Conflicting frames: a case of misalignment between professional development efforts and a teacher’s practice in a high school mathematics classroom


We examine the case of a lesson planning session within the context of professional development for dialogic instruction, and the lesson enacted following this session, which was intended to provide opportunities to 11th and 12th grade algebra students to explore polynomial functions in terms of their roots and linear factors. Our goal was, through the close analysis of the planning and enactment of the lesson, to gain deeper understanding of how the two participants were framing mathematical learning and how such different frames may explain the disparity between the planned lesson and its outcome. The analysis and discussion point to the complexities of supporting teachers in transitioning from a “doing” frame to an “exploring” frame.

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


  1. 1.

    All names, except Munter’s, are pseudonyms.

  2. 2.

    In this case, conceptual distinctions such as Skemp’s (1976) “instrumental” vs. “relational” understanding or Lithner’s (2008) “creative” vs. “imitative” reasoning are also relevant. However, we chose to employ Smith and Stein’s (1998) mathematical tasks lens because it more directly relates to an expectation for Ms. Q’s practice at the time—implementing a more conceptually oriented curriculum.

  3. 3.

    An “Algebra 2” course in the USA is a second, year-long algebra course that typically follows a first algebra course and a geometry course and focuses largely on expanding work with functions to polynomial, rational, radical, and possibly trigonometric functions.

  4. 4.

    For more information on Accountable Talk, see

  5. 5.

    In her “teacher-leader” role, Ms. Q’s teaching load was reduced to allow time for her to provide direct instructional support to other teachers (e.g., co-teaching, observing, and other instructional “coaching” activities).


  1. Atkinson, J. M., & Heritage, J. (2006). Jefferson’s transcript notation. In A. Jaworski & N. Coupland (Eds.), The dis-course reader (pp. 158–165). London: Routledge. (Reprinted from Structures of social action: Studies in conversation analysis, pp. ix–xvi, by J. M. Atkinson & J. Heritage, Eds., 1984, Cambridge, England: Cambridge University Press).

  2. Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15.

  3. Cobb, P., & Jackson, K. (2011). Towards an empirically grounded theory of action for improving the quality of mathematics teaching at scale. Mathematics Teacher Education and Development, 13(1), 6–33.

    Google Scholar 

  4. Coburn, C. E., & Stein, M. K. (Eds.). (2010). Research and practice in education: Building alliances, bridging the divide. Lanham: Rowman & Littlefield Publishers.

  5. Goffman, E. (1974). Frame analysis: An essay on the organization of experience. Cambridge, MA: Harvard University Press.

    Google Scholar 

  6. Gresalfi, M. S., & Cobb, P. (2011). Negotiating identities for mathematics teaching in the context of professional development. Journal for Research in Mathematics Education, 42(3), 270–304.

    Article  Google Scholar 

  7. Grossman, P. L., Smagorinsky, P., & Valencia, S. (1999). Appropriating tools for teaching English: A theoretical framework for research on learning to teach. American Journal of Education, 108(1), 1–29.

    Article  Google Scholar 

  8. Hammer, D., Elby, A., Scherr, R. E., & Redish, E. (2005). Resources, framing and transfer. In J. Mestre (Ed.), Transfer of learning from a modern multidisciplinary perspective (pp. 89–119). Greenwich, CT: Information Age Publishing.

    Google Scholar 

  9. Horn, I. S., & Kane, B. D. (2015). Opportunities for Professional Learning in Mathematics Teacher Workgroup Conversations: Relationships to Instructional Expertise. Journal of the Learning Sciences, 24(3), 373-418.

  10. Lavie, I., & Sfard, A. (2016). Atzamin mdiburim: Keytzad yeladim ktanim yotzrim misparim betoch siah (Objects from talk: How young children create numbers throughout discourse). [In Hebrew] Mehkar VeIyun BeHinuch Matemati, 4. Retrieved from

  11. Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276.

  12. Ma, J., Munter, C., Heyd-Metzuyanim, E., Greeno, J., Kelton, M., Hall, R. & Gresalfi, M. (2014). Disrupting learning: Changing local practice for good. In J. L. Polman, E. A. Kyza, D. K. O'Neill, I. Tabak, W. R. Penuel, A. S. Jurow, K. O'Connor, T. Lee, & L. D'Amico (Eds.), Learning and becoming in practice: The International Conference of the Learning Sciences (ICLS), Volume 1 (pp. 1396–1405). Boulder, CO: International Society of the Learning Sciences.

  13. Munter, C., Stein, M. K., & Smith, M. S. (2015). Dialogic and direct instruction: Two distinct models of mathematics instruction and the debate(s) surrounding them. Teachers College Record, 117(11).

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

    Google Scholar 

  15. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.

  16. Nelson, B. S. (1997). Learning about teacher change in the context of mathematics education reform: Where have we come from? In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 3-15). Mahwah: Lawrence Erlbaum.

  17. Sfard, A. (2008). Thinking as communicating. New York: Cambridge University Press.

    Google Scholar 

  18. Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different? — Early numerical thinking revisited. Cognition and Instruction, 23(2), 237–309.

  19. Simon, M. A., Tzur, R., Heinz, K., Kinzel, M., & Smith, M. S. (2000). Characterizing a perspective underlying the practice of mathematics teachers in transition. Journal for Research in Mathematics Education, 31(5), 579–601.

    Article  Google Scholar 

  20. Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.

  21. Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350.

    Google Scholar 

  22. 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 

  23. Tannen, D. (1993). What’s in a frame? Surface evidence for underlying expectations. In D. Tannen (Ed.), Framing in discourse (pp. 14–56). New York: Oxford University Press.

  24. Tate, W. F., King, K. D., & Anderson, C. R. (Eds.). (2011). Disrupting tradition: Research and practice pathways in mathematics education. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  25. van de Sande, C. C., & Greeno, J. G. (2012). Achieving alignment of perspectival framings in problemsolving discourse. Journal of the Learning Sciences, 21, 1–44.

  26. Voigt, J. (1995). Thematic patterns of interaction and sociomathematical norms. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 163–201). Hillsdale, NJ: Lawrence Erlbaum Associates.

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

Download references

Author information



Corresponding author

Correspondence to Einat Heyd-Metzuyanim.



Transcript conventions used in the examples were adapted from those developed by Gail Jefferson (see Atkinson & Heritage, 1984/2006):

[X.Y] Turns at talk numbered for excerpt X and turn Y

((text)) Descriptions of actions or paraphrases

(text) Transcriber uncertainty

Text Emphatic talk

te::ext Elongated speech

(Zs) Pauses in speech, where Z is the duration of the pause in seconds

[text Onsetofoverlappingtalk

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Heyd-Metzuyanim, E., Munter, C. & Greeno, J. Conflicting frames: a case of misalignment between professional development efforts and a teacher’s practice in a high school mathematics classroom. Educ Stud Math 97, 21–37 (2018).

Download citation


  • Professional development
  • High school algebra
  • Frames
  • Discourse
  • Lesson planning
  • Secondary school teaching
  • Dialogic instruction