Session Information
24 SES 07, Mathematics Teachers' Training (Part 1)
Paper Session to be continued in 24 SES 08 A
Contribution
There is a growing consensus that teachers’ noticing or professional vision related to classroom situations is a substantial indicator of teacher expertise (Sherin et al.,2011; Berliner, 1991; Seidel et al., 2011; Schneider et al., submitted). In classrooms, expert teachers not only identify meaningful events which are relevant for classroom management (Schneider et al., submitted), but they notice e.g. understanding difficulties of students and even probable reasons for them. This points to the use of professional knowledge in the noticing process, which is in particular a requirement for mathematics teachers when they are being confronted e.g. with videotaped classroom situations that show how mathematical contents are dealt with. Indeed, the aspect of knowledge-based reasoning plays a key role (cf. Sherin et al., 2011), as professional knowledge (such as e.g. pedagogical content knowledge; Shulman, 1986) is often necessary to analyse classroom situations in order to notice potential challenges for learners when mathematical contents are dealt with, for instance. With a content-specific emphasis, Kuntze, Dreher & Friesen (in press) use the notion of mathematics teachers’ analysing of classroom situations: By analysing we understand an awareness-driven, knowledge-based process which connects the subject of analysis with relevant criterion knowledge and is marked by criteria-based explanation and argumentation (Kuntze et al., in press). Classroom situations can be the subject of analysis, in which teachers have to connect aspects of their pedagogical content knowledge with relevant situation observations.
As a framework model for components of professional knowledge, we use a multi-layer model (Kuntze, 2012), which combines the distinction of Shulman’s (1986) domains (content knowledge, pedagogical content knowledge, pedagogical knowledge in particular) with the spectrum between knowledge and views/convictions/beliefs (e.g. Pajares, 1992, Törner, 2002) – for pragmatic reasons, views are included as individual professional knowledge components. The model further distinguishes layers according to the “globality” vs. situatedness of professional knowledge, which can be situation-bound and structured episodically (e.g. Leinhardt & Greeno, 1986) on the one side or have a rather non-situation-specific character on the other hand.
When mathematics teachers are confronted with classroom situations, they are likely to develop or activate individual situation-related views (Lerman, 1990; Kuntze, 2012). Such views may interdepend with non-situation-specific epistemological beliefs (e.g. Törner, 2002) or orientations (e.g. Staub & Stern, 2002), but they can also be independent from them (Kuntze, 2012). Consequently, it is likely that the teachers’ situation-related analysis of the classroom directly interdepends with their views. In a comparative study with English and German pre-service teachers (Dreher, Kuntze & Lerman, 2015), we have approached such interdependencies in two European countries. However to our knowledge, there is hardly any quantitative empirical study that investigates the relationship between teachers’ analysis of mathematics classroom situations and their situation-related views in more depth, despite the relevance of this research interest for practice in European teacher professional development and theory development.
Consequently, this paper concentrates on exploring the potential interrelatedness of situation-related views and the quality of teachers’ knowledge-based analysis of classroom situations. We assert that interdependencies can be bi-directional and examine data from teacher surveys according to the following research questions:
(a) Do teachers who show a higher quality of analysis of specific classroom situations hold different situation-specific views from teachers who show a lower analysis quality? In particular: In case teachers bring forward criticism concerning a classroom situation in their analysis and substantiate this criticism with specific observations, does this lead to more negative situation-related views of the teachers?
The potential impact of views on the analysis can rather be explored in a qualitative approach according to the following question:
(b) Can situation-related views impede or obstruct the teachers’ knowledge-based analysis of classroom situations?
Method
Expected Outcomes
References
Berliner, D. C. (1991). Perceptions of student behavior as a function of expertise. Journal of Classroom Interaction, 26(1), 1-8. Dreher, A., Kuntze, S. & Lerman, S. (2015). Pre-service teachers’ views and PCK on using multiple representations in mathematics classrooms – an inter-cultural study. International Journal of Science and Mathematics Education. [Published on Online First; DOI: 10.1007/s10763-015-9633-6]. 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., & Friesen, M. (2015, in press). Teachers’ resources in analysing mathematical content and classroom situations. CERME 2015. Leinhardt, G. & Greeno, J. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78, 75–95. Lerman, S. (1990). Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. British Educational Research Journal, 16(1), 53–61. Pajares, F. M. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332. Schneider, J., Bohl, T., Kleinknecht, M., Rehm, M., Kuntze, S. & Syring, M. (submitted). Unterricht analysieren und reflektieren mit unterschiedlichen Fallmedien: Eine Untersuchung zur vermeintlichen Überlegenheit von Video gegenüber Text. [Analysing and reflecting cases of instruction in different media]. Unterrichtswissenschaft. Seidel, T., Stürmer, K., Blomberg, G., Kobarg, M., & Schwindt, K. (2011). Teacher learning from analysis of videotaped classroom situations: Does it make a difference whether teachers observe their own teaching or that of others? Teaching and Teacher Education, 27, 259-267. Sherin, M., Jacobs, V., Philipp, R. (2011). Mathematics Teacher Noticing. Seeing Through Teachers’ Eyes. New York: Routledge. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. 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.
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