Skip to main content
Log in

Levels of introspection in mathematics instruction

  • Article
  • Published:
Mathematics Education Research Journal Aims and scope Submit manuscript

Abstract

Case studies of five teachers who participated in a three-year staff-development project formed the basis for this grounded study which focused on primary factors that dominated teachers’ instructional decision making. As the analysis progressed, qualitatively different levels of introspection, rank ordered by the degree to which children’s thinking was utilised in the decision-making process, were identified. These distinct levels were robust in that they consistently reappeared across all coded categories of decisions made by these teachers. Moreover, these levels were positively correlated with the quality of students’ thinking based on what they said or did during instruction (ρ = .60). Further, when all project teachers were categorisation the basis of their dominant level of introspection, a positive correlation was found between these levels and their belief scores on a mathematics teaching and learning survey (ρ = .61).

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

  • Australian Education Council. (1990).A national statement on mathematics for Australian schools. Carton, Victoria: Author.

    Google Scholar 

  • Bogdan, R. C., & Biklen, S. K. (1992).Qualitative research for education: An introduction to theory and methods. Boston: Allyn and Bacon.

    Google Scholar 

  • Carpenter, T. P., & Peterson, P. L. (Eds.). (1988). Learning mathematics from instruction (special issue).Educational Psychologist.

  • 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), 499–532.

    Google Scholar 

  • Clark, C. M., & Peterson, P. L. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.),Handbook of research on teaching (3rd ed., pp. 255–296). New York: Macmillan.

    Google Scholar 

  • Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactionalanalysis.American Educational Research Journal, 29(3), 573–604.

    Google Scholar 

  • Department of Education and Science and Welsh Office (1991).National curriculum: Mathematics for Ages 5–16. London: Author.

    Google Scholar 

  • Dougherty, B. J. (1990). Influences of teacher cognitive/conceptual levels on problem-solving instruction. In G. Booker, P. Cobb & T. N. de Mendicuti (Eds.)Proceedings of the Fourteenth International Conference for the Psychology of Mathematics Education (pp. 119–126). Oaxtepec, Mexico: International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.),Mathematics teaching: The state of the art (pp. 249–253). New York: Falmer Press.

    Google Scholar 

  • Fennema, E., Carpenter, T. P., & Peterson, P. L. (1989). Teachers’ decision making and cognitively guided instruction: A new paradigm for curriculum development. In N. F. Ellerton & M. A. (Ken) Clements (Eds.),School mathematics: The challenge to change (pp. 174–187). Geelong, Victoria: Deakin University.

    Google Scholar 

  • Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.),Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan.

    Google Scholar 

  • Fisher, C. W., Berliner, D. C., Filby, N. N., Marliave, R., Cahn, L. S., & Dishaw, M. M. (1980). Teaching behaviors, academic learning time, and student achievement: An overview. In C. Denham & A. Lieberman (Eds.),Time to learn (pp. 7–32). Washington, D. C.: United States Department of Education.

    Google Scholar 

  • Kuhs, T. M. & Ball, D. L. (1986).Approaches to teaching mathematics: Mapping the domains of knowledge, skills, and dispositions. East Lansing: Michigan State University, Center on Teacher Education.

    Google Scholar 

  • Leinhart, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge.Journal of Education Psychology, 77(3), 247–217.

    Article  Google Scholar 

  • Leinhart, G., Putman, R. T., Stein, M. K., & Baxter, J. (1991). Where subject knowledge matters. In J. B. Brophy (Ed.),Advances in research on teaching: Teachers’ subject matter knowledge and classroom instruction (Vol. 2, pp. 87–113). Greenwich, CT: JAI Press.

    Google Scholar 

  • Lubinski, C. A. (1990). Cognitively-guided mathematics instruction and teachers’ decision making (Doctoral dissertation, University of Wisconsin-Madison, 1989).Dissertation Abstracts International, 50, 09A, p. 2773. (University Microfilms No. DA 8917661).

    Google Scholar 

  • Miles, M. B. & Huberman, A.M. (1984).Qualitative data analysis: A sourcebook of new methods. Beverly Hills, CA: Sage Publications.

    Google Scholar 

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

    Google Scholar 

  • National Council of Teachers of Mathematics. (1991).Professional standards for teaching mathematics. Reston, VA: Author.

    Google Scholar 

  • National Research Council. (1989).Everybody counts: A report to the nation on the future of mathematics education. Washington, DC.: National Academy Press.

    Google Scholar 

  • Nesher, P. (1986). Learning mathematics: A cognitive perspective.American Psychologist, 41 (10), 1114–1122.

    Article  Google Scholar 

  • Parker, W. C. (1984). Developing teachers’ decision making.Journal of Experimental Education.52(4), 220–226.

    Google Scholar 

  • Peterson, P. L., Fennema, E., Carpenter, T. P., & Loef, M. (1989). Teachers’ pedagogical content beliefs in mathematics.Cognition and Instruction.6(1), 1–40.

    Article  Google Scholar 

  • Shavelson, R. J., & Stern, P. (1981). Research on teachers’ pedagogical thoughts, judgments, decisions, and behavior.Review of Educational Research.51(4), 455–498.

    Google Scholar 

  • Shulman, L. S. (1986). Paradigms and research programs in the study of teaching: A contemporary perspective. In M. C. Wittrock (Ed.),Handbook of research on teaching (pp. 3–36). New York: Macmillan.

    Google Scholar 

  • Skemp, R. R. (1972).The psychology of learning mathematics. New York: Penguin.

    Google Scholar 

  • Solas, J. (1992). Investigating teacher and student thinking about the process of teaching and learning using autobiography and repertory grid.Review of Educational Research, 62(2), 205–225.

    Google Scholar 

  • Stodolsky, S. S. (1983).Classroom activity structures in the fifth grade. (ERIC Document Reproduction Service No. ED 242 212).

  • Strauss, A. L. (1987).Qualitative analysis for social scientists. New York: Cambridge University Press.

    Book  Google Scholar 

  • Strauss, A. L., & Corbin, J. (1990).Basics of qualitative research: Grounded theory procedures and techniques. Newberry Park, CA: Sage.

    Google Scholar 

  • Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics teaching to instructional practice.Educational Studies in Mathematics, 15, 105–127.

    Article  Google Scholar 

  • Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.),Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.

    Google Scholar 

  • Yackel, E., Cobb, P., & Wood, T. (1992). Instructional development and assessment from a socioconstructivist perspective. In G. Leder, (Ed.)Assessment and learning of mathematics (pp. 63–82). Victoria, Australia: Australian Council for Educational Research.

    Google Scholar 

  • Zahorik, J. A. (1975). Teachers’ planning models.Educational Leadership, 33, 134–139.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lubinski, C.A., Thornton, C.A., Heyl, B.S. et al. Levels of introspection in mathematics instruction. Math Ed Res J 6, 113–130 (1994). https://doi.org/10.1007/BF03217267

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03217267

Keywords

Navigation