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Professional Noticing of Mathematics Teachers: a Comparative Study Between Germany and China

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Abstract

Research on teacher noticing in the field of mathematics education research has increased in the last decade; however, only a few studies have investigated the social and cultural impact on teachers’ noticing. This paper describes results of an international comparative study on (in-service) mathematics teachers’ professional noticing in China and Germany, representing Eastern and Western cultures. In this study, 203 teachers in China and 118 teachers in Germany participated in a video-based assessment of their professional noticing, i.e. perception, interpretation, and decision-making competencies. Item response theory (IRT) and differential item functioning (DIF) were employed for data analysis. Findings of the study revealed that German teachers performed significantly better than Chinese teachers on noticing aspects related to general pedagogy; in contrast, Chinese teachers outperformed their German counterparts on noticing aspects connected to mathematics instruction. Further DIF detection analysis found that German mathematics teachers demonstrated particular strengths in “perception” as a sub-facet of noticing; in contrast, Chinese teachers tended to demonstrate strength in “analyzing and decision making” as other sub-facets of noticing. These findings suggest that societal and cultural factors, such as different philosophical paradigms, traditions of teacher education, and teaching and mathematics curriculum traditions are main influencing factors on teachers’ professional noticing.

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References

  • Alexander, R. (1999). Culture in pedagogy, pedagogy across cultures. In R. Alexander, P. Broadfoot, & D. Philips (Eds.), Learning from comparing. New directions in comparative educational research (Vol. 1, pp. 149–180). Oxford, England: Symposium Books.

    Google Scholar 

  • Ball, D. L. (2011). Foreword. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. xx–xxiv). New York, NY: Routledge.

    Google Scholar 

  • Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers’ ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83–93.

    Article  Google Scholar 

  • Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223, 3–13.

    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, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Blömeke, S., & Kaiser, G. (2017). Understanding the development of teachers’ professional competencies as personally, situationally, and socially determined. In D. J. Clandinin & J. Husu (Eds.), International handbook of research on teacher education (pp. 783–802). Thousand Oaks, CA: Sage.

    Chapter  Google Scholar 

  • Cai, J., & Nie, B. (2007). Problem solving in Chinese mathematics education: Research and practice. ZDM Mathematics Education, 39(5–6), 459–473.

    Article  Google Scholar 

  • Cai, J., & Wang, T. (2006). US and Chinese teachers’ conceptions and constructions of representations: A case of teaching ratio concept. International Journal of Science and Mathematics Education, 4(1), 145–186.

    Article  Google Scholar 

  • Cai, J., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context: Perspectives of teachers from China and the United States. Journal of Mathematics Teacher Education, 13(3), 265–287.

    Article  Google Scholar 

  • Carter, K., Cushing, K., Sabers, D., Stein, P., & Berliner, D. C. (1988). Expert-novice differences in perceiving and processing visual information. Journal of Teacher Education, 39, 25–31.

    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 

  • Ding, L., & Domínguez, H. (2016). Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson. Journal of Mathematics Teacher Education, 19(4), 325–347.

    Article  Google Scholar 

  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114.

    Article  Google Scholar 

  • Erickson, F. (2011). On noticing teacher noticing. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 17–34). New York, NY: Routledge.

    Google Scholar 

  • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.

    Article  Google Scholar 

  • Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage.

    Google Scholar 

  • Han, X., & Paine, L. (2010). Teaching mathematics as deliberate practice through public lessons. The Elementary School Journal, 110(4), 519–541.

    Article  Google Scholar 

  • Huang, R., Barlow, A. T., & Prince, K. (2016). The same tasks, different learning opportunities: An analysis of two exemplary lessons in China and the US from a perspective of variation. The Journal of Mathematical Behavior, 41, 141–158.

    Article  Google Scholar 

  • Huang, R., Su, H., & Xu, S. (2014). Developing teachers’ and teaching researchers’ professional competence in mathematics through Chinese lesson study. ZDM Mathematics Education, 46(2), 239–251.

    Article  Google Scholar 

  • Jacobs, V., Lamb, L., Philipp, R., & Schappelle, B. (2011). Deciding how to respond on the basis of children’s understandings. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 97–116). New York, NY: Routledge.

    Google Scholar 

  • Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.

    Google Scholar 

  • Jodoin, M. G., & Gierl, M. J. (2001). Evaluating type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14, 329–349.

    Article  Google Scholar 

  • Jones, V., & Jones, L. (2012). Comprehensive classroom management: Creating communities of support and solving problems. Boston, MA: Pearson.

