Journal of Mathematics Teacher Education

, Volume 22, Issue 2, pp 205–225 | Cite as

Using theories and research to analyze a case: learning about example use

  • Dina Tirosh
  • Pessia Tsamir
  • Esther S. LevensonEmail author
  • Ruthi Barkai


This paper raises the possibility of enhancing prospective and practicing teachers’ awareness of example use in classrooms by using theories to analyze an authentic case. The study was carried out in the context of a university course where participants analyzed an excerpt from a tenth-grade geometry class. A qualitative analysis of participants’ comments related to example use in the case revealed that different participants related to different theories when discussing the same example. The most frequent aspect of example use noted was the psychological aspect, such as the use of intuitive and non-intuitive examples. In general, teachers felt that the case activity contributed to their understanding of example use in the classroom, although not necessarily to a great extent. One implication of the study is that analyzing an authentic case while focusing on certain theories, such as example use, may serve as a rehearsal for the teacher who wishes to reflect on and analyze example use in her or his classroom. Thus, theory is brought into the practice of teaching.


Examples Theories Case analysis Teacher perspectives Prospective teachers 



This research was supported by The Trump Foundation (grant No. 145).


  1. Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214.Google Scholar
  2. Ball, D. L., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497–511.Google Scholar
  3. 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.Google Scholar
  4. Bruner, J. S. (1968). Towards a theory of instruction. New York: Norton.Google Scholar
  5. Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.Google Scholar
  6. Clarke, B. (2008). A framework of growth points as a powerful teacher development tool. In D. Tirosh & T. Wood (Eds.), The International handbook of mathematics teacher education (pp. 235–256). Rotterdam: Sense Publishers.Google Scholar
  7. Conner, A., Wilson, P. S., & Kim, H. J. (2011). Building on mathematical events in the classroom. ZDM—The International Journal on Mathematics Education, 43(6–7), 979–992.Google Scholar
  8. Goldenberg, P., & Mason, J. (2008). Shedding light on and with example spaces. Educational Studies in Mathematics, 69(2), 183–194.Google Scholar
  9. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.Google Scholar
  10. Kazemi, E., Ghousseini, H., Cunard, A., & Turrou, A. C. (2016). Getting inside rehearsals: Insights from teacher educators support work on complex practice. Journal of Teacher Education, 67(1), 1–14.Google Scholar
  11. Klausmeier, H. J. (1992). Concept learning and concept teaching. Educational Psychologist, 27(3), 267–286.Google Scholar
  12. Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., et al. (2013). Keeping it complex using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226–243.Google Scholar
  13. Levenson, E., Tsamir, P., & Tirosh, D. (2007). Neither even nor odd: Sixth grade students’ dilemmas regarding the parity of zero. The Journal of Mathematical Behavior, 26(2), 83–95.Google Scholar
  14. Lin, P. J. (2005). Using research-based video-cases to help pre-service primary teachers conceptualize a contemporary view of mathematics teaching. International Journal of Science and Mathematics Education, 3(3), 351–377.Google Scholar
  15. Markovits, Z., & Even, R. (1999). The decimal point situation: A close look at the use of mathematics-classroom-situations in teacher education. Teaching and Teacher Education, 15(6), 653–665.Google Scholar
  16. Markovitz, Z., & Smith, M. (2008). Cases as tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education (pp. 39–64). Rotterdam: Sense Publishers.Google Scholar
  17. Mason, J. (1991). Epistemological foundations for frameworks which stimulate noticing. In R. Underhill (Ed.), Proceedings of PME-NA 13 (Vol. 2, pp. 36–42). Blacksburg, VA: Division of Curriculum & Instruction, Virginia Polytechnic Institute and State University.Google Scholar
  18. Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267.Google Scholar
  19. Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 277–289.Google Scholar
  20. Michener, E. R. (1978). Understanding understanding mathematics. Cognitive Science, 2, 361–383.Google Scholar
