Advertisement

Journal of Mathematics Teacher Education

, Volume 14, Issue 6, pp 441–463 | Cite as

Prospective teachers’ learning to provide instructional explanations: how does it look and what might it take?

  • Charalambos Y. Charalambous
  • Heather C. Hill
  • Deborah L. Ball
Article

Abstract

Several studies have documented prospective teachers’ (PSTs) difficulties in offering instructional explanations. However, less is known about PSTs’ learning to provide explanations. To address this gap, we trace changes in the explanations offered by a purposeful sample of PSTs before and after a mathematics content/methods course sequence. Consistent with prior research, our study reveals the limitations in PSTs’ explanations at their entrance to the course sequence. It also documents PSTs’ progress in providing explanations, thus providing existence proof that this practice is learnable. Using evidence from multiple sources, we also propose a component entailed in this learning—learning how to unpack one’s thinking through the use of representations as explanatory tools—and four factors associated with it, including PSTs’ subject-matter knowledge, active and deliberate reflection on practice, productive images for engaging in this work, and productive dispositions about engaging in this practice. We discuss the implications of our findings for teacher education and offer directions for future research.

Keywords

Instructional explanations Mathematics Prospective teachers Teacher education 

References

  1. Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing.Google Scholar
  2. Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 annual meeting of the Canadian mathematics education study group (pp. 3–14). Edmonton, AB: CMESC/GCEDM.Google Scholar
  3. Ball, D. L., Sleep, L., Boerst, T. A., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. The Elementary School Journal, 109(5), 458–474.CrossRefGoogle Scholar
  4. Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194–222.CrossRefGoogle Scholar
  5. Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, CD: National Academy Press.Google Scholar
  6. Charalambous, C. Y. (2008). Prospective teachers’ mathematical knowledge for teaching and their performance in selected teaching practices: Exploring a complex relationship. Unpublished doctoral dissertation, University of Michigan, Ann Arbor.Google Scholar
  7. Charalambous, C. Y. (2010). Mathematical knowledge for teaching and task unfolding: An exploratory study. The Elementary School Journal, 110(3), 247–278.CrossRefGoogle Scholar
  8. Dewey, J. (1906). The child and the curriculum. Chicago: The University of Chicago.Google Scholar
  9. Duffy, G. G., Roehler, L. R., Meloth, M. S., & Vavrus, L. G. (1986). Conceptualizing instructional explanation. Teaching and Teacher Education, 2, 197–214.CrossRefGoogle Scholar
  10. Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15, 273–289.CrossRefGoogle Scholar
  11. Grossman, P., & McDonald, M. (2008). Back to the future: Directions for research in teaching and teacher education. American Educational Research Journal, 45, 184–205.CrossRefGoogle Scholar
  12. Inoue, N. (2009). Rehearsing to teach: Content-specific deconstruction of instructional explanations in pre-service teacher training. Journal of Education for Teaching, 35(1), 47–60.CrossRefGoogle Scholar
  13. Izsák, A., Tillema, E., & Tunç-Pekkan, Z. (2008). Teaching and learning fraction addition on number line. Journal for Research in Mathematics Education, 39, 33–62.Google Scholar
  14. Kinach, B. M. (2002). Understanding and learning-to-explain by representing mathematics: Epistemological dilemmas facing teacher educators in the secondary mathematics “methods” course. Journal of Mathematics Teacher Education, 5, 153–186.CrossRefGoogle Scholar
  15. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.Google Scholar
  16. Lampert, M. (2010). Learning teaching in, from, and for practice: What do we mean? Journal of Teacher Education, 60(1–2), 21–34.CrossRefGoogle Scholar
  17. Larreamendy-Joerns, J., & Muñoz, T. (2010). Learning, identity, and instructional explanations. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 23–40). New York: Springer.CrossRefGoogle Scholar