    Google Scholar 

  • Kaiser, G., & Blömeke, S. (2013). Learning from the Eastern and the Western debate: The case of mathematics teacher education. ZDM Mathematics Education, 45(1), 7–19.

    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 

  • Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of vid-eo-based assessments: Theoretical and methodological approaches to overcoming short-comings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13(2), 369–387.

    Article  Google Scholar 

  • Kersting, N. B., Givvin, K. B., Sotelo, F. L., & Stigler, J. W. (2010). Teachers’ analyses of classroom video predict student learning of mathematics: Further explorations of a novel measure of teacher knowledge. Journal of Teacher Education, 61(1–2), 172–181.

    Article  Google Scholar 

  • Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2015). Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers. Teaching and Teacher Education, 46, 115–126.

    Article  Google Scholar 

  • König, J. (2013). First comes the theory, then the practice? On the acquisition of general pedagogical knowledge during initial teacher education. International Journal of Science and Mathematics Education, 11, 999–1028.

    Article  Google Scholar 

  • König, J., Blömeke, S., Klein, P., Suhl, U., Busse, A., & Kaiser, G. (2014). Is teachers’ general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach. Teaching and Teacher Education, 38, 76–88.

    Article  Google Scholar 

  • König, J., Blömeke, S., Paine, L., Schmidt, B., & Hsieh, F.-J. (2011). General pedagogical knowledge of future middle school teachers. On the complex ecology of teacher education in the United States, Germany, and Taiwan. Journal of Teacher Education, 62(2), 188–201.

    Article  Google Scholar 

  • Louie, N. L. (2018). Culture and ideology in mathematics teacher noticing. Educational Studies in Mathematics, 97(1), 55–69.

    Article  Google Scholar 

  • Mason, J. (2016). Perception, interpretation and decision making: Understanding gaps between competence and performance—A commentary. ZDM Mathematics Education, 48(1–2), 219–226.

    Article  Google Scholar 

  • Meschede, N., Fiebranz, A., Möller, K., & Steffensky, M. (2017). Teachers’ professional vision, pedagogical content knowledge and beliefs: On its relation and differences between pre-service and in-service teachers. Teaching and Teacher Education, 66, 158–170.

    Article  Google Scholar 

  • Mesic, V. (2012). Identifying country-specific cultures of physics education: A differential item functioning approach. International Journal of Science Education, 34(16), 2483–2500.

    Article  Google Scholar 

  • Miller, K., & Zhou, X. (2007). Learning from classroom video: What makes it compelling and what makes it harder. In R. Goldman-Segal & R. Pea (Eds.), Video research in the learning sciences (pp. 321–334). Mahwah, NJ: Lawrence Erlbaum.

    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 

  • Seidel, T., & Stürmer, K. (2014). Modeling and measuring the structure of professional vision in preservice teachers. American Educational Research Journal, 51(4), 739–771.

    Article  Google Scholar 

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

    Google Scholar 

  • Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27, 361–370.

    Article  Google Scholar 

  • Thomas, J. N. (2017). The ascendance of noticing: Connections, challenges, and questions. In E. O. Schack, H. F. Molly, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 507–514). New York, NY: Springer.

    Chapter  Google Scholar 

  • van Es, E. A., Cashen, M., Barnhart, T., & Auger, A. (2017). Learning to notice mathematics instruction: Using video to develop preservice teachers’ vision of ambitious pedagogy. Cognition and Instruction, 35(3), 1–23.

    Google Scholar 

  • van Es, E. A., Hand, V., & Mercado, J. (2017). Making visible the relationship between teachers’ noticing for equity and equitable teaching practice. In E. O. Schack, H. F. Molly, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 251–270). New York, NY: Springer.

    Google Scholar 

  • van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571–596.

    Google Scholar 

  • van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244–276.

    Article  Google Scholar 

  • Wang, T. Y., & Tang, S. J. (2013). Profiles of opportunities to learn for TEDS-M future secondary mathematics teachers. International Journal of Science and Mathematics Education, 11(4), 847–877.

    Article  Google Scholar 

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Correspondence to Gabriele Kaiser.

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Yang, X., Kaiser, G., König, J. et al. Professional Noticing of Mathematics Teachers: a Comparative Study Between Germany and China. Int J of Sci and Math Educ 17, 943–963 (2019). https://doi.org/10.1007/s10763-018-9907-x

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  • DOI: https://doi.org/10.1007/s10763-018-9907-x

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