Skip to main content
SpringerLink
Log in

Competence as a continuum in the COACTIV study: the “cascade model”

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

Two different tools for assessing pedagogical content knowledge (PCK) of mathematics teachers used in the framework of the COACTIV study are systematically compared in this paper, namely the paper-and-pencil test consisting of items on the three facets knowledge of explaining and representation, knowledge of student thinking and typical mistakes, and knowledge of the potential of mathematical tasks, and the video vignettes instrument that examines teachers' proposed continuations for presented lesson video clips specific to their subject-related and methodological competence aspects. Initially, both COACTIV PCK assessment tools are systematically contrasted for the first time with respect to their predictive validity for instructional quality (N = 163 German secondary mathematics teachers) as well as student learning gains (N = 3806 PISA students from 169 different classes) by means of path models showing that PCK, when assessed by the paper-and-pencil method, can better predict instructional quality than the video vignettes instrument can. Next, we theoretically propose the cascade model as capable of integrating pertinent theories on teacher competence and instructional quality. This model implies five ‘columns’ that are ordered according to a sequential causal chain (teacher disposition → situation-specific skills → observable teaching behavior → student mediation → learning gains). Finally, we specify four out of the five ‘columns’ of this cascade model, based empirically on the COACTIV data.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. The COACTIV program was funded by the German research foundation (DFG) from 2002 to 2006 (Directors: Jürgen Baumert, Max-Planck-Institute for Human Development Berlin; Werner Blum, University of Kassel; Michael Neubrand, University of Oldenburg).

References

  • Ball, D. L., Hill, H. H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator,29(3), 14–46.

    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. (2013). The COACTIV model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers, Mathematics Teacher Education, 8 (pp. 25–48). New York: Springer.

    Chapter  Google Scholar 

  • Baumert, J., Blum, W., Brunner, M., Dubberke, T., Jordan, A., Klusmann, U., et al. (2009). Professionswissen von Lehrkräften, kognitiv aktivierender Mathematikunterricht und die Entwicklung von mathematischer Kompetenz (COACTIV): Dokumentation der Erhebungsinstrumente (Materialien aus der Bildungsforschung 83). Berlin: Max-Planck-Institut für Bildungsforschung.

    Google Scholar 

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Dubberke, 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. https://doi.org/10.3102/0002831209345157.

    Article  Google Scholar 

  • Baumgartner, M. (2018). “…Kompetenz ohne Performanz ist leer! Performanz ohne Kompetenz blind…!” Zu einem integrativen Kompetenzstrukturmodell von Sportlehrkräften. Zeitschrift für sportpädagogische Forschung (ZsF),6(1), 49–68.

    Google Scholar 

  • Berliner, D. C. (2001). Learning about and learning from expert teachers. International Journal of Educational Research,35(5), 463–482.

    Article  Google Scholar 

  • Blömeke, S., & Kaiser, G. (2014). Theoretical framework, study design and main results of TEDS-M. In S. Blömeke, F.-J. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 19–48). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies. Competence viewed as a continuum. Zeitschrift für Psychologie,223(1), 3–13. https://doi.org/10.1027/2151-2604/a000194.

    Article  Google Scholar 

  • Blum, W., Neubrand, M., Ehmke, T., Senkbeil, M., Jordan, A., Ulfig, F., et al. (2004). Mathematische Kompetenz. In M. Prenzel, J. Baumert, W. Blum, R. Lehmann, D. Leutner, M. Neubrand, et al. (Eds.), PISA 2003. Der Bildungsstand der Jugendlichen in Deutschland. Ergebnisse des zweiten internationalen Vergleichs (pp. 47–92). Münster: Waxmann.

    Google Scholar 

  • Bruckmaier, G., Krauss, S., Blum, W., & Leiss, D. (2016). Measuring mathematical teachers’ professional competence by using video clips (COACTIV video). ZDM—The International Journal on Mathematics Education,48(1–2), 111–124. https://doi.org/10.1007/s11858-016-0772-1.

    Article  Google Scholar 

  • Charalambous, C. Y., & Praetorius, A.-K. (2018). Studying instructional quality in mathematics through different lenses: In search for common ground. Special Issue Published in ZDM Mathematics Education, 50(3), 355–366.

    Article  Google Scholar 

  • Chi, M. T. H. (2011). Theoretical perspectives, methodological approaches, and trends in the study of expertise. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction: An international perspective (pp. 17–39). Boston: Springer.

    Chapter  Google Scholar 

  • Clausen, M. (2002). Unterrichtsqualität: Eine Frage der Perspektive?. Münster: Waxmann.

    Google Scholar 

  • Cornelius-White, J. (2007). Learner-centered teacher–student relationships are effective: A meta-analysis. Review of Educational Research,77(1), 113–143.

    Article  Google Scholar 

  • Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education,34, 12–25.

