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Micro-analysis of noticing: a lens on prospective teachers’ trajectories of learning to notice

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Abstract

Micro-analysis of noticing is introduced as a method to analyze prospective teacher noticing, one that privileges the high variation exhibited by novice learners. The intent was to understand how prospective teachers’ noticing moments suggest trajectories within and across whole-class discussions. We also focused on how prospective teachers’ responses suggest individual trajectories of noticing in these discussions. We examined prospective teachers’ engagement with a videocase curriculum in a mathematics content course in a teacher preparation program in the US. We contrast prospective teachers’ development of noticing using commonly employed analytic methods in noticing research and discuss the limitations of these methods for characterizing prospective (novice) teacher development of noticing. Findings illustrate how a micro-analysis of noticing as an analytic method illuminates nuanced patterns of prospective teacher noticing in their development of learning to notice in both whole-class and individual scenarios.

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References

  • Amador, J. M. (2017). Preservice teachers’ video simulations and subsequent noticing: A practice-based method to prepare mathematics teachers. Research in Mathematics Education, 19(3), 217–235. https://doi.org/10.1080/14794802.2017.1315317.

    Article  Google Scholar 

  • Amador, J. M., Bragelman, J., & Superfine, A. C. (2021). Prospective teachers’ noticing: A literature review of methodological approaches to support and analyze noticing. Teaching and Teacher Education. https://doi.org/10.1016/j.tate.2020.103256.

    Article  Google Scholar 

  • Baldinger, E. M. (2017). “Maybe it’s a status problem”. Development of mathematics teacher noticing for equity. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 231–249). Cham: Springer International.

    Chapter  Google Scholar 

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

    Google Scholar 

  • Ball, D. L., Sleep, L., Boerst, T. A., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. The Elementary School Journal, 109(5), 458–474.

    Article  Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.

    Article  Google Scholar 

  • Beisiegel, M., Mitchell, R. N., & Hill, H. C. (2018). The design of video-based professional development: An exploratory experiment intended to idenfity effective features. Journal of Teacher Education, 69(1), 69–89.

    Article  Google Scholar 

  • Borko, H., & Livingston, C. (1989). Cognitiion and improvision: Differences in mathematics instruction by expert and novice teachers. American Educational Research Journal, 26(4), 473–498.

    Article  Google Scholar 

  • Castro Superfine, A., Li, W., Bragelman, J., & Fisher, A. (2015). Examining the use of video to support preservice elementary teachers' noticing of children's thinking. Journal of Technology and Teacher Education, 23(2), 137–157.

  • Carter, I. S., Weiland, I., & Amador, J. M. (2015). Lexical and indexical conversational components that mediate professional noticing during lesson study. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1339–1361. https://doi.org/10.12973/eurasia.2015.1392a.

    Article  Google Scholar 

  • Chi, M. T. H. (2011). Theoretical perspectives, methodological approaches, and trends in the study of expertise. In Y. Li & G. Kaiser (Eds.), Expertise in Mathematics Instruction, (pp. 17–39) Boston, MA: Springer.

  • de Araujo, Z., Estapa, A., Aming-Attai, R., Amador, J., Weston, T. L., & Kosko, K. W. (2015). Animating preservice teachers’ noticing. Mathematics Teacher Education and Development, 17(2), 25–44.

    Google Scholar 

  • de Bot, K., Lowie, W., & Verspoor, M. (2007). A dynamic systems theory approach to second language acquisition. Bilingualism: Language and Cognition, 10(01), 7–21. https://doi.org/10.1017/s1366728906002732.

    Article  Google Scholar 

  • Ding, L., & Domínguez, H. (2015). Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson. Journal of Mathematics Teacher Education, 19(4), 325–347. https://doi.org/10.1007/s10857-015-9301-3.

    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. https://doi.org/10.1007/s10649-014-9577-8.

    Article  Google Scholar 

  • Granott, N., Fischer, K. W., & Parziale, J. (2002). Bridging to the unknown: A transition mechanism in learning and development. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 131–156). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Grossman, P. L., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. W. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.

    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(2), 169–202.

    Article  Google Scholar 

  • Jacobs, J. K., & Morita, E. (2002). Japanese and American teachers’ evaluations of videotaped mathematics lessons. Journal for Research in Mathematics Education, 33(3), 154–175.

  • Jacobs, V. R., & Philipp, R. A. (2004). Mathematical thinking: Helping prospective and practicing teachers focus. Teaching Children Mathematics, 11(4), 194–201.

    Article  Google Scholar 

  • Jacobs, V. R., Empson, S. B. (2015). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM Mathematics Education, 48(1-2), 185–197.

  • Kang, H., & van Es, E. (2018). Articulating design principles for productive use of video in preservice education. Journal of Teacher Education, 00, 1–14.

    Google Scholar 

  • Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. Instructional explanations in the disciplines (pp. 129–141). Boston, MA: Springer.

    Chapter  Google Scholar 

  • Magiera, M. T., van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84, 93–113.

    Article  Google Scholar 

  • Mason, J. (2002). Researching your own practice: The discipline of noticing. New York: Routledge.

