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PISA Mathematics in Germany: Extending the Conceptual Framework to Enable a More Differentiated Assessment

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Research on PISA

Abstract

Assessing mathematical literacy—as PISA does—claims for comprehensive views of the domain tested. Since mathematics is not a homogenous body of knowledge one needs inner structures of that domain in order to be able to interpret the data gained. There are several possibilities, e.g. to differentiate between the main content strands as geometry, algebra etc. However the German PISA options differentiated according to cognitive activities connected with mathematics. These activities contain the performance of procedures as well as conceptual thinking, in both intra- and extra-mathematical situations. This paper exhibits the basis of that framework, i.e. a model for mathematical tasks, and shows evidences and findings from that approach, as the cognitive balances of several tests, and the striking cognitive profiles we found in different parts of the country.

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Notes

  1. 1.

    The overemphasis of technical tasks is increasingly emerging (see Neubrand, 2002, for TIMSS) to be a characteristic of German mathematics classes Analyses conducted in the context of a representative study of mathematics teachers’ professional knowledge, the COACTIV study (Baumert et al., 2010), revealed that up to 90% of the tasks set in high-stakes classroom tests are of the technical type (Jordan et al., 2008).

  2. 2.

    As a similar pattern of findings emerged for some analogous sub-competencies in the PISA science test (Rost, Carstensen, Bieber, Prenzel, & Neubrand, 2003), these data can usefully inform discussion of curricula and their implementation. Note that boys’ and girls’ performance on the three types of mathematical activities also differed (Neubrand & Neubrand, 2004).

References

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.

    Article  Google Scholar 

  • Blum, W., Drüke-Noe, C., Hartung, R., & Köller, O. (Eds.). (2006). Bildungsstandards Mathematik: konkret. Sekundarstufe I: Aufgabenbeispiele, Unterrichtsanregungen, Fortbildungsideen [Educational standards for mathematics at lower secondary level: Sample tasks, suggestions for lessons, ideas for continuing education]. Berlin, Germany: Cornelsen.

    Google Scholar 

  • Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education: The 14th ICMI study. Berlin, Germany: Springer.

    Google Scholar 

  • Blum, W., vom Hofe, R., Jordan, A., & Kleine, M. (2004). Grundvorstellungen als aufgabenanalytisches und diagnostisches Instrument bei PISA [Basic mathematical concepts (‚Grundvorstellungen‘) as a diagnostic and analytic instrument in PISA]. In M. Neubrand (Ed.), Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland: Vertiefende Analysen im Rahmen von PISA 2000 (pp. 145–158). Wiesbaden, Germany: VS Verlag für Sozialwissenschaften.

    Chapter  Google Scholar 

  • Cohors-Fresenborg, E., Sjuts, J., & Sommer, N. (2004). Komplexität von Denkvorgängen und Formalisierung von Wissen [Complexity of thought processes and formalization of knowledge]. In M. Neubrand (Ed.), Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland: Vertiefende Analysen im Rahmen von PISA 2000 (pp. 109–144). Wiesbaden, Germany: VS Verlag für Sozialwissenschaften.

    Chapter  Google Scholar 

  • Hiebert, J. (Ed.). (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Jordan, A., Krauss, S., Löwen, K., Blum, W., Neubrand, M., Brunner, M., et al. (2008). Aufgaben im COACTIV-Projekt: Zeugnisse des kognitiven Aktivierungspotentials im deutschen Mathematikunterricht [Tasks in the COACTIV project: Evidence of the potential for cognitive activation in German mathematics instruction]. Journal für Mathematik-Didaktik, 29(2), 83–107.

    Google Scholar 

  • Kilpatrick, J. (2001). Understanding mathematical literacy: The contribution of research. Educational Studies in Mathematics, 47, 101–116.

    Article  Google Scholar 

  • Klieme, E., Neubrand, M., & Lüdtke, O. (2001). Mathematische Grundbildung: Testkonzeption und Ergebnisse [Mathematical literacy: Test conception and results]. In J. Baumert, E. Klieme, M. Neubrand, M. Prenzel, U. Schiefele, W. Schneider, P. Stanat, K.-J. Tillmann, & M. Weiß (Eds.), PISA 2000. Basiskompetenzen von Schülerinnen und Schülern im internationalen Vergleich (pp. 139–190). Opladen, Germany: Leske & Budrich.

    Google Scholar 

  • Neubrand, J. (2002). Eine Klassifikation mathematischer Aufgaben zur Analyse von Unterrichtssituationen: Schülerarbeitsphasen und Selbsttätigkeit in den Stunden der TIMSS-Video-Studie [A classification of mathematics tasks for the analysis of instructional situations: Phases of independent student work in the TIMSS Video Study lessons]. Berlin/Hildesheim, Germany: Franzbecker.