  21. Pang, J. (2011). Case-based pedagogy for prospective teachers to learn how to teach elementary mathematics in Korea. ZDM—The International Journal on Mathematics Education, 43(6–7), 777–789.Google Scholar
  22. Petty, O. S., & Jansson, L. C. (1987). Sequencing examples and nonexamples to facilitate concept attainment. Journal for Research in Mathematics Education, 18, 112–125.Google Scholar
  23. Pimm, D. (1993). From should to could: Reflections on possibilities of mathematics teacher education. For the Learning of Mathematics, 13(2), 27–32.Google Scholar
  24. Roesken-Winter, B. (2013). Capturing mathematics teachers’ professional development in terms of beliefs. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics—Learning from Alan Schoenfeld and Günter Törner (pp. 157–178). Rotterdam: Sense Publishers.Google Scholar
  25. Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69(2), 149–163.Google Scholar
  26. Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.Google Scholar
  27. Santagata, R., & Guarino, J. (2011). Using video to teach future teachers to learn from teaching. ZDM—The International Journal on Mathematics Education, 43(1), 133–145.Google Scholar
  28. Schoenfeld, A. H. (2000). Purposes and methods of research in mathematics education. Notices of the AMS, 47(6), 641–649.Google Scholar
  29. Sherin, M. G., & Russ, R. (2014). Teacher noticing via video: The role of interpretive frames. In B. Calandra & P. Rich (Eds.), Digital video for teacher education: Research and practice (pp. 3–20). New York: Routledge.Google Scholar
  30. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  31. Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.Google Scholar
  32. Tabach, M., Levenson, E., Barkai, R., Tirosh, D., Tsamir, P., & Dreyfus, T. (2010). Secondary school teachers’ awareness of numerical examples as proof. Research in Mathematics Education, 12(2), 117–131.Google Scholar
  33. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.Google Scholar
  34. Tirosh, D., Tsamir, P., Levenson, E., & Barkai, R. (2016). Using cases as materials in professional development. In: Presented at Educating the educatorsinternational approaches to scaling-up professional development in maths and science education’, 7–8 November 2016, Freiburg, Germany.Google Scholar
  35. Tirosh, D., Tsamir, P., & Levenson, E. (2011). Using theories to build kindergarten teachers’ mathematical knowledge for teaching. In K. Ruthven & T. Rowland (Eds.), Mathematical knowledge in teaching (pp. 231–250). Dordrecht: Springer.Google Scholar
  36. Tsamir, P. (2008). Using theories as tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education (pp. 211–234). Rotterdam: Sense Publishers.Google Scholar
  37. Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81–95.Google Scholar
  38. Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM Mathematics Education, 47(3), 497–509.Google Scholar
  39. Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(5), 356–366.Google Scholar
  40. Walen, S. B., & Williams, S. R. (2000). Validating classroom issues: Case method in support of teacher change. Journal of Mathematics Teacher Education, 3(1), 3–26.Google Scholar
  41. Watson, A., & Chick, H. (2011). Qualities of examples in learning and teaching. ZDM—The International Journal on Mathematics Education, 43(2), 283–294.Google Scholar
  42. Zaslavsky, O., & Zodik, I. (2007). Mathematics teachers’ choices of examples that potentially support or impede learning. Research in Mathematics Education, 9(1), 143–155.Google Scholar
  43. Zazkis, R., & Chernoff, E. J. (2008). What makes a counterexample exemplary? Educational Studies in Mathematics, 68(3), 195–208.Google Scholar
  44. Zazkis, R., & Leikin, R. (2007). Generating examples: From pedagogical tool to a research tool. For the Learning of Mathematics, 27(2), 15–21.Google Scholar
  45. Zeichner, K. (2010). Rethinking the connections between campus courses and field experiences in college-and university-based teacher education. Journal of Teacher Education, 61(1–2), 89–99.Google Scholar
  46. Zodik, I., & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69(2), 165–182.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Dina Tirosh
    • 1
  • Pessia Tsamir
    • 1
  • Esther S. Levenson
    • 1
    Email author
  • Ruthi Barkai
    • 1
  1. 1.School of EducationTel Aviv UniversityTel AvivIsrael

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