Skip to main content
SpringerLink
Log in

Teachers’ responses to an investigative mathematics syllabus: Their goals and practices

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

Abstract

Despite attempts to encourage teachers to adopt investigative teaching behaviours, there is strong evidence of the resilience of teacher-centred school mathematics teaching. This study uses interpretive research methods to explore teachers’ practices and relate these to their goals. Analysis of case studies indicates that syllabus documents have influenced teachers’ choices of teaching strategies. Most teachers had calculation-based goals for less able students and conceptual goals for more able students. Three distinct teaching strategies were identified and described. The relationships between teachers’ goals, beliefs, and practices can guide the construction of teacher programmes that focus on student construction of knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allen, F. B. (1998).Repairing school mathematics in the US. Retrieved January 7, 1999, from the Mathematically Correct Web site: http://mathematicallycorrect.com/report.htm

  • Anderson, P. (1994).Years 1–7 mathematics syllabus support document: A content core for a school-based program in Queensland primary schools. Brisbane: Queensland Department of Education.

    Google Scholar 

  • Atweh, B., & Cooper, T. (1995). The construction of gender, social class and mathematics in the classroom.Educational Studies in Mathematics, 28, 293–310.

    Article  Google Scholar 

  • Australian Association of Mathematics Teachers. (1996).Statement on the use of calculators and computers for mathematics in Australian schools. Adelaide: Australian Association of Mathematics Teachers Inc.

    Google Scholar 

  • Australian Education Council (AEC). (1990).A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.

    Google Scholar 

  • Barnes, M. (1991).Investigating change: An introduction to calculus for Australian schools. Melbourne: Curriculum Corporation.

    Google Scholar 

  • Barnes, M., Clarke, D., & Stephens, M. (1996). The impact of external assessment on teaching practice: Constraints on change in the classroom. In P. Clarkson (Ed.),Technology in mathematics education (Proceedings of the 18th annual conference of the Mathematics Education Research Group of Australasia, pp. 65–71). Melbourne: MERGA.

    Google Scholar 

  • Board of Senior Secondary School Studies (BSSSS). (1992).Senior Syllabus in Mathematics B. Brisbane: Author.

    Google Scholar 

  • Board of Studies NSW. (1997).Mathematics 2/3 Unit Years 11–12. Sydney: Author.

    Google Scholar 

  • Brousseau, G. (1984). The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics. In H.-G. Steiner (Ed.),Theory of Mathematics Education (pp. 110–119). Occasional Paper 54. Bielefeld, Geremany: University of Bielefeld, Institut fur Didaktik der Mathematik.

    Google Scholar 

  • Carrol, W. M. (1997). Results of third-grade students in a reform curriculum on the Illinios State Mathematics Test.Journal for Research in Mathematics Education, 28(2), 237–242.

    Article  Google Scholar 

  • Clarke, D. M. (1999). Classroom reform five years down the track: The experiences of two teachers.Mathematics Education Research Journal, 11(1), 4–24.

    Article  Google Scholar 

  • Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education.Educational Psychologist, 23(2), 87–101.

    Article  Google Scholar 

  • Cobb, P. (1989). Experiential, cognitive and anthropological perspective in mathematics education.For the Learning of Mathematics, 9(2), 32–42.

    Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education.Journal for Research in Mathematics Education, 23(1), 2–33.

    Article  Google Scholar 

  • Cooper, G. (1998).Research into cognitive load theory and instructional design at UNSW. Retrieved August 18, 2001, from http://www.arts.unsw.edu.au/education/CLT_NET_Aug_97.HTML

  • Crawford, K. (1996). Vygotskian approaches in human development in the information era.Educational Studies in Mathematics, 31(1), 63–93.

    Article  Google Scholar 

  • Cuban, L. (1984).How teachers taught: Constancy and change in American classrooms, 1890–1980. New York: Longman.

    Google Scholar 

  • Curriculum Council. (1998).Curriculum framework for kindergarten to Year 12 education in Western Australia. Osborne Park, WA: Author.

    Google Scholar 

  • Denzin, N., & Lincoln, Y. (1994). Part V: The art of interpretation, evaluation, and presentation. In N. K. Denzin, & Y. S. Lincoln (Eds.),Handbook of qualitative research (pp. 479–483). Thousand Oaks, CA: Sage.

    Google Scholar 

  • Ernest, P. (1989). What’s the use of LOGO? In P. Ernest (Ed.),Mathematics teaching: “The state of the art” (pp. 33–44). London: Falmer.

    Google Scholar 

  • Ernest, P. (1991).The philosophy of mathematics education. London: Falmer.

    Google Scholar 

  • Ernest, P. (1996).The nature of mathematics and teaching. Retrieved November 24, 1998, from http://www.ex.ac.uk/~PErnest/pome/pompart7.htm

  • Fontana, A., & Frey, J. H. (1994). Interviewing the art of science. In N. K. Denzin, & Y. Lincoln (Eds.),Handbook of qualitative research (pp. 361–376). Thousand Oaks, CA: Sage.