    Google Scholar 

  • Neubrand, M. (Ed.). (2004). Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland: Vertiefende Analysen im Rahmen von PISA 2000 [Mathematical competencies of students in Germany: In-depth analyses in the context of PISA 2000]. Wiesbaden, Germany: VS Verlag für Sozialwissenschaften.

    Google Scholar 

  • Neubrand, J. (2006). The TIMSS 1995 and 1999 video studies. In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West: The 13th ICMI Study (pp. 291–318). Berlin, Germany: Springer.

    Chapter  Google Scholar 

  • Neubrand, M., Biehler, R., Blum, W., Cohors-Fresenborg, E., Flade, L., Knoche, N., et al. (2001). Grundlagen der Ergänzung des internationalen PISA-Mathematik-Tests in der deutschen Zusatzerhebung [Framework for the supplementation of the international PISA mathematics test in the German national PISA extension study]. Zentralblatt für Didaktik der Mathematik, 33(2), 33–45.

    Article  Google Scholar 

  • Neubrand, M., Klieme, E., Lüdtke, O., & Neubrand, J. (2002). Kompetenzstufen und Schwierigkeitsmodelle für den PISA-Test zur mathematischen Grundbildung [Proficiency levels and difficulty models for the PISA test of mathematical literacy]. Unterrichtswissenschaft, 30(2), 100–119.

    Google Scholar 

  • Neubrand, J., & Neubrand, M. (2003). Profiles of mathematical achievement in the PISA 2000 mathematics test and the different structure of achievement in Japan and Germany. Paper presented at the AERA 2003 Annual Meeting, Chicago.

    Google Scholar 

  • Neubrand, J., & Neubrand, M. (2004). Innere Strukturen mathematischer Leistung im PISA 2000 Test [Internal structures of mathematics achievement in the PISA 2000 test]. In M. Neubrand (Ed.), Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland: Vertiefende Analysen im Rahmen von PISA 2000 (pp. 87–108). Wiesbaden, Germany: VS Verlag für Sozialwissenschaften.

    Chapter  Google Scholar 

  • OECD. (1999). Measuring student knowledge and skills: The PISA 2000 assessment of reading, mathematical and scientific literacy. Paris, France: OECD.

    Google Scholar 

  • OECD. (2001). Knowledge and skills for life: First results from PISA 2000. Paris, France: OECD.

    Book  Google Scholar 

  • Rost, J., Carstensen, C., Bieber, G., Prenzel, M., & Neubrand, M. (2003). Naturwissenschaftliche Teilkompetenzen im Ländervergleich [Aspects of science literacy in German cross-state comparison]. In J. Baumert, C. Artelt, E. Klieme, M. Neubrand, M. Prenzel, U. Schiefele, W. Schneider, K.-J. Tillmann, & M. Weiß (Eds.), PISA 2000: Ein differenzierter Blick auf die Länder der Bundesrepublik Deutschland (pp. 109–128). Opladen, Germany: Leske & Budrich.

    Chapter  Google Scholar 

  • Stigler, J., & 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 

  • vom Hofe, R., Kleine, M., Blum, W., & Pekrun, R. (2005). On the role of “Grundvorstellungen” for the development of mathematical literacy: First results of the longitudinal study PALMA. Mediterranean Journal for Research in Mathematics Education, 4, 67–84.

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Education, Institute for Mathematics, Carl-von-Ossietzky University, D-26111, Oldenburg, Germany

    Michael Neubrand

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  1. Michael Neubrand
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Correspondence to Michael Neubrand .

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Editors and Affiliations

  1. , School of Education, Technische Universität München, Schellingstraße 33, München, 80799, Germany

    Manfred Prenzel

  2. , Leibniz-Institut für die Pädagogik der N, IPN, Olshausenstrasse 62, Kiel, 24118, Germany

    Mareike Kobarg

  3. , Leibniz-Institut für die Pädagogik der N, IPN, Olshausenstraße 62, Kiel, 24118, Germany

    Katrin Schöps

  4. , Leibniz-Institut für die Pädagogik der N, IPN, Olshausenstraße 62, Kiel, 24118, Germany

    Silke Rönnebeck

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Neubrand, M. (2013). PISA Mathematics in Germany: Extending the Conceptual Framework to Enable a More Differentiated Assessment. In: Prenzel, M., Kobarg, M., Schöps, K., Rönnebeck, S. (eds) Research on PISA. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4458-5_3

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