  18. Leinhardt, G. (1987). Development of an expert explanation: An analysis of a sequence of subtraction lessons. Cognition and Instruction, 4, 225–282.CrossRefGoogle Scholar
  19. Leinhardt, G. (1989). Math lessons: A contrast of novice and expert competence. Journal for Research in Mathematics Education, 20, 52–75.CrossRefGoogle Scholar
  20. Leinhardt, G. (2001). Instructional explanations: A commonplace for teaching and location for contrast. In V. Richardson (Ed.), Handbook for research on teaching (4th ed., pp. 333–357). Washington, DC: American Educational Research Association.Google Scholar
  21. Leinhardt, G. (2010). Introduction: Explaining instructional explanations. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 1–5). NY: Springer.CrossRefGoogle Scholar
  22. Leinhardt, G., Putnam, R. T., Stein, M. K., & Baxter, J. (1991). Where subject knowledge matters. In J. Brophy (Ed.), Advances in research on teaching (Vol. 2, pp. 87–113). London: JAI Press Inc.Google Scholar
  23. Leinhardt, G., & Steele, M. D. (2005). Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction, 23, 87–163.CrossRefGoogle Scholar
  24. Lloyd, G. M., & Wilson, M. R. (1998). Supporting innovation: The impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29, 248–274.CrossRefGoogle Scholar
  25. Lo, J., Grant, T., & Flowers, J. (2004). Developing mathematics justification: The case of prospective elementary school teachers. In D. McDougall & J. Ross (Eds.), Proceedings of the twenty-sixth annual meeting of the north American chapter of the international group for the psychology of mathematics education (Vol. 3, pp. 1159–1166). Toronto: University of Toronto.Google Scholar
  26. Lubinksi, C. A., Thomason, R., & Fox, T. (1998). Learning to make sense of division of fractions: One K-8 preservice teacher’s perspective. School Science and Mathematics, 98, 247–253.CrossRefGoogle Scholar
  27. Martin, J. R. (1970). Explaining, understanding, and teaching. New York: McGraw-Hill.Google Scholar
  28. Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage Publications.Google Scholar
  29. Schoenfeld, A. H. (2010). How and why do teachers explain things the way they do? In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 83–106). New York: Springer.CrossRefGoogle Scholar
  30. Schwab, J. J. (1978). Education and the structure of the disciplines. In I. Westbury & N. J. Wilfolk (Eds.), Science, curriculum, and liberal education: Selected essays (pp. 229–272). Chicago: The University of Chicago Press.Google Scholar
  31. Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston, MA: Houghton-Mifflin.Google Scholar
  32. Simon, M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 31, 5–25.Google Scholar
  33. Stecher, B., Vi-Nhuan, L., Hamilton, L., Ryan, G., Robyn, A., & Lockwood, J. R. (2006). Using structured classroom vignettes to measure instructional practices in mathematics. Educational Evaluation and Policy Analysis, 28, 101–130.CrossRefGoogle Scholar
  34. Stein, M. K., Baxter, J. A., & Leinhardt, G. (1990). Subject-matter knowledge and elementary instruction: A case from functions and graphing. American Educational Research Journal, 27, 639–663.Google Scholar
  35. Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks, CA: Sage.Google Scholar
  36. Thanheiser, E. (2009). Preservice elementary school teachers’ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40, 252–281.Google Scholar
  37. Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, part I: A teacher’s struggle. Journal for Research in Mathematics Education, 25, 279–303.CrossRefGoogle Scholar
  38. Thompson, A. G., & Thompson, P. W. (1996). Talking about rates conceptually, part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27, 2–24.CrossRefGoogle Scholar
  39. Weiss, I. R., & Parsley, J. D. (2004). What is high-quality instruction? Educational Leadership, 65(1), 24–28.Google Scholar
  40. Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Charalambos Y. Charalambous
    • 1
  • Heather C. Hill
    • 2
  • Deborah L. Ball
    • 3
  1. 1.Department of EducationUniversity of CyprusNicosiaCyprus
  2. 2.Harvard Graduate School of EducationCambridgeUSA
  3. 3.School of EducationAnn ArborUSA

Personalised recommendations