholar
  41. Gorard, S., & Smith, E. (2004). An international comparison of equity in education systems. Comparative Education, 40(1), 15–28.CrossRefGoogle Scholar
  42. Gravemeijer, K. (1994). Educational development and developmental research in mathematics education. Journal for Research in Mathematics Education, 25(5), 443–471.CrossRefGoogle Scholar
  43. Gravemeijer, K. (1998). Developmental research as a research method. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (Vol. 4, pp. 277–295). Dordrecht: Springer.CrossRefGoogle Scholar
  44. Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics Education. Mathematical Thinking and Learning, 6(2), 105–128.CrossRefGoogle Scholar
  45. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1–3), 111–129.CrossRefGoogle Scholar
  46. Guedj, D. (1985). Nicholas bourbaki, collective mathematician: An interview with Claude Chevalley. The Mathematical Intelligencer, 7(2), 18–22.CrossRefGoogle Scholar
  47. Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567–590.CrossRefGoogle Scholar
  48. Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6–13.CrossRefGoogle Scholar
  49. Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 195–222.CrossRefGoogle Scholar
  50. Itkonen, T., & Jahnukainen, M. (2007). An analysis of accountability policies in Finland and the United States. International Journal of Disability, Development and Education, 54(1), 5–23.CrossRefGoogle Scholar
  51. 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.CrossRefGoogle Scholar
  52. Keijzer, R., & Terwel, J. (2003). Learning for mathematical insight: A longitudinal comparative study on modelling. Learning and Instruction, 13(3), 285–304.CrossRefGoogle Scholar
  53. Kilpatrick, J. (2012). The new math as an international phenomenon. ZDM, 44(4), 563–571.CrossRefGoogle Scholar
  54. Klein, D. (2003). A brief history of American K-12 mathematics education in the 20th century. In J. M. Royer (Ed.), Mathematical cognition: Current perspectives on cognition, learning and instruction (pp. 175–225). Charlotte NC: Information Age.Google Scholar
  55. Kroesbergen, E., & van Luit, J. (2002). Teaching multiplication to low math performers: Guided versus structured instruction. Instructional Science, 30(5), 361–378.CrossRefGoogle Scholar
  56. Landry, E. (2007). Shared structure need not be shared set-structure. Synthese, 158(1), 1–17.CrossRefGoogle Scholar
  57. Laukkanen, R. (2008). Finnish strategy for high-level education for all. In N. C. Soguel & P. Jaccard (Eds.), Governance and performance of education systems (pp. 305–324). Dordrecht: Springer.Google Scholar
  58. Leflot, G., van Lier, P. A. C., Onghena, P., & Colpin, H. (2013). The role of children’s on-task behavior in the prevention of aggressive behavior development and peer rejection: A randomized controlled study of the good behavior game in Belgian elementary classrooms. Journal of School Psychology, 51(2), 187–199.CrossRefGoogle Scholar
  59. Linnakylä, P. (2002). Reading in Finland. In C. Papanastasiou & V. Froese (Eds.), Reading literacy in 14 countries. Lefkosia: University of Cyprus Press.Google Scholar
  60. Maasz, J., & Schlöglmann, W. (2006). Introduction. In J. Maasz & W. Schloeglmann (Eds.), New mathematics education research and practice (pp. 1–6). Rotterdam: Sense.Google Scholar
  61. Martio, O. (2009). Long term effects in learning mathematics in Finland—curriculum changes and calculators. The Teaching of Mathematics, 12(2), 51–56.Google Scholar
  62. Meyer, H.-D. (2013). OECD’s PISA: A tale of flaws and hubris. Teachers College Record.Google Scholar
  63. Mullis, I., Martin, M., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Boston: TIMSS & PIRLS International Study Center, Boston College.Google Scholar
  64. Mullis, I., Martin, M., Gonzalez, E., Gregory, K., Garden, R., O’Connor, K., et al. (2000). TIMSS 1999 international mathematics report. Boston: Boston College.Google Scholar