    Google Scholar 

  • Gregg, J. (1995). The tensions and contradictions of the school mathematics tradition.Journal for Research in Mathematics Education, 26(5), 442–466.

    Article  Google Scholar 

  • Guba, E., & Lincoln, Y. (1989).Fourth generation evaluation. London: Sage.

    Google Scholar 

  • Kagan, D. M. (1992). Implications of research on teacher belief.Educational Psychologist, 27(1), 65–90.

    Article  Google Scholar 

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

    Google Scholar 

  • Lesh, R., & Kelly, A. E. (1997). Teachers’ evolving conceptions of one-to-one tutoring: A three-tiered teaching experiment.Journal for Research in Mathematics Education, 28(4), 398–427.

    Article  Google Scholar 

  • Lo, J., Wheatley, G., & Smith, A. (1994). The participation, beliefs and development of arithmetic meaning of a third-grade student in mathematics class discussions.Journal for Research in Mathematics Education, 25(1), 30–49.

    Article  Google Scholar 

  • Lowe, I., Johnston, J., Kissane, B., & Willis, B. (1993).Access to algebra. Melbourne: Curriculum Corporation.

    Google Scholar 

  • Maykut, P., & Morehouse, R. (1994).Beginning qualitative research: A philosophical and practical guide. London: Falmer.

    Google Scholar 

  • McDonald, H., & Ingvarson, L. (1995).Free at last? Teachers, computers and independent learning. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA. (ERIC Document Reproduction Service No. ED 389 278).

  • McRobbie, C., & Tobin, K. (1995). Restraints to reform: The congruence of teacher and student actions in a chemistry classroom.Journal of Research in Science Teaching, 32(4), 373–385.

    Article  Google Scholar 

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

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics: A vision for school mathematics. Retrieved May 23, 2001, from NCTM Web site: http://standards.nctm.org/document/chapter1/index.htm

  • Neyland, J. (1996).Teachers’ knowledge: The starting point for a critical analysis of mathematics teaching. Retrieved November 24, 1997, from http://www.ex.ac.uk/~PErnes/pome/pompart4.htm

  • Perry, B., Howard, P., & Tracey, D. (1999). Head mathematics teachers’ beliefs about the learning and teaching of mathematics.Mathematics Education Research Journal, 11(1), 39–53.

    Article  Google Scholar 

  • Queensland School Curriculum Council. (2000).Draft syllabus P-10. Brisbane: Author.

    Google Scholar 

  • Schwandt, T. (1994). Constructivism, interpretist approaches to human inquiry. In N. K. Denzin, & Y. S. Lincoln (Eds.),Handbook of qualitative research (pp. 118–123). Thousand Oaks, CA: Sage.

    Google Scholar 

  • Senger, E. S. (1999). Reflective reform in mathematics: The recursive nature of teacher change.Educational Studies in Mathematics, 37, 199–221.

    Article  Google Scholar 

  • Senior Secondary Assessment Board of South Australia. (2000).Mathematics 2. Stage 2 Detailed Syllabus Statement. Adelaide: Mathematics Board Field of Study.

    Google Scholar 

  • Skemp, R. (1978). Relational understanding and instrumental understanding.Mathematics Teaching, 77, 20–26.

    Google Scholar 

  • Stenhouse, L. (1990). Case study methods. In H. J. Walberg, & G. D. Haertel (Eds.),The international encyclopedia of educational evaluation (pp. 644–649). Oxford, UK: Pergamon.

    Google Scholar 

  • Tall, D. O., & Thomas, M. O. J. (1991). Encouraging versatile thinking in algebra using the computer,Educational Studies in Mathematics, 22, 125–147.

    Article  Google Scholar 

  • Thompson, A., Phillip, R., Thompson, P., & Boyd, B. (1994). Calculational and conceptual orientations in teaching mathematics. In D. Aichele, & A. Coxford (Eds.),Professional development for teachers of mathematics (pp. 79–92). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Vygotsky, L. S. (1987).The collected works of L. S. Vygotsky (Volume 1). New York: Plenum.

    Google Scholar 

  • Wasley, B., Manche, D., & Winter, R. (1996).Mathematics Year 10 for Queensland. Melbourne: Oxford University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Science and Technology Education, Queensland University of Technology, Q 4059, Kelvin Grove

    Stephen Norton, Campbell J. McRobbie & Tom J. Cooper

Authors
  1. Stephen Norton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Campbell J. McRobbie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tom J. Cooper
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Norton, S., McRobbie, C.J. & Cooper, T.J. Teachers’ responses to an investigative mathematics syllabus: Their goals and practices. Math Ed Res J 14, 37–59 (2002). https://doi.org/10.1007/BF03217115

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03217115

Keywords

Search

Navigation