Abstract
This study investigated a highly accomplished third-grade teacher’s noticing of students’ mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom teaching as opposed to professional development environments. Noticing was conceptualized as both attending to different elements of classroom instruction and making sense of classroom events. The teacher paid most attention to student thinking and was able to offer a variety of rich interpretations of student thinking which were presented in an emergent framework. The results also indicated how the teacher’s noticing might influence her instructional decisions. Implications for both research methods in studying noticing and teacher learning and practices are discussed.
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Ainley, J., & Luntley, M. (2007). The role of attention in expert classroom practice. Journal of Mathematics Teacher Education, 10, 3–22.
Ball, D. L. (2001). Teaching, with respect to mathematics and students. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 11–22). Mahwah, NJ: Erlbaum.
Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433–456). New York: Macmillan.
Bogdan, R. C., & Biklen, S. K. (1992). Qualitative research for education. An introduction to theory and methods. Boston, MA: Allyn & Bacon.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.
Cobb, P., McClain, K., Lamberg, T. S., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and district. Educational Researcher, 32, 13–24.
Colestock, A. (2009). A case study of one secondary mathematics teacher’s in the-moment noticing of student thinking while teaching. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 1459–1466). Atlanta, GA: Georgia State University.
Even, R., & Gottlib, O. (2011). Responding to students: Enabling a significant role for students in the class discourse. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction: An international perspective (pp. 109–130). New York: Springer.
Fennema, E., Carpenter, T., Franke, M., Levi, L., Jacobs, V., & Empson, S. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434.
Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (1993). Using children’s knowledge in instruction. American Educational Research Journal, 30(3), 555–583.
Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38, 653–689.
Ginsburg, H. P. (2009). The challenge of formative assessment in mathematics education: Children’s minds, teachers’ minds. Human Development, 52, 109–128.
Glaser, B., & Strauss, A. (1967). The discovery of grounded theory. Hawthorne, NY: Aldine Publishing Company.
Goldsmith, L. T., & Seago, N. (2011). Using classroom artifacts to focus teachers’ noticing: Affordances and opportunities. In M. Sherin, R. Philipp, & V. Jacobs (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 169–187). New York: Routledge.
Goodwin, C. (1994). Professional vision. American Anthropologist, 96, 606–633.
Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. Educational Studies in Mathematics, 38, 189–208.
Hatch, J. A. (2002). Doing qualitative research in education settings. Albany: State University of New York Press.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30, 393–425.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38, 258–288.
Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.
Jacobs, V. R., Lamb, L. L. C., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children's understandings. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 97–116). New York: Routledge.
Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203–235.
Li, Y., & Kaiser, G. (2011). Expertise in mathematics instruction: Advancing research and practice from an international perspective. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction: An international perspective (pp. 3–15). New York: Springer.
Luna, M., Russ, R., & Colestock, A. (2009). Teacher noticing in-the-moment of instruction: The case of one high school teacher. In: Paper presented at the annual meeting of the National Association for research in science teaching (NARST), Garden Grove, CA.
Mack, N. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3), 267–296.
Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge-Falmer.
Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other fields? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 51–65). New York: Routledge.
National Research Council. (2005). How students learn: History, mathematics, and science in the classroom. In M. S. Donovan and J. D. Bransford (Eds.), Washington, DC: The National Academies Press.
Russ, S., & Sherin, (2011). Images of expertise in mathematics teaching. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction: An international perspective (pp. 41–60). Berlin: Springer.
Schifter, D. (2011). Examining the behavior of operations: Noticing early algebraic ideas. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 204–220). New York: Routledge.
Schoenfeld, A. H. (1998). Towards a theory of teaching-in-context. Issues in Education, 4(1), 1–94.
Schoenfeld, A. H. (2011a). 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: Routledge.
Schoenfeld, A. H. (2011b). Toward professional development for teachers grounded in a theory of decision making. ZDM, 43, 457–469.
Seidel, T., Sturmer, 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. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20, 163–183.
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011a). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–13). New York: Routledge.
Sherin, M. G., Russ, R. S., & Colestock, A. A. (2011b). Accessing mathematics teachers’ in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79–94). New York: Routledge.
Sherin, M. G., Russ, R. S., Sherin, B. L., & Colestock, A. (2008). Professional vision in action: An exploratory study. Issues in Teacher Education, 17(2), 27–46.
Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475–491.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new form. Harvard Educational Review, 57(1), 1–22.
Son, J., & Crespo, S. (2009). Prospective teachers’ reasoning about students’ non-traditional strategies when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 236–261.
Spitzer, S. M., Phelps, C. M., Beyers, J. E. R., Johnson, D. Y., & Sieminski, E. M. (2011). Developing prospective elementary teachers’ abilities to identify evidence of student mathematical achievement. Journal of Mathematics Teacher Education, 14(1), 67–87.
Strauss, A. L., & Corbin, J. M. (1998). Basics of qualitative research: Grounded theory procedures and techniques. Beverley Hills: Sage Publications.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). Reston, VA: National Council of Teachers of Mathematics.
Tirosh, D., & Graeber, A. O. (1991). The effect of problem type and common misconceptions on preservice elementary teachers’ thinking about division. School Science and Mathematics, 91(4), 157–163.
van Es, E. A. (2011). A framework for learning to notice student thinking. In M. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teacher’s eyes (1st ed., pp. 134–151). London: Routledge.
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, 244–276.
Wallcott, (2010). Writing up qualitative research. Thousand Oaks: Sage Publication.
Wiliam, D. (2007). Keeping learning on track: Classroom assessment and the regulation of learning. In F. K. Lester Jr (Ed.), Second handbook of mathematics teaching and learning. Greenwich, CT: Information Age Publishing.
Acknowledgments
This paper is part of a larger study, which is an unpublished dissertation. I wish to thank my dissertation committee, especially my chair Dr. James Tarr, for the insightful feedback and comments on earlier drafts of this work. I would also like to acknowledge my indebtedness to colleagues Somnath Sinha who helped to maintain interrater reliability in the coding process, and Dr. Dung Tran and Dr. Luz Edith Valoyes for their valuable feedback and support. A final thanks goes to Dr. Kathyrn Chval who inspired me to do this work.
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Taylan, R.D. Characterizing a highly accomplished teacher’s noticing of third-grade students’ mathematical thinking. J Math Teacher Educ 20, 259–280 (2017). https://doi.org/10.1007/s10857-015-9326-7
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DOI: https://doi.org/10.1007/s10857-015-9326-7