  65. Mullis, I., Martin, M., Ruddock, G., O’Sullivan, C., & Preuschoff, C. (2009). TIMSS 2011 assessment frameworks. Boston: TIMSS & PIRLS International Study Center, Boston College.Google Scholar
  66. Munson, A. (2010). Bourbaki at seventy-five: Its influence in France and beyond. Journal of Mathematics Education at Teachers College, 1(Fall–Winter), 18–21.Google Scholar
  67. Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2006). Epistemic dimensions of students’ mathematics-related belief systems. International Journal of Educational Research, 45(1), 57–70.CrossRefGoogle Scholar
  68. Opdenakker, M.-C., Van Damme, J., De Fraine, B., Van Landeghem, G., & Onghena, P. (2002). The effect of schools and classes on mathematics achievement. School Effectiveness and School Improvement, 13(4), 399–427.CrossRefGoogle Scholar
  69. Organisation for Economic Cooperation and Development. (2003). The PISA 2003 assessment framework: Mathematics, reading, science and problem solving knowledge and skills. Paris: OECD.Google Scholar
  70. Organisation for Economic Cooperation and Development. (2010). The high cost of low educational performance: The long-run economic impact of improving PISA outcomes. Paris: OECD.Google Scholar
  71. Prais, S. J. (2003). Cautions on OECD’s recent educational survey. Oxford Review of Education, 29(2), 139–163.CrossRefGoogle Scholar
  72. Prokic-Breuer, T., & Dronkers, J. (2012). The high performance of Dutch and Flemish 15-year-old native pupils: Explaining country differences in math scores between highly stratified educational systems. Educational Research and Evaluation, 18(8), 749–777.CrossRefGoogle Scholar
  73. Pugh, G., & Telhaj, S. (2007). Faith schools, social capital and academic attainment: Evidence from TIMSS-R mathematics scores in Flemish secondary schools. British Educational Research Journal, 34(2), 235–267.CrossRefGoogle Scholar
  74. Pustjens, H., Van de Gaer, E., Van Damme, J., Onghena, P., & Van Landeghem, G. (2007). The short-term and the long-term effect of primary schools and classes on mathematics and language achievement scores. British Educational Research Journal, 33(3), 419–440.CrossRefGoogle Scholar
  75. Rasmussen, C., & King, K. (2000). Locating starting points in differential equations: A realistic mathematics education approach. International Journal of Mathematical Education in Science & Technology, 31(2), 161–172.CrossRefGoogle Scholar
  76. Rindermann, H. (2007). The g-factor of international cognitive ability comparisons: The homogeneity of results in PISA, TIMSS, PIRLS and IQ-tests across nations. European Journal of Personality, 21(5), 667–706.CrossRefGoogle Scholar
  77. Sahlberg, P. (2007). Education policies for raising student learning: The Finnish approach. Journal of Education Policy, 22(2), 147–171.CrossRefGoogle Scholar
  78. Schleicher, A. (2007). Can competencies assessed by PISA be considered the fundamental school knowledge 15-year-olds should possess? Journal of Educational Change, 8(4), 349–357.CrossRefGoogle Scholar
  79. Shapira, M. (2012). An exploration of differences in mathematics attainment among immigrant pupils in 18 OECD countries. European Educational Research Journal, 11(1), 68–95.CrossRefGoogle Scholar
  80. Simola, H. (2005). The Finnish miracle of PISA: Historical and sociological remarks on teaching and teacher education. Comparative Education, 41(4), 455–470.CrossRefGoogle Scholar
  81. 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
  82. Stigler, J., Lee, S.-Y., Lucker, G., & Stevenson, H. (1982). Curriculum and achievement in mathematics: A study of elementary school children in Japan, Taiwan, and the United States. Journal of Educational Psychology, 74(3), 315–322.CrossRefGoogle Scholar
  83. Stigler, J., & Perry, M. (1988). Mathematics learning in Japanese, Chinese, and American classrooms. New Directions for Child and Adolescent Development, 1988(41), 27–54.CrossRefGoogle Scholar
