Skip to main content
Log in

Extending students’ mathematical thinking during whole-group discussions

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

Abstract

Studies show that extending students’ mathematical thinking during whole-group discussions is a challenging undertaking. To better understand what extending student thinking looks like and how teachers’ mathematical knowledge for teaching (MKT) supports teachers in their efforts to extend student thinking, the teaching of six experienced elementary school teachers was explored. During group discussions, all six teachers created opportunities for extending student thinking about important mathematical ideas and solution methods. Findings on the nature of these episodes include identification of individual instructional actions and the ways in which teachers’ MKT was connected to these actions.

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.

Similar content being viewed by others

References

  • Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373–397.

    Article  Google Scholar 

  • Ball, D. L., & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In D. Phillips (Ed.), Yearbook of the national society for the study of education: Constructivism in education (pp. 193–224). Chicago: University of Chicago Press.

    Google Scholar 

  • Ball, D. L., Bass, H., & Hill, H. C. (2004). Knowing and using mathematical knowledge in teaching: Learning what matters. Paper presented at the 12th annual conference of the Southern African association for research in mathematics, science, and technology education, Cape Town, South Africa.

  • Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching. New York: Macmillan.

    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 

  • Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148–170.

    Article  Google Scholar 

  • Grant, T. J., Kline, K., Crumbaugh, C., Kim, O. K., & Cengiz, N. (2009). How can curriculum materials support teachers in pursuing student thinking during whole-group discussions? In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work connecting curriculum materials and classroom instruction (pp. 103–117). New York, NY: Routledge.

    Google Scholar 

  • Heaton, R. M. (2000). Teaching mathematics to the new standards: Relearning the dance. New York: Teachers College Press.

    Google Scholar 

  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on student learning. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Hill, H., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., et al. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26, 430–511.

    Article  Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11–30.

    Article  Google Scholar 

  • Lampert, M. (1990). When the problem is not the questions and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.

    Google Scholar 

  • Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Research Ware, I. (2007). HyperResearch: Qualitative analysis tool (version 2.8). Randolph, MA: ResearchWare, Inc.

    Google Scholar 

  • Russell, S. J. (2007). The case of investigations in number, data, and space. In C. R. Hirsch (Ed.), Perspectives on design and development of school mathematics curricula (pp. 23–35). Reston, VA: NCTM.

    Google Scholar 

  • Schifter, D., & Fosnot, C. T. (1993). Reconstructing mathematics education. New York: Teacher College Press.

    Google Scholar 

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

    Google Scholar 

  • Stein, M. K., Grover, B. W., & Hanningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.

    Google Scholar 

  • Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). New York, NY: Teachers College Press.

    Google Scholar 

  • TERC. (1998). Investigations in number, data, and space. Menlo Park, CA: Dale Seymour.

    Google Scholar 

  • TERC. (2008). Investigations in number, data, and space (2nd ed.). Glenview, IL: Pearson.

    Google Scholar 

  • Wood, T. (1999). Creating a context for argument in mathematics class. Journal for Research in Mathematics Education, 30(2), 171–191.

    Article  Google Scholar 

  • Wood, T., Cobb, P., & Yackel, E. (1991). Change in teaching mathematics: A case study. American Educational Research Journal, 28(3), 587–616.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nesrin Cengiz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cengiz, N., Kline, K. & Grant, T.J. Extending students’ mathematical thinking during whole-group discussions. J Math Teacher Educ 14, 355–374 (2011). https://doi.org/10.1007/s10857-011-9179-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-011-9179-7

Keywords

Navigation