Skip to main content
SpringerLink
Log in

Instructional reasoning about interpretations of student thinking that supports responsive teaching in secondary mathematics

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

Basing instruction on the substance of student thinking, or responsive teaching, is a critical strategy for supporting student learning. Previous research has documented responsive teaching by identifying observable teaching practices in a broad range of disciplines and classrooms. However, this research has not provided access to the teacher thinking that is at play leading to these responsive practices. In this study, we use an innovative methodology to explore the cognitive dimensions of responsive teaching as they take place during the moments of instruction. Data include 17 point-of-view observations in which two high school mathematics teachers saved video of important moments in real time and discussed the moments during an interview immediately following instruction. Both teachers were observed to use sophisticated responsive teaching practices, providing a window into consequential teacher thinking around student thinking. An open coding of teachers’ comments about the moments they selected to capture during instruction was used to identify three types of instructional reasoning about interpretations of student thinking used by the teachers: (a) making connections between multiple specific moments of student thinking, (b) considering the relation between the mathematics of student thinking and the structure of a mathematical task, and (c) developing tests of student thinking. We provide contextualized examples of each of the types of instructional reasoning and discuss how these findings relate to current theory on responsive teaching. We conclude by considering the implications of this study for the necessary mathematical and pedagogical expertise required to engage in responsive teaching, and consider how this instructional reasoning can be supported through professional development.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Ball, D. L. (2001). Teaching, with respect to mathematics and students. Beyond classical pedagogy: Teaching elementary school mathematics (pp. 11–22). Mahwah, NJ: Lawrence Erlbaum Associates.

    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.

    Article  Google Scholar 

  • Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2003). Assessment for learning: Putting it into practice. McGraw-Hill International.

  • Brantlinger, A., Sherin, M. G., & Linsenmeier, K. A. (2011). Discussing discussion: a video club in the service of math teachers’ national board preparation. Teachers and Teaching: Theory and Practice, 17(1), 5–33.

    Article  Google Scholar 

  • Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Franke, M. L. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: an experimental study. American Educational Research Journal, 26(4), 499–531.

    Article  Google Scholar 

  • Charalambous, C. Y., & Hill, H. C. (2012). Teacher knowledge, curriculum materials, and quality of instruction: unpacking a complex relationship. Journal of Curriculum Studies, 44(4), 443–466.

    Article  Google Scholar 

  • Coffey, J. E., Hammer, D., Levin, D. M., & Grant, T. (2011). The missing disciplinary substance of formative assessment. Journal of Research in Science Teaching, 48(10), 1109–1136.

    Article  Google Scholar 

  • Cohen, S. (2004). Teachers’ professional development and the elementary mathematics classroom: bringing understandings to light. Mahwah, NJ: Lawrence Erlbaum Associates.

  • Colestock, A., & Sherin, M. G. (2009). Teachers’ sense-making strategies while watching video of mathematics instruction. Journal of Technology and Teacher Education, 17(1), 7–29.

    Google Scholar 

  • Crespo, S. (2000). Seeing more than right and wrong answers: prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3(2), 155–181.

    Article  Google Scholar 

  • Dyer, E. B. (2015). Exploring teachers’ in-the-moment reasoning in experimentation around responsive teaching in secondary mathematics. In: Proceedings of the 37th annual conference of PME-NA, East Lansing.

  • Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: tools and processes in mathematics teacher education (Vol. 2, pp. 257–281). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380–392.

    Article  Google Scholar 

  • Ginsburg, H. P. (1997). Entering the child’s mind: the clinical interview in psychological research and practice (1st ed.). New York, NY: Cambridge University Press.

    Book  Google Scholar 

  • Hammer, D., Goldberg, F., & Fargason, S. (2012). Responsive teaching and the beginnings of energy in a third grade classroom. Review of Science, Mathematics and ICT Education, 6(1), 51–72.

    Google Scholar 

  • Herbst, P., & Chazan, D. (2012). On the instructional triangle and sources of justification for actions in mathematics teaching. ZDM—The International Journal on Mathematics Education, 44(5), 601–612.

