The role of professional knowledge for teachers’ analysing of classroom situations regarding the use of multiple representations

References

• Acevedo Nistal, A., van Dooren, W., Clareboot, G., Elen, J., & Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: A critical review. ZDM Mathematics Education, 41(5), 627–636.
   Google Scholar
• Ainsworth, S. (2006). A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198.
   Web of Science ®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.
   Web of Science ®Google Scholar
• Berliner, D. C. (2001). Learning about and learning from expert teachers. International Journal of Educational Research, 35, 463–482.
   Google Scholar
• Bodemer, D., & Faust, U. (2006). External and mental referencing of multiple representations. Computers in Human Behavior, 22, 27–42.
   Web of Science ®Google Scholar
• Bond, T. G., & Fox, C. M. (2015). Applying the Rasch model. Fundamental measurement in the human sciences. New York, NY: Routledge.
   Google Scholar
• Bromme, R. (1992). Der Lehrer als Experte. Zur Psychologie des professionellen Wissens. [ The teacher as an expert. On the psychology of professional knowledge]. Bern: Hans Huber.
   Google Scholar
• Bromme, R. (1997). Kompetenzen, Funktionen und unterrichtliches Handeln des Lehrers. [ Competencies, functions and instruction-related actions of teachers]. In F. Weinert (Ed.), Enzyklopädie der Psychologie: Psychologie des Unterrichts und der Schule. [ Encyclopedia of psychology: Psychology of instruction and school]. (pp. 177–212). Göttingen: Hogrefe.
   Google Scholar
• Charalambous, Y. C., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64, 293–316.
   Google Scholar
• Charalambous, Y. C., & Pitta-Pantazi, D. (2016). Perspectives on priority mathematics education. Unpacking and understanding a complex relationship linking teacher knowledge, teaching, and learning. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 19–59). New York, NY: Routledge.
   Google Scholar
• Deliyianni, E., Gagatsis, A., Elia, I., & Panaoura, A. (2016). Representational flexibility and problem-solving ability in fraction and decimal number addition: A structural model. International Journal of Science and Mathematics Education, 14(2), 397–417.
   Web of Science ®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.
   Web of Science ®Google Scholar
• Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339–358). Cham: Springer.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Dreher, A., Kuntze, S., & Lerman, S. (2016). Why use multiple representations in the mathematics classroom? Views of English and German preservice teachers. International Journal of Science and Mathematics Education, 14(2), 363–382.
   Web of Science ®Google Scholar
• Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.
   Google Scholar
• Field, A. (2013). Discovering statistics using IBM SPSS statistics. London: Sage.
   Google Scholar
• Friesen, M. (2017). Teachers’ competence of analyzing the use of multiple representations in mathematics classroom situations and its assessment in a vignette-based test. (Dissertation Study). Ludwigsburg: Pädagogische Hochschulbibliothek.
   Google Scholar
• Friesen, M., & Kuntze, S. (2018). Competence assessment with representations of practice in text, comic and video format. In O. Buchbinder & S. Kuntze (Eds.), Mathematics teachers engaging with representations of practice (pp. 113–130). ICME-13 Monograph. Cham: Springer.
   Google Scholar
• Goldin, G. (2008). Perspectives on representation in mathematical learning and problem solving. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 176–201). New York: Routledge.
   Google Scholar
• 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, VA: NCTM.
   Google Scholar
• Herbst, P., & Kosko, K. W. (2014). Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: A comparison of responses to animations and videos. Journal of Mathematics Teacher Education, 17(6), 515–537.
   Google Scholar
• Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68(5), 845–861.
   Web of Science ®Google Scholar
• Kersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., & Stigler, J. W. (2012). Measuring usable knowledge: Teachers’ analyzes of mathematics class-room videos predict teaching quality and student learning. American Educational Research Journal, 49(3), 568–589.
   Web of Science ®Google Scholar
• Kline, P. (1999). The handbook of psychological testing. London: Routledge.
   Google Scholar
• Kuntze, S. (2012). Pedagogical content beliefs: Global, content domain-related and situation-specific components. Educational Studies in Mathematics, 79(2), 273–292.
   Web of Science ®Google Scholar
• Kuntze, S., Dreher, A., & Friesen, M. (2015). Teachers’ resources in analyzing mathematical content and classroom situations – The case of using multiple representations. In K. Krainer & N. Vondrová (Eds.), Proceedings of the ninth conference of the European Society for Research in Mathematics Education (pp. 3213–3219). Prague: Charles University in Prague, Faculty of Education and ERME.
   Google Scholar
• Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33–40). Hillsdale, NJ: Lawrence Erlbaum.
   Google Scholar
• Mitchell, R., Charalambous, C. Y., & Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17, 37–60.
   Google Scholar
• Oser, F., Salzmann, P., & Heinzer, S. (2009). Measuring the competence-quality of vocational teachers: An advocatory approach. Empirical Research in Vocational Education and Training, 1, 65–83.
   Google Scholar
• Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning Up a Messy construct. Review of Educational Research, 62(3), 307–332.
   Web of Science ®Google Scholar
• Santagata, R., & Yeh, C. (2016). The role of perception, interpretation, and decision making in the development of beginning teachers’ competence. ZDM Mathematics Education, 48(1), 153–165.
   Google Scholar
• Schoenfeld, A. H. (2011). Noticing matters. A lot. Now what? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 223–238). New York, NY: Routledge.
   Google Scholar
• Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Mathematics teacher noticing. Seeing through teachers' eyes. New York: Routledge.
   Google Scholar
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Edu-cational Researcher, 15(2), 4–14.
   Google Scholar
• Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1–22.
   Web of Science ®Google Scholar
• Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: A systematic review of empirical mathematics education research. ZDM Mathematics Education, 48(1), 1–27.
   Google Scholar
• Stylianou, D. (2010). Teachers’ conceptions of representations in middle school mathematics. Journal of Mathematics Teacher Education, 13, 325–434.
   Google Scholar
• Toerner, 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.
   Google Scholar
• van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). New York, NY: Routledge.
   Google Scholar