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Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks pp 467–480Cite as

Noticing Distinctions Among and Within Instances of Student Mathematical Thinking

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Part of the book series: Research in Mathematics Education ((RME))

Abstract

In this chapter, we argue that there are two critical aspects of noticing student mathematical thinking: noticing within an instance of student thinking and noticing among instances of student thinking. We use the noticing literature to illustrate these distinctions. We then discuss how the MOST Analytic Framework analysis provides structure and guidance for noticing both within and among instances, and illustrate the complex interaction of these two types of noticing through the analysis of an excerpt of classroom dialogue. We conclude by offering the perspective that studies of noticing must go beyond placing value on student mathematical thinking to discriminating among instances of student thinking based on their potential to be used to support students’ understanding of important mathematics.

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References

  • 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 

  • Confrey, J. (1993). Learning to see children’s mathematics: Crucial challenges in constructivist reform. In K. Tobin (Ed.), The practice of constructivism in science education (pp. 299–321). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10, 441–468.

    Google Scholar 

  • Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching: theory and practice, 15, 273–289. doi:10.1080/13540600902875340

    Article  Google Scholar 

  • Haltiwanger, L., & Simpson, A. (2014). Secondary mathematics preservice teachers’ noticing of students’ mathematical thinking. In G. T. Matney & S. M. Che (Eds.), Proceedings of the 41st annual meeting of the Research Council on Mathematics Learning (pp. 49–56). San Antonio, TX.

    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 

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

    Google Scholar 

  • Kazemi, E., Franke, M., & Lampert, M. (2009). Developing pedagogies in teacher education to support teachers’ ability to enact ambitious instruction. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the mathematics education research group of Australasia (Vol. 1, pp. 11–29). Palmerston North, New Zealand: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2006). Connected mathematics 2, grade 8: Variables and patterns. Upper Saddle River, NJ: Prentice Hall.

    Google Scholar 

  • Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46, 88–124.

    Article  Google Scholar 

  • Llinares, S. (2013). Professional noticing: A component of the mathematics teacher’s professional practice. Journal of Education, 1(3), 76–93.

    Google Scholar 

  • Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44, 809–850.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

    Google Scholar 

  • National Research Council. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Russ, R. S., & Luna, M. J. (2013). Inferring teacher epistemological framing from local patterns in teacher noticing. Journal of Research in Science Teaching, 50, 284–314. doi: 10.1002/tea.21063

    Article  Google Scholar 

  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: an empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10, 123–140. doi:10.1007/s10857-007-9029-9

    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. doi:10.1007/s10857-013-9240-9

    Article  Google Scholar 

  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp, R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 1–13). New York, NY: Routledge.

    Google Scholar 

  • 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.

    Google Scholar 

  • Sherin, M. G., Russ, R. S., Colestock, A. A. (2011). Accessing mathematics teachers’ in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp, R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79–94). New York, NY: Routledge.

    Google Scholar 

  • 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, 475–491.

    Google Scholar 

  • Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60, 20–37. doi:10.1177/0022487108328155

    Article  Google Scholar 

  • Star, J. R., Lynch, K., & Perova, N. (2011). Using video to improve preservice mathematics teachers’ abilities to attend to classroom features: A replication study. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp, R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 117–133). New York, NY: Routledge.

    Google Scholar 

  • Stockero, S. L. (2014). Transitions in prospective mathematics teachers’ noticing. In J. J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 239–259). New York, NY: Springer.

    Chapter  Google Scholar 

  • Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384–395.

    Google Scholar 

  • Stockero, S. L., Peterson, B. E., Leatham, K. R., & Van Zoest, L. R. (2014). The “MOST” productive student mathematical thinking. Mathematics Teacher, 108, 308–312.

    Article  Google Scholar 

  • Wager, A. A. (2014). Noticing children’s participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45, 312–350.

    Article  Google Scholar 

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

    Article  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, 571–596.

    Google Scholar 

  • van Es, E. A. (2011). A framework for learning to notice student thinking. A replication study. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp, R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). New York, NY: Routledge.

    Google Scholar 

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Acknowledgments

This research report is based on work supported by the U.S. National Science Foundation (NSF) under Grant Nos. 1220141, 1220357, and 1220148. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.

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Authors and Affiliations

  1. Michigan Technological University, Houghton, MI, USA

    Shari L. Stockero

  2. Brigham Young University, Provo, UT, USA

    Keith R. Leatham & Blake E. Peterson

  3. Western Michigan University, Kalamazoo, MI, USA

    Laura R. Van Zoest

Authors
  1. Shari L. Stockero
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  2. Keith R. Leatham
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  3. Laura R. Van Zoest
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  4. Blake E. Peterson
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Corresponding author

Correspondence to Shari L. Stockero .

Editor information

Editors and Affiliations

  1. Morehead State University, Morehead, Kentucky, USA

    Edna O. Schack

  2. University of Kentucky, Lexington, Kentucky, USA

    Molly H. Fisher

  3. STEM Education, University of Kentucky, Lexington, Kentucky, USA

    Jennifer A. Wilhelm

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Stockero, S.L., Leatham, K.R., Van Zoest, L.R., Peterson, B.E. (2017). Noticing Distinctions Among and Within Instances of Student Mathematical Thinking. In: Schack, E., Fisher, M., Wilhelm, J. (eds) Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-46753-5_27

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  • DOI: https://doi.org/10.1007/978-3-319-46753-5_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46752-8

  • Online ISBN: 978-3-319-46753-5

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