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ZDM

, Volume 50, Issue 3, pp 475–490 | Cite as

Subject-specific characteristics of instructional quality in mathematics education

  • Lena Schlesinger
  • Armin Jentsch
  • Gabriele Kaiser
  • Johannes König
  • Sigrid Blömeke
Original Article
First Online:

Abstract

Instructional research in German-speaking countries has conceptualized teaching quality recently according to three generic dimensions, namely, classroom management, student support and cognitive activation. However, as these dimensions are mainly regarded as generic, subject-specific aspects of mathematics instruction, e.g., the mathematical depth of argumentation or the adequacy of concept introductions, are not covered in depth. Therefore, a new instrument for the analysis of instructional quality was developed, which extended this three-dimensional framework by relevant subject-specific aspects of instructional quality. In this paper, the newly developed observational protocol is applied to three videotaped mathematics lessons from the NCTE video library of Harvard University to explore strengths and weaknesses of this instrument, and to examine in more detail how the instrument works in practice. Therefore, we used a mixed-methods design to extend the quantitative observer ratings, which enable high inference, by methods from qualitative content analysis. The results suggest the conclusion that the framework differentiates well between the lessons under a subject-specific perspective.

Keywords

Instructional quality Subject-specific aspects High-inference ratings Standardized classroom observations Mathematics education 
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References

