Abstract
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.
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REFERENCES
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.
Ashlock, R.B. (2002). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Merrill Prentice Hall.
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.
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.
Bloom, B.S. (1956). Taxonomy of educational objectives: The classification of educational goals (Handbook I: Cognitive domain). New York: David McKay Company, Inc.
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.
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.
Buschman, L. (2001). Using student interviews to guide classroom instruction: An action research project. Teaching Children Mathematics, 8(4), 222–227.
Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L. & Empson, S.B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, N.H.: Heinemann.
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: http://www.wcer.wisc.edu/ncisla/publications
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.
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.
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.
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.
Gall, M.D., Borg, W.R. & Gall, J.P. (1996). Educational research: An introduction. White Plains, NY: Longman.
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.
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 MILEWICZ
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.
Lampert, M. (1986). Knowing, doing and teaching multiplication. Cognition and Instruction, 3(4), 305–342.
Leinhardt, G. & Greeno, J. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78(2), 75–95.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Hillsdale, NJ: Lawrence Erlbaum Associates.
Merriam, S.B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass Publishers.
Mewborn, D.S. & Huberty, P.D. (1999). Questioning your way to the standards. Teaching Children Mathematics, 6(4), 226–227, 243–246.
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.
National Council of Teacher of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.
National Council of Teacher of Mathematics (1995). Assessment standards for school mathematics. Reston, VA: Author.
National Council of Teacher of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
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.
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.
Piaget, J. (1929). The child's conception of the world (translated by Joan and Andrew Tomlinson). London: Kegan Paul, Trench, Taubner, & Company.
Posner, G.J. & Gertzog, W.A. (1982). The clinical interview and the measurement of conceptual change. Science Education, 66(2), 195–209.
Ralph, E.G. (1999a). Developing novice teachers' oral-questioning skills. McGill Journal of Education, 34(1), 29–47.
Ralph, E.G. (1999b). Oral-questioning skills of novice teachers:... any questions? Journal of Instructional Psychology, 26(4), 286–296.
Reys, R.E., Suydam, M.N., Lindquist, M.M., & Smith, N.L. (1998). Helping children learn mathematics. Needham Heights, MA: Allyn and Bacon.
Schwartz, S.L. (1996). Hidden messages in teacher talk: Praise and empowerment. Teaching Children Mathematics, 2(7), 396–401.
Stenmark, J.K. (1991). Mathematics assessment: Myths, models, good questions, and practical suggestions. Reston, VA: NCTM.
Stigler, J.W. & Hiebert, J. (1999). The teaching gap. New York: The Free Press.
Stone, J. (1993). Caregiver and teacher language: Responsive or restrictive? Young Children, 48(4), 12–18. LEARNING TO QUESTION 315
Strauss, A. (1987). Qualitative analysis for social scientists. New York: Cambridge University Press.
Wassermann, S. (1991). The art of the question. Childhood Education, 67(4), 257–259.
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Moyer, P.S., Milewicz, E. Learning to Question: Categories of Questioning Used by Preservice Teachers During Diagnostic Mathematics Interviews. Journal of Mathematics Teacher Education 5, 293–315 (2002). https://doi.org/10.1023/A:1021251912775
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DOI: https://doi.org/10.1023/A:1021251912775