    Article  Google Scholar 

  • Dreher, A., Lindmeier, A., Heinze, A., & Niemand, C. (2018). What kind of content knowledge do secondary mathematics teachers need? Journal für Mathematik-Didaktik,39(2), 319–341.

    Article  Google Scholar 

  • Embretson, S. (1983). Construct validity: Construct representation versus nomothetic span. Psychological Bulletin,93, 179–197. https://doi.org/10.1037/0033-2909.93.1.179.

    Article  Google Scholar 

  • Enders, C. K. (2010). Applied missing data analysis. New York: Guilford.

    Google Scholar 

  • Evertson, C. M., & Weinstein, C. S. (Eds.). (2006). Handbook of classroom management: Research, practice, and contemporary issues. Mahwah: Erlbaum.

    Google Scholar 

  • Goodwin, C. (1994). Professional vision. American Anthropologist,96, 606–633. https://doi.org/10.1525/aa.1994.96.3.02a00100.

    Article  Google Scholar 

  • Heller, K. A., & Perleth, C. (2000). Kognitiver Fähigkeitstest für 4.–12. Klassen: Revision (KFT 4–12+R). Göttingen: Hogrefe.

    Google Scholar 

  • Helmke, A. (2010). Unterrichtsqualität und Lehrerprofessionalität. Diagnose, Evaluation und Verbesserung des Unterrichts (3rd ed.). Seelze-Velber: Klett.

    Google Scholar 

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

    Article  Google Scholar 

  • Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education,13(2), 369–387. https://doi.org/10.1007/s10763-015-9616-7.

    Article  Google Scholar 

  • Kaiser, G., Blömeke, S., König, J., Busse, A., Döhrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—Cognitive versus situated approaches. Educational Studies in Mathematics,94(2), 161–182.

    Article  Google Scholar 

  • Kersting, N., Givvin, K., Thompson, B., Santagata, R., & Stigler, J. (2012). Measuring usable knowledge: Teachers’ analyses of mathematics classroom videos predict teaching quality and student learning. American Educational Research Journal,49(3), 568–589.

    Article  Google Scholar 

  • Klieme, E., Schümer, G., & Knoll, S. (2001). Mathematikunterricht in der Sekundarstufe I: “Aufgabenkultur” und Unterrichtsgestaltung. TIMSS—Impulse für Schule und Unterricht (pp. 43–57). Bonn: BMBF.

    Google Scholar 

  • Knievel, I., Lindmeier, A. M., & Heinze, A. (2015). Beyond knowledge: Measuring primary teachers’ subject-specific competences in and for teaching mathematics with items based on video vignettes. International Journal of Science and Mathematics Education,13(2), 309–329.

    Article  Google Scholar 

  • König, J., Blömeke, S., & Kaiser, G. (2015). Early career mathematics teachers' general pedagogical knowledge and skills: Do teacher education, teaching experience, and working conditions make a difference? International Journal of Science and Mathematics Education,13(2), 331–350.

    Article  Google Scholar 

  • Krauss, S., Brunner, M., & Kunter, M. (2004). Expertise von Ma-thematiklehrkräften. Paper presented at the 65. Tagung der Ar-beitsgruppe für empirische pädagogische Forschung (AEPF). Nürnberg, Germany.

    Google Scholar 

  • Krauss, S., & Bruckmaier, G. (2014). Das Experten-Paradigma in der Forschung zum Lehrerberuf. In E. Terhart, H. Bennewitz, & M. Rothland (Eds.), Handbuch der Forschung zum Lehrerberuf (2nd ed., pp. 241–261). Münster: Waxmann.

    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., Blum, W., Brunner, M., Neubrand, M., Baumert, J., Kunter, M., et al. (2013). Mathematics teachers’ domain-specific professional knowledge: Conceptualization and test construction in COACTIV. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers, Mathematics Teacher Education, 8 (pp. 147–174). New York: Springer.

    Chapter  Google Scholar 

  • Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., et al. (2008b). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology,100(3), 716–725. https://doi.org/10.1037/0022-0663.100.3.716.

    Article  Google Scholar 

  • Krauss, S., Lindl, A., Schilcher, A., Fricke, M., Göhring, A., Hofmann, B., et al. (2017). FALKO: Fachspezifische Lehrerkompetenzen. Konzeption von Professionswissenstests in den Fächern Deutsch, Englisch, Latein, Physik, Musik, Evangelische Religion und Pädagogik. Münster: Waxmann.

    Google Scholar 

  • Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (Eds.). (2013a). Cognitive activation in the mathematics classroom and professional competence of teachers, Mathematics Teacher Education, 8. New York: Springer.

    Google Scholar 

  • Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013b). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology,105(3), 805–820. https://doi.org/10.1037/a0032583.

    Article  Google Scholar 

  • Lindmeier, A. (2011). Modeling and measuring knowledge and competencies of teachers: A threefold domain-specific structure model for mathematics. Münster: Waxmann.