  1. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., & Tsai, Y.-M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.CrossRefGoogle Scholar
  2. Blazar, D., Braslow, D., Charalambous, C. Y., & Hill, H. C. (2017). Attending to general and mathematics-specific dimensions of teaching: Exploring factors across two observation instruments. Educational Assessment, 22(2), 71–94.CrossRefGoogle Scholar
  3. Blum, W., Drüke-Noe, C., Hartung, R., & Köller, O. (2006). Bildungsstandards Mathematik: Konkret. Sekundarstufe 1: Aufgabenbeispiele, Unterrichtsanregungen, Fortbildungsideen. Berlin: Cornelsen Scriptor.Google Scholar
  4. Brophy, J. (2000). Teaching. Brüssel: International Academy of Education.Google Scholar
  5. Bruner, J. (1974). Toward a theory of instruction. Cambridge: Harvard University Press.Google Scholar
  6. Buchholtz, N., Kaiser, G., & Blömeke, S. (2014). Die Erhebung mathematikdidaktischen Wissens–Konzeptualisierung einer komplexen Domäne. Journal für Mathematik Didaktik, 35(1), 101–128.CrossRefGoogle Scholar
  7. Casabianca, J. M., McCaffrey, D. F., Gitomer, D. H., Bell, C. A., Hamre, B. K., & Pianta, R. C. (2013). Effect of observation mode on measures of secondary mathematics teaching. Educational and Psychological Measurement, 73(5), 757–783.CrossRefGoogle Scholar
  8. Charalambous, C., & Praetorius, A.-K. (2018). Studying mathematics instruction through different lenses: setting the ground for understanding instructional quality more comprehensively. ZDM Mathematics Education, 50(3).  https://doi.org/10.1007/s11858-018-0914-8. (this issue).
  9. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Perspectives in social psychology. New York: Plenum.CrossRefGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. Drollinger-Vetter, B. (2011). Verstehenselemente und strukturelle Klarheit: Fachdidaktische Qualität der Anleitung von mathematischen Verstehensprozessen im Unterricht. Münster: Waxmann.Google Scholar
  12. Helmke, A. (2012). Unterrichtsqualität und Lehrerprofessionalität: Diagnose, Evaluation und Verbesserung des Unterrichts. Seelze: Klett-Kallmeyer.Google Scholar
  13. Hiebert, J., Gallimore, R., Garnier, H., & Stigler, J. (2003). Teaching mathematics in seven countries. Results from the TIMSS 1999 video study. Washington: National Center for Education Statistics.CrossRefGoogle Scholar
  14. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte: Information Age.Google Scholar
  15. Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511.CrossRefGoogle Scholar
  16. Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.CrossRefGoogle Scholar
  17. Kelle, U., & Buchholtz, N. (2015). The combination of qualitative and quantitative research methods in mathematics education: A “mixed methods” study on the development of the professional knowledge of teachers. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 321–364). Dordrecht: Springer.Google Scholar
  18. Kersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., & Stigler, J. W. (2012). Measuring usable knowledge: Teachers’ analyses of mathematics classroom videos predict teaching quality and student learning. American Educational Research Journal, 49(3), 568–589.CrossRefGoogle Scholar
  19. Klieme, E., Pauli, C., & Reusser, K. (2009). The Pythagoras study. In T. Janik & T. Seidel (Eds.), The power of video studies in investigating teaching and learning in the classroom (pp. 137–160). Münster: Waxmann.Google Scholar
  20. Klieme, E., & Rakoczy, K. (2008). Empirische Unterrichtsforschung und Fachdidaktik. Outcome-orientierte Messung und Prozessqualität des Unterrichts. Zeitschrift für Pädagogik, 54, 222–237.Google Scholar
  21. Klieme, E., Schümer, G., & Knoll, S. (2001). Mathematikunterricht in der Sekundarstufe I: “Aufgabenkultur” und Unterrichtsgestaltung. In BMBF (Ed.), TIMSS–Impulse für Schule und Unterricht, Forschungsbefunde, Reforminitiativen, Praxisberichte und Video- Dokumente (pp. 43–58). Bonn: BMBF.Google Scholar
  22. Kounin, J. S. (1970). Discipline and group management in classrooms. New York: Holt, Rinehart and Winston.Google Scholar
  23. Kunter, M., Baumert, J., & Köller, O. (2007). Effective classroom management and the development of subject-related interest. Learning and Instruction, 17(5), 494–509.CrossRefGoogle Scholar
  24. Learning Mathematics for Teaching Project (2011). Measuring the mathematical quality of instruction. Journal of Mathematics Teacher Education, 14, 25–47.CrossRefGoogle Scholar
  25. Liang, J. (2015). Live video classroom observation: An effective approach to reducing reactivity in collecting observational information for teacher professional development. Journal of Education for Teaching: International Research and Pedagogy, 41(3), 235–253.CrossRefGoogle Scholar
  26. Lipowsky, F., Rakoczy, K., Pauli, C., Drollinger-Vetter, B., Klieme, E., & Reusser, K. (2009). Quality of geometry instruction and its short-term impact on students’ understanding of the Pythagorean Theorem. Learning and Instruction, 19(6), 527–537.CrossRefGoogle Scholar
  27. Marder, M., & Walkington, C. (2014). Classroom observation and value-added models give complementary information about quality of mathematics teaching. In T. Kane, K. Kerr & R. Pianta (Eds.), Designing teacher evaluation systems: New guidance from the Measuring Effective Teaching project (pp. 234–277). New York: Wiley.Google Scholar
  28. Matsumura, L. C., Garnier, H. E., Pascal, J., & Valdés, R. (2002). Measuring instructional quality in accountability systems: Classroom assignments and students achievement. Educational Assessment, 8, 207–229.CrossRefGoogle Scholar
  29. Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education. Examples of methodology and methods (pp. 365–380). Dordrecht: Springer.Google Scholar
  30. Pianta, R. C., & Hamre, B. K. (2009). Conceptualization, measurement, and improvement of classroom processes: Standardized observation can leverage capacity. Educational Researcher, 38(2), 109–119.CrossRefGoogle Scholar
  31. Pietsch, M., & Tosana, S. (2008). Beurteilereffekte bei der Messung von Unterrichtsqualität. Zeitschrift für Erziehungswissenschaft, 11(3), 430–452.CrossRefGoogle Scholar
  32. 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).  https://doi.org/10.1007/s11858-018-0918-4. (this issue).
  33. Praetorius, A.-K., Lenske, G., & Helmke, A. (2012). Observer ratings of instructional quality: Do they fulfill what they promise? Learning and Instruction, 22, 387–400.CrossRefGoogle Scholar
  34. Praetorius, A.-K., Pauli, C., Reusser, K., Rakoczy, K., & Klieme, E. (2014). One lesson is all you need? Stability of instructional quality across lessons. Learning and Instruction, 31, 2–12.CrossRefGoogle Scholar
  35. Rakoczy, K. (2006). Motivationsunterstützung im Mathematikunterricht: Zur Bedeutung von Unterrichtsmerkmalen für die Wahrnehmung der Schülerinnen und Schüler. Zeitschrift für Pädagogik, 52(6), 822–843.Google Scholar
  36. Schlesinger, L., & Jentsch, A. (2016). Theoretical and methodological challenges in measuring instructional quality in mathematics education using classroom observations. ZDM Mathematics Education, 48(1), 29–40.CrossRefGoogle Scholar
  37. Schlesinger, L., Jentsch, A., Kaiser, G., Blömeke, S., & König, J. (under review). Messung fachspezifischer Unterrichtsqualität im Mathematikunterricht. (Manuscript submitted).Google Scholar
  38. Schoenfeld, A. H. (2013). Classroom observations in theory and practice. ZDM Mathematics Education, 45(4), 607–621.CrossRefGoogle Scholar
  39. Seidel, T., & Shavelson, R. J. (2007). Teaching effectiveness research in the past decade: The role of theory and research design in disentangling meta-analysis results. Review of Educational Research, 77(4), 454–499.CrossRefGoogle Scholar
  40. Steinweg, A. S. (2011). Einschätzung der Qualität von Lehr-Lernsituationen im mathematischen Anfangsunterricht—ein Vorschlag. Journal für Mathematik Didaktik, 32(1), 1–26.CrossRefGoogle Scholar
  41. Taut, S., & Rakoczy, K. (2016). Observing instructional quality in the context of school evaluation. Learning and Instruction, 46, 45–60.CrossRefGoogle Scholar
  42. Thompson, C. J., & Davis, S. B. (2014). Classroom observation data and instruction in primary mathematics education: improving design and rigour. Mathematics Education Research Journal, 26(2), 301–323.CrossRefGoogle Scholar
  43. Walkowiak, T. A., Berry, R. Q., Meyer, J. P., Rimm-Kaufman, S. E., & Ottmar, E. R. (2014). Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability. Educational Studies in Mathematics, 85(1), 109–128.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.Faculty of Education, Mathematics EducationUniversität HamburgHamburgGermany
  2. 2.Australian Catholic UniversitySydneyAustralia
  3. 3.Universität zu KölnCologneGermany
  4. 4.Centre of Educational Measurement (CEMO) at University of OsloOsloNorway

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