Abstract
When teachers analyse mathematics classrooms, it can be expected that they use their professional knowledge, including their instruction-related views. In the case of analysing classroom situations regarding the use of representations, prior research suggests interdependencies. Consequently, when assessing teachers’ competence of analysing, the role of teachers’ views should be taken into account so as to explore their potential role for the competence construct. This need for research is therefore addressed in this study. For a sample consisting of 31 in-service teachers, interdependencies between instruction-related views and the teachers’ analysis were examined by quantitative and qualitative analyses. The results indicate such interdependencies and give insight into possible reasons for these.
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References
Ainsworth, S. E. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198.
Blömeke, S., Kaiser, G., & Lehmann, R. (Eds.). (2010). TEDS-M 2008–Professionelle Kompetenz und Lerngelegenheiten angehender Mathematiklehrkräfte für die Sekundarstufe I im internationalen Vergleich. Münster: Waxmann.
Bromme, R. (1992). Der Lehrer als Experte. Zur Psychologie des professionellen Wissens. Bern: Hans Huber.
Bromme, R. (1997). Kompetenzen, Funktionen und unterrichtliches Handeln des Lehrers. In F. Weinert (Ed.), Enzyklopädie der Psychologie: Psychologie des Unterrichts und der Schule (pp. 177–212). Göttingen: Hogrefe.
Doerr, H., & Lerman, S. (2009). The procedural and the conceptual in mathematics pedagogy: What teachers learn from their teaching. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 433–440). Thessaloniki, Greece.
Dreher, A., & Kuntze, S. (2015a). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114.
Dreher, A., & Kuntze, S. (2015b). Teachers facing the dilemma of multiple representations being aid and obstacle for learning: Evaluations of tasks and theme-specific noticing. Journal für Mathematik-Didaktik, 36(1), 23–44. https://doi.org/10.1007/s13138-014-0068-3
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.
Fennema, E., Carpenter, T. P., & Loef, M. (1990). Teacher belief scale: Cognitively guided instruction project. Madison: University of Wisconsin.
Friesen, M., Dreher, A., & Kuntze, S. (2015). Pre-service teachers’ growth in analysing classroom videos. In K. Krainer & N. Vondrová (Eds.), Proceedings of CERME 9 (pp. 2783–2789). Prague: Charles University in Prague and ERME.
Friesen, M., & Kuntze, S. (2016). Teacher students analyse texts, comics and video-based classroom vignettes regarding the use of representations - does format matter? In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 259–266). Szeged: PME.
Gagné, R., Briggs, L., & Wager, W. (1992). Principles of instructional design. Orlando, FL: Hartcourt Brace Jovanovich Pulishers.
Goldin, G., & Shteingold, N. (2001). Systems of representation and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.), The role of representation in school mathematics (pp. 1–23). Boston, Virginia: NCTM.
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.
Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (2013). Cognitive activation in the mathematics classroom and professional competence of teachers. Results from the COACTIV project. New York: Springer.
Kuntze, S. (2012). Pedagogical content beliefs: Global, content domain-related and situation-specific components. Educational Studies in Mathematics, 79(2), 273–292.
Kuntze, S., & Dreher, A. (2015). PCK and the awareness of affective aspects reflected in teachers’ views about learning opportunities–a conflict? In B. Pepin & B. Rösken-Winter (Eds.), From beliefs and affect to dynamic systems: (Exploring) a mosaic of relationships and interactions (pp. 295–318). New York: Springer.
Kuntze, S., Dreher, A., & Friesen, M. (2015). Teachers’ resources in analysing mathematical content and classroom situations. In K. Krainer & N. Vondrová (Eds.), Proceedings of CERME 9 (pp. 3213–3219). Prague: Charles University and ERME.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Hillsdale, NJ: Lawrence Erlbaum.
Lipowsky, F., Thußbas, C., Klieme, E., Reusser, K., & Pauli, C. (2003). Professionelles Lehrerwissen, selbstbezogene Kognitionen und wahrgenommene Schulumwelt. Unterrichtswissenschaft, 31(3), 206–237.
Mason, J. (2002). Researching your own practice. The discipline of noticing. London: Routledge Falmer.
Mayring, P. (2015). Qualitative Inhaltsanalyse. Weinheim: Beltz.
Pajares, F. M. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.
Schoenfeld, A. (2011). Toward professional development for teachers grounded in a theory of decision making. ZDM Mathematics Education, 43(4), 457–469.
Seidel, T., Blomberg, G., & Renkl, A. (2013). Instructional strategies for using video in teacher education. Teaching and Teacher Education, 34, 56–65.
Sherin, M., Jacobs, V., & Philipp, R. (2011). Mathematics teacher noticing. Seeing through teachers’ eyes. New York: Routledge.
Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
Skinner, B. (1958). Teaching machines. Science, 128, 969–977.
Staub, F., & Stern, E. (2002). The nature of teacher’s pedagogical content beliefs matters for students’ achievement gains. Journal of Educational Psychology, 94(2), 344–355.
Törner, G. (2002). Mathematical beliefs—A search for a common ground. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 73–94). Dordrecht: Kluwer.
Weinert, F. E. (Ed.). (2001). Leistungsmessung in Schulen. Weinheim: Belt.
Acknowledgements
This study is supported in the framework of the project EKoL supported by the Ministry of Science, Research and the Arts in Baden-Wuerttemberg.
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Kuntze, S., Friesen, M. (2018). The Role of Mathematics Teachers’ Views for Their Competence of Analysing Classroom Situations. In: Rott, B., Törner, G., Peters-Dasdemir, J., Möller, A., Safrudiannur (eds) Views and Beliefs in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-01273-1_17
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