Journal of Mathematics Teacher Education

, Volume 5, Issue 4, pp 293–315 | Cite as

Learning to Question: Categories of Questioning Used by Preservice Teachers During Diagnostic Mathematics Interviews

  • Patricia S. Moyer
  • Elizabeth Milewicz


Developing appropriate questioning techniquesis an important part of mathematics teachingand assessment. This study examined thequestioning strategies used by 48 preserviceteachers during one-on-one diagnosticmathematics interviews with children. Eachparticipant conducted an audiotaped interviewwith one child, followed by an analysis andreflection of the interview. Data wereanalyzed to develop general categories ofquestions used by the preservice teachers. These categories included: 1) checklisting, 2) instructing rather thanassessing, and 3) probing and follow-upquestions. The analyses and reflectionscompleted by preservice teachers indicated thatusing the diagnostic interview format allowedthem to recognize and reflect on effectivequestioning techniques. Through an examinationof these categories of questions, we offersuggestions for teaching the skill ofmathematics questioning in preservice teachereducation courses.

interviewing mathematics questions preservice teacher education questioning techniques 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams, N.H. (1994, March). Ask, don't tell: The value of asking young children questions. Paper presented at the annual conference of the Association for Childhood Education International.Google Scholar
  2. Ashlock, R.B. (2002). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Merrill Prentice Hall.Google Scholar
  3. Ball, D. (1991). Research on teaching mathematics: Making subject matter knowledge part of the equation. In J. Brophy (Ed.), Advances in research on teaching, Vol. 2 (pp. 1–41). Greenwich: JAI Press.Google Scholar
  4. Baroody, A.J. & Ginsburg, H.P. (1990). Children's mathematical learning: A cognitive view. In R.B. Davis, C.A. Maher & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 51–64). Reston, VA: NCTM.Google Scholar
  5. Bloom, B.S. (1956). Taxonomy of educational objectives: The classification of educational goals (Handbook I: Cognitive domain). New York: David McKay Company, Inc.Google Scholar
  6. Bowman, A.H., Bright, G.W. & Vacc, N.N. (1998, April). Teachers' beliefs across the first two years of implementation of cognitively guided instruction. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.Google Scholar
  7. Bright, G.W. & Vacc, N.N. (1994, April). Changes in undergraduate preservice teachers' beliefs during an elementary teacher-certification program. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  8. Buschman, L. (2001). Using student interviews to guide classroom instruction: An action research project. Teaching Children Mathematics, 8(4), 222–227.Google Scholar
  9. Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L. & Empson, S.B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, N.H.: Heinemann.Google Scholar
  10. Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L., & Empson, S.B. (2000, September). Cognitively guided instruction: A research-based teacher professional development program for elementary school mathematics. National Center for Improving Student Learning and Achievement in Mathematics and Science, Report No. 003. Madison, WI: Wisconsin Centre for Education Research, The University of Wisconsin-Madison. Available: Scholar
  11. Carpenter, T.P., Fennema, E., Peterson, P.L., Chiang, C. & Loef, M. (1989). Using children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499–531.Google Scholar
  12. Fennema, E. & Carpenter, T.P. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434.Google Scholar
  13. Fennema, E., Carpenter, T.P., Franke, M.L. & Carey, D.A. (1993). Learning to use children's mathematics thinking: A case study. In C. Maher & R. Davis (Eds.), schools, mathematics, and the world of reality (pp. 93–118). Needham Heights, MA: Allyn Bacon.Google Scholar
  14. Fennema, E., Franke, M.L., Carpenter, T.P. & Carey, D.A. (1993). Using children's mathematical knowledge in instruction. American Educational Research Journal, 30, 555–585.Google Scholar