  84. Streefland, L. (1993). The design of a mathematics course. A theoretical reflection. Educational Studies in Mathematics, 25(1), 109–135.CrossRefGoogle Scholar
  85. Tarvainen, K., & Kivelä, S. (2006). Severe shortcomings in Finnish mathematics skills. Matilde, 29, 10.Google Scholar
  86. Tweed, R., & Lehman, D. (2002). Learning considered within a cultural context: Confucian and Socratic approaches. American Psychologist, 57(2), 89–99.CrossRefGoogle Scholar
  87. Välijärvi, J., Linnakylä, P., Kupari, P., Reinikainen, P., & Arffman, I. (2002). The Finnish succes in PISA—and some reasons behind it. Jyväskylä: Institute for Educational Research, University of Jyväskylä.Google Scholar
  88. Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35.CrossRefGoogle Scholar
  89. Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–23.Google Scholar
  90. Van Dijk, I., van Oers, B., & Terwel, J. (2003). Providing or designing? Constructing models in primary maths education. Learning and Instruction, 13(1), 53–72.CrossRefGoogle Scholar
  91. Van Heule, K. (2000). Mixed education in Flanders: How well prepared are teachers? Pedagogy, Culture and Society, 8(2), 143–155.CrossRefGoogle Scholar
  92. Van Houtte, M., & Stevens, P. (2009). School ethnic composition and students’ integration outside and inside schools in Belgium. Sociology of Education, 82, 217–239.CrossRefGoogle Scholar
  93. Van Putten, C., Van den Brom-Snijders, P., & Beishuizen, M. (2005). Progressive mathematization of long division strategies in Dutch primary schools. Journal for Research in Mathematics Education, 36(1), 44–73.Google Scholar
  94. Vanpaemel, G., De Bock, D., & Verschaffel, L. (2012). Defining modern mathematics: Willy Servais (1913–1979) and mathematical curriculum reform in Belgium. In K. Bjarnadóttir, F. Furinghetti, J. Matos & G. Schubring (Eds.), Dig where you stand (pp. 419–439). Lisbon.Google Scholar
  95. Verhoeven, J., Aelterman, A., Rots, I., & Buvens, I. (2006). Public perceptions of teachers’ status in Flanders. Teachers and Teaching: theory and practice, 12(4), 479–500.CrossRefGoogle Scholar
  96. Verschaffel, L., & De Corte, E. (1997). Word problems. A vehicle for promoting authentic mathematical understanding and problem solving in the primary school. In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 69–97). Hove: Psychology Press.Google Scholar
  97. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273–294.CrossRefGoogle Scholar
  98. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1(3), 195–229.CrossRefGoogle Scholar
  99. Verschaffel, L., Janssens, S., & Janssen, R. (2005). The development of mathematical competence in Flemish preservice elementary school teachers. Teaching and Teacher Education, 21(1), 49–63.CrossRefGoogle Scholar
  100. Vincent, J., & Stacey, K. (2008). Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS video study criteria to Australian eighth-grade mathematics textbooks. Mathematics Education Research Journal, 20(1), 82–107.CrossRefGoogle Scholar
  101. Waldow, F., Takayama, K., & Sung, Y.-K. (2014). Rethinking the pattern of external policy referencing: Media discourses over the “Asian Tigers’’ PISA success in Australia. Germany and South Korea. Comparative Education, 50(3), 302–321.Google Scholar
  102. Weintraub, E., & Mirowski, P. (1994). The pure and the applied: Bourbakism comes to mathematical economics. Science in Context, 7(02), 245–272.CrossRefGoogle Scholar
  103. Wong, N.-Y. (2004). The CHC learner’s phenomenon: Its implications on mathematics education. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 503–534). Singapore: World Scientific.CrossRefGoogle Scholar
  104. Wubbels, T., Korthagen, F., & Broekman, H. (1997). Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32(1), 1–28.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Science EducationStockholm UniversityStockholmSweden

Personalised recommendations