    Article  Google Scholar 

  • Hutchison, P., & Hammer, D. (2010). Attending to student epistemological framing in a science classroom. Science Education, 94(3), 506–524.

    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.

    Google Scholar 

  • Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.

    Google Scholar 

  • Lineback, J. E. (2012). Mrs. Miller’s evolution in teaching science as inquiry: a case study of a teacher’s change in responsiveness (unpublished dissertation). University of California, San Diego, San Diego, CA.

  • Lineback, J. E. (2015). The redirection: an indicator of how teachers respond to student thinking. Journal of the Learning Sciences (in press).

  • Maskiewicz, A. C., & Winters, V. A. (2012). Understanding the co-construction of inquiry practices: a case study of a responsive teaching environment. Journal of Research in Science Teaching, 49(4), 429–464.

    Article  Google Scholar 

  • Pierson, J. L. (2008). The relationship between patterns of classroom discourse and mathematics learning (unpublished dissertation). Austin, TX: University of Texas at Austin.

    Google Scholar 

  • Schoenfeld, A. H. (2011). How we think: A theory of goal-oriented decision making and its educational applications. Routledge.

  • Sherin, M. G. (2001). Developing a professional vision of classroom events. In T. Wood, T. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 75–93). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

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

    Google Scholar 

  • Sherin, M. G., Louis, D., & Mendez, E. P. (2000). Students’ building on one another’s mathematical ideas. Mathematics Teaching in the Middle School, 6(3), 186–190.

    Google Scholar 

  • Sherin, M. G., Russ, R. S., & Colestock, A. A. (2011b). Accessing mathematics teachers’ in-the-moment noticing. In: Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79–94).

  • Sherin, M. G., Russ, R., Sherin, B. L., & Colestock, A. (2008). Professional vision in action: an exploratory study. Issues in Teacher Education, 17(2), 27–46.

    Google Scholar 

  • Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.

    Article  Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: an analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.

    Article  Google Scholar 

  • Steinberg, R. M., Empson, S. B., & Carpenter, T. P. (2004). Inquiry into children’s mathematical thinking as a means to teacher change. Journal of Mathematics Teacher Education, 7(3), 237–267.

    Article  Google Scholar 

  • Tyminski, A. M., Zambak, V. S., Drake, C., & Land, T. J. (2014). Using representations, decomposition, and approximations of practices to support prospective elementary mathematics teachers’ practice of organizing discussions. Journal of Mathematics Teacher Education, 17(5), 463–487.

    Article  Google Scholar 

  • Van Es, E. A., & Sherin, M. G. (2010). The influence of video clubs on teachers’ thinking and practice. Journal of Mathematics Teacher Education, 13(2), 155–176.

    Article  Google Scholar 

  • Wilhelm, A. G. (2014). Mathematics teachers’ enactment of cognitively demanding tasks: investigating links to teachers’ knowledge and conceptions. Journal for Research in Mathematics Education, 45(5), 636–674.

    Article  Google Scholar 

  • Wood, T., Cobb, P., & Yackel, E. (1991). Change in teaching mathematics: a case study. American Educational Research Journal, 28(3), 587–616.

    Article  Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

  • Yeh, C., & Santagata, R. (2015). Preservice teachers’ learning to generate evidence-based hypotheses about the impact of mathematics teaching on learning. Journal of Teacher Education, 66(1), 21–34.

    Article  Google Scholar 

Download references

Acknowledgments

This material is based upon work supported by the Arthur Vining Davis Foundations, the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-0824162, and the NAEd/Spencer Dissertation Fellowship Program.

Author information

Authors and Affiliations

  1. Northwestern University, Evanston, USA

    Elizabeth B. Dyer & Miriam Gamoran Sherin

Authors
  1. Elizabeth B. Dyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miriam Gamoran Sherin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elizabeth B. Dyer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dyer, E.B., Sherin, M.G. Instructional reasoning about interpretations of student thinking that supports responsive teaching in secondary mathematics. ZDM Mathematics Education 48, 69–82 (2016). https://doi.org/10.1007/s11858-015-0740-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-015-0740-1

Keywords

Search

Navigation