    Book  Google Scholar 

  • McDuffie, A. R., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J., Bartell, T. G., et al. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple knowledge bases. Journal of Mathematics Teacher Education, 17, 245–270. https://doi.org/10.1007/s10857-013-9257-0.

    Article  Google Scholar 

  • Osmanoglu, A., Isiksal, M., & Koc, Y. (2015). Getting ready for the profession: Prospective teachers’ noticing related to teacher actions. Australian Journal of Teacher Education, 40(2), 29–51. https://doi.org/10.14221/ajte.2015v40n2.3.

    Article  Google Scholar 

  • Roller, S. A. (2015). What they notice in video: A study of prospective secondary mathematics teachers learning to teach. Journal of Mathematics Teacher Education, 19(5), 477–498. https://doi.org/10.1007/s10857-015-9307-x.

    Article  Google Scholar 

  • Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16, 379–397.

    Article  Google Scholar 

  • Schack, E. O., Fisher, M. H., & Wilhelm, J. A. (Eds.). (2017). Teacher noticing: Bridging and broadening perspectives, context, and frameworks. Cham: Springer International Publishing.

    Google Scholar 

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

    Google Scholar 

  • Siegler, R. S. (2007). Cognitive variability. Developmental Science, 10(1), 104–109.

    Article  Google Scholar 

  • Smith, L. B., & Thelen, E. (2003). Development as a dynamic system. TRENDS in Cognitive Sciences, 7(8), 343–348. https://doi.org/10.1016/S1364-6613(03)00156-6.

    Article  Google Scholar 

  • Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107–125. https://doi.org/10.1007/s10857-007-9063-7.

    Article  Google Scholar 

  • Superfine, A. C., Wenjuan Li, Bragelman, J., & Fisher, A. (2015). Examining the use of video to support preservice elementary teachers’ noticing of children’s thinking. Journal of Technology & Teacher Education, 23(2), 137–157.

  • Superfine, A. C., Amador, J. M., & Bragelman, J. (2019). Facilitating video-based discussions to support prospective teacher noticing. The Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2018.11.002.

    Article  Google Scholar 

  • Superfine, A. C., & Bragelman, J. (2018). Analyzing the impact of video representation complexity on preservice teacher noticing of children’s thinking. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/99501.

    Article  Google Scholar 

  • Superfine, A. C., Fisher, A., Bragelman, J., & Amador, J. M. (2017). Shifting perspectives on preservice teachers’ noticing of children’s mathematical thinking. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives (pp. 409–426). Cham: Springer.

    Chapter  Google Scholar 

  • Thomas, J. N., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 25(2), 3–25.

    Google Scholar 

  • van Es, E. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, & R. Phillip (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 165–180). New York, NY: Routledge.

    Google Scholar 

  • van Es, E., 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), 165–187. https://doi.org/10.1080/07370008.2017.1317125.

    Article  Google Scholar 

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

    Google Scholar 

  • van Es, E., & Sherin, M. G. (2006). How different video club designs support teachers in “Learning to Notice.” Journal of Computing in Teacher Education, 22(4), 125–135.

    Google Scholar 

  • van Es, E., Tunney, J., Goldsmith, L. T., & Seago, N. (2014). A framework for the facilitation of teachers’ analysis of video. Journal of Teacher Education, 65(4), 340–356. https://doi.org/10.1177/0022487114534266.

    Article  Google Scholar 

  • van Geert, P. (1994). Vygotskians dynamics of development. Human Development, 37, 246–365.

    Article  Google Scholar 

  • van Geert, P., & van Dijk, M. (2002). Focus on variability: New tools to study intra-individual variability in developmental data. Infant Behavior and Development, 25, 340–374.

    Article  Google Scholar 

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

  • van Zoest, L. R., & Stockero, S. L. (2012). Capitalizing on productive norms to support teacher learning. Mathematics Teacher Educator, 1(1), 41–52.

    Article  Google Scholar 

  • Vygotsky, L. S. (1978). Mnd in society: The development of higher psychological processes. Cambridge: Cambridge University Press.

    Google Scholar 

  • Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523–550. https://doi.org/10.1007/s10857-014-9289-0

  • Wolff, C. E., Jarodzka, H., van den Bogert, N., & Boshuizen, H. P. A. (2016). Teacher vision: Expert and novice teachers’ perception of problematic classroom management scenes. Instructional Science, 44(3), 243–265. https://doi.org/10.1007/s11251-016-9367-z.

    Article  Google Scholar 

  • Walkoe, J., & Luna, M. J. (2019). What we are missing in studies of teacher jearning: A call for microgenetic, interactional analyses to examine teacher learning processes. Journal of the Learning Sciences, 29(2), 285–307. https://doi.org/10.1080/10508406.2019.1681998

  • Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between Chinese mathematics teachers’ knowledge and their professional noticing. International Journal of Science and Mathematics Education (online first).

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Bragelman, J., Amador, J.M. & Superfine, A.C. Micro-analysis of noticing: a lens on prospective teachers’ trajectories of learning to notice. ZDM Mathematics Education 53, 215–230 (2021). https://doi.org/10.1007/s11858-021-01230-9

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