  15. Gall, M.D., Borg, W.R. & Gall, J.P. (1996). Educational research: An introduction. White Plains, NY: Longman.Google Scholar
  16. Huinker, D.M. (1993). Interview: A window to students' conceptual knowledge of the operations. In N.L. Webb (Ed.), Assessment in the mathematics classroom (pp. 80–86). Reston, VA: NCTM.Google Scholar
  17. Kamii, C. & DeVries, R. (1978). Physical knowledge in preschool education: Implications of Piaget's theory. Englewood Cliffs, NJ: Prentice Hall. 314 PATRICIA S. MOYER AND ELIZABETH MILEWICZGoogle Scholar
  18. Kamii, C. & Warrington, M.A. (1999). Teaching fractions: Fostering children's own reasoning. In L. V. Stiff & F.R. Curcio (Eds.), Developing mathematical reasoning grades K-12: 1999 Yearbook (pp. 82–92). Reston, VA: NCTM.Google Scholar
  19. Lampert, M. (1986). Knowing, doing and teaching multiplication. Cognition and Instruction, 3(4), 305–342.Google Scholar
  20. Leinhardt, G. & Greeno, J. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78(2), 75–95.Google Scholar
  21. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  22. Merriam, S.B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass Publishers.Google Scholar
  23. Mewborn, D.S. & Huberty, P.D. (1999). Questioning your way to the standards. Teaching Children Mathematics, 6(4), 226–227, 243–246.Google Scholar
  24. Moyer, P.S. & Moody, V.R. (1998). Shifting beliefs: Preservice teacher's reflections on assessing students' mathematical ideas. In S.B. Berenson & K.R. Dawkins (Eds.), Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education, Vol. 2 (pp. 613–619). Columbus,OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.Google Scholar
  25. National Council of Teacher of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.Google Scholar
  26. National Council of Teacher of Mathematics (1995). Assessment standards for school mathematics. Reston, VA: Author.Google Scholar
  27. National Council of Teacher of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  28. Nilssen, V., Gudmundsdottir, S. & Wangsmo-Cappelen, V. (1995, April). Unexpected answers: Case study of a student teacher derailing in a math lesson. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.Google Scholar
  29. Piaget, J. (1926). The language and thought of the child (Preface by E. Claparede; translated by Marjorie and Ruth Gabain). London: Routledge and Kegan Paul.Google Scholar
  30. Piaget, J. (1929). The child's conception of the world (translated by Joan and Andrew Tomlinson). London: Kegan Paul, Trench, Taubner, & Company.Google Scholar
  31. Posner, G.J. & Gertzog, W.A. (1982). The clinical interview and the measurement of conceptual change. Science Education, 66(2), 195–209.Google Scholar
  32. Ralph, E.G. (1999a). Developing novice teachers' oral-questioning skills. McGill Journal of Education, 34(1), 29–47.Google Scholar
  33. Ralph, E.G. (1999b). Oral-questioning skills of novice teachers:... any questions? Journal of Instructional Psychology, 26(4), 286–296.Google Scholar
  34. Reys, R.E., Suydam, M.N., Lindquist, M.M., & Smith, N.L. (1998). Helping children learn mathematics. Needham Heights, MA: Allyn and Bacon.Google Scholar
  35. Schwartz, S.L. (1996). Hidden messages in teacher talk: Praise and empowerment. Teaching Children Mathematics, 2(7), 396–401.Google Scholar
  36. Stenmark, J.K. (1991). Mathematics assessment: Myths, models, good questions, and practical suggestions. Reston, VA: NCTM.Google Scholar
  37. Stigler, J.W. & Hiebert, J. (1999). The teaching gap. New York: The Free Press.Google Scholar
  38. Stone, J. (1993). Caregiver and teacher language: Responsive or restrictive? Young Children, 48(4), 12–18. LEARNING TO QUESTION 315Google Scholar
  39. Strauss, A. (1987). Qualitative analysis for social scientists. New York: Cambridge University Press.Google Scholar
  40. Wassermann, S. (1991). The art of the question. Childhood Education, 67(4), 257–259.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Patricia S. Moyer
    • 1
  • Elizabeth Milewicz
    • 1
  1. 1.George Mason UniversityCentrevilleUSA

Personalised recommendations