    Google Scholar 

  • McDaniel, M. A., Morgeson, F. P., Finnegan, E. B., Campion, M. A., & Braverman, E. P. (2001). Use of situational judgment tests to predict job performance: A clarification of the literature. Journal of Applied Psychology,86(4), 730–740.

    Article  Google Scholar 

  • Neubrand, M., Jordan, A., Krauss, S., Blum, W., & Löwen, K. (2013). Task analysis in COACTIV: Examining the potential for cognitive activation in German mathematics classrooms. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers, Mathematics Teacher Education, 8 (pp. 125–144). New York: Springer.

    Chapter  Google Scholar 

  • Neuweg, G. H. (2015). Kontextualisierte Kompetenzmessung: Eine Bilanz zu aktuellen Konzeptionen und forschungsmethodischen Zugängen. Zeitschrift für Pädagogik,61(3), 377–383.

    Google Scholar 

  • Oser, F., Heinzer, S., & Salzmann, P. (2010). Die Messung der Qua-lität von professionellen Kompetenzprofilen von Lehrpersonen mit Hilfe der Einschätzung von Filmvignetten. Chancen und Grenzen des advokatorischen Ansatzes. Unterrichtswissenschaft,38(1), 5–28.

    Google Scholar 

  • Pintrich, P. R., Marx, R. W., & Boyle, R. A. (1993). Beyond cold conceptual change: The role of motivational beliefs and classroom contextual factors in the process of conceptual change. Review of Educational Research,63(2), 167–199.

    Article  Google Scholar 

  • Praetorius, A.-K., Klieme, E., Herbert, B., & Pinger, P. (2018). Generic dimensions of teaching quality: The German framework of Three Basic Dimensions. ZDM Mathematics Education,50(3), 407–426. https://doi.org/10.1007/s11858-018-0918-4.

    Article  Google Scholar 

  • Prenzel, M., Baumert, J., Blum, W., Lehmann, R., Leutner, D., Neubrand, M., et al. (Eds.). (2004). PISA 2003. Der Bildungsstand der Jugendlichen in Deutschland—Ergebnisse des zweiten internationalen Vergleichs. Münster: Waxmann.

    Google Scholar 

  • Prenzel, M., Carstensen, C. H., Schöps, K., & Maurischat, C. (2006). Die Anlage des Längsschnitts bei PISA 2003. In M. Prenzel, J. Baumert, W. Blum, R. Lehmann, D. Leutner, M. Neubrand, et al. (Eds.), PISA 2003: Untersuchungen zur Kompetenzentwicklung im Verlauf eines Schuljahres (pp. 29–62). Münster: Waxmann.

    Google Scholar 

  • Rowland, T., & Ruthven, K. (2011). Introduction: Mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 1–5). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Seidel, T., & Shavelson, J. R. (2007). Teaching effectiveness research in the past decade: Role of theory and research design in disentangling meta-analysis results. Review of Educational Research,77(4), 454–499.

    Article  Google Scholar 

  • Seidel, T., & Stürmer, K. (2014). Modeling and measuring the structure of professional vision in pre-service teachers. American Educational Research Journal,51(4), 739–771. https://doi.org/10.3102/0002831214531321.

    Article  Google Scholar 

  • Shavelson, R. J. (2010). On the measurement of competency. Empirical Research in Vocational Education and Training,1, 43–65.

    Google Scholar 

  • Sherin, M., Jacobs, V., & Philipp, R. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge.

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Voss, T., & Kunter, M. (2013). Teachers’ general pedagogical/psychological knowledge. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers, Mathematics Teacher Education, 8 (pp. 207–228). New York: Springer.

    Chapter  Google Scholar 

  • Weinert, F. E., Schrader, F.-W., & Helmke, A. (1989). Quality of instruction and achievement outcomes. International Journal of Educational Research,13(8), 895–914.

    Article  Google Scholar 

Download references

Acknowledgements

We thank Frances Lorie for English editing, which was funded by the Deutsche Telekom Stiftung.

Author information

Authors and Affiliations

  1. University of Regensburg, Regensburg, Germany

    S. Krauss, A. Lindl, S. Hilbert, K. Binder & N. Steib

  2. FHNW University of Applied Sciences and Arts Northwestern Switzerland, Windisch, Switzerland

    G. Bruckmaier

  3. University of Kassel, Kassel, Germany

    W. Blum

Authors
  1. S. Krauss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Bruckmaier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Lindl
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Hilbert
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. Binder
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. N. Steib
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. W. Blum
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Krauss.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krauss, S., Bruckmaier, G., Lindl, A. et al. Competence as a continuum in the COACTIV study: the “cascade model”. ZDM Mathematics Education 52, 311–327 (2020). https://doi.org/10.1007/s11858-020-01151-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-020-01151-z

Keywords

Search

Navigation