Skip to main content
Log in

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

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

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.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

  • 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.

    Article  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 

  • Bruner, J. S. (1968). Towards a theory of instruction. New York: Norton.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Goldenberg, P., & Mason, J. (2008). Shedding light on and with example spaces. Educational Studies in Mathematics, 69(2), 183–194.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Klausmeier, H. J. (1992). Concept learning and concept teaching. Educational Psychologist, 27(3), 267–286.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

  • 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.

    Article  Google Scholar 

  • Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 277–289.

    Article  Google Scholar 

  • Michener, E. R. (1978). Understanding understanding mathematics. Cognitive Science, 2, 361–383.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Petty, O. S., & Jansson, L. C. (1987). Sequencing examples and nonexamples to facilitate concept attainment. Journal for Research in Mathematics Education, 18, 112–125.

    Article  Google Scholar 

  • 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 

  • 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.

  • Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69(2), 149–163.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Schoenfeld, A. H. (2000). Purposes and methods of research in mathematics education. Notices of the AMS, 47(6), 641–649.

    Google Scholar 

  • 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 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Chapter  Google Scholar 

  • 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 

  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81–95.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(5), 356–366.

  • 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.

    Article  Google Scholar 

  • Watson, A., & Chick, H. (2011). Qualities of examples in learning and teaching. ZDM—The International Journal on Mathematics Education, 43(2), 283–294.

    Article  Google Scholar 

  • Zaslavsky, O., & Zodik, I. (2007). Mathematics teachers’ choices of examples that potentially support or impede learning. Research in Mathematics Education, 9(1), 143–155.

    Article  Google Scholar 

  • Zazkis, R., & Chernoff, E. J. (2008). What makes a counterexample exemplary? Educational Studies in Mathematics, 68(3), 195–208.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Esther S. Levenson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tirosh, D., Tsamir, P., Levenson, E.S. et al. Using theories and research to analyze a case: learning about example use. J Math Teacher Educ 22, 205–225 (2019). https://doi.org/10.1007/s10857-017-9386-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-017-9386-y

Keywords

Navigation