Educational Studies in Mathematics

, Volume 79, Issue 1, pp 127–147 | Cite as

Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice

Article

Abstract

There is broad acceptance that mathematics teachers’ beliefs about the nature of mathematics influence the ways in which they teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the mathematical activity of mathematicians. This paper presents case studies of two secondary mathematics teachers, one experienced and the other relatively new to teaching, and considers their beliefs about the nature of mathematics, as a discipline and as a school subject. Possible origins and future developments of the structures of their belief systems are discussed along with implications of such structures for their practice. It is suggested that beliefs about mathematics can usefully be considered in terms of a matrix that accommodates the possibility of differing views of school mathematics and the discipline.

Keywords

Teacher beliefs Nature of mathematics School mathematics Belief systems 

References

  1. Ball, D. L. (1990). Breaking with experience in learning to teach mathematics: The role of a preservice methods course. For the Learning of Mathematics, 10(2), 10–16.Google Scholar
  2. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it so special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  3. Beswick, K. (2003). Accounting for the contextual nature of teachers' beliefs in considering their relationship to practice. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics education research: Innovation, networking, opportunity: Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 152–159). Melbourne: Deakin University.Google Scholar
  4. Beswick, K. (2004). The impact of teachers' perceptions of student characteristics on the enactment of their beliefs. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 111–118). Bergen: Bergen University College.Google Scholar
  5. Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68.CrossRefGoogle Scholar
  6. Beswick, K. (2007). Teachers' beliefs that matter in secondary mathematics classrooms. Educational Studies in Mathematics, 65(1), 95–120.CrossRefGoogle Scholar
  7. Beswick, K. (2009). School mathematics and mathematicians’ mathematics: Teachers’ beliefs about the nature of mathematics. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33 rd annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 153–160). Thessaloniki, Greece: IGPME.Google Scholar
  8. Beswick, K. (2011). Knowledge/beliefs and their relationship to emotion. In K. Kislenko (Ed.), Current state of research on mathematical beliefs XVI: Proceedings of the MAVI-16 conference June 26–29, 2010 (pp. 43–59). Tallinn, Estonia: Institute of Mathematics and Natural Sciences, Tallinn University.Google Scholar
  9. Burton, L. (2002). Recognising commonalities and reconciling differences in mathematics education. Educational Studies in Mathematics, 50, 157–175.CrossRefGoogle Scholar
  10. Callingham, R., & Griffin, P. (2001). Beyond the basics: Improving indigenous students' numeracy. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and Beyond: Proceedings of the 24th annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 122–129). Sydney: MERGA.Google Scholar
  11. Cooney, T. J., & Shealy, B. E. (1997). On understanding the structure of teachers' beliefs and their relationship to change. In E. Fennema & B. Nelson (Eds.), Mathematics teachers in transition (pp. 87–109). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  12. 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.Google Scholar
  13. Ernest, P. (1999). Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives. Educational Studies in Mathematics, 38, 67–83.CrossRefGoogle Scholar
  14. Frykholm, J. A. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105.CrossRefGoogle Scholar
  15. Green, T. F. (1971). The activities of teaching. New York: McGraw-Hill.Google Scholar
  16. Guba, E. G., & Lincoln, Y. S. (1989). Fourth generation evaluation. Newbury Park, California: Sage.Google Scholar
  17. Howard, P., Perry, B., & Lindsay, M. (1997). Secondary mathematics teachers' beliefs about the learning and teaching of mathematics. In F. Biddulph & K. Carr (Eds.), People in Mathematics Education: Proceedings of the 20th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 231–238). Aotearoa, New Zealand: MERGA.Google Scholar
  18. Knoll, E., Ernest, P., & Morgan, S. (2004). Experiencing research practice in pure mathematics in a teacher training context. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 161–168). Bergen: Bergen University College.Google Scholar
  19. Leatham, K. R. (2006). Viewing mathematics teachers' beliefs as sensible systems. Journal of Mathematics Teacher Education, 9, 91–102.CrossRefGoogle Scholar
  20. Liljedahl, P. (2008). Teachers' insights into the relationship between beliefs and practice. In J. Maab & W. Schloglmann (Eds.), Beliefs and attitudes in mathematics education: New research results (pp. 33–44). Rotterdam, NL: Sense Publishers.Google Scholar
  21. Mewborn, D. S. (2000, April). Changing actions vs. changing beliefs: What is the goal of mathematics teacher education. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  22. Moreira, P. C., & David, M. M. (2008). Academic mathematics and mathematical knowledge needed in school teaching practice: Some conflicting elements. Journal of Mathematics Teacher Education, 11, 23–40.CrossRefGoogle Scholar
  23. Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338–355.CrossRefGoogle Scholar
  24. Schoenfeld, A. H. (2003). How can we examine the connections between teachers' world views and their educational practices? Issues in Education, 8(2), 217–227.Google Scholar
  25. Schuck, S. (1999). Teaching mathematics: A brightly wrapped but empty gift box. Mathematics Education Research Journal, 11(2), 109–123.CrossRefGoogle Scholar
  26. Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9–15.Google Scholar
  27. Sosniak, L. A., Ethington, C. A., & Varelas, M. (1991). Teaching mathematics without a coherent point of view: Findings from the IEA Second International Mathematics Study. Journal of Curriculum Studies, 23(2), 199–131.CrossRefGoogle Scholar
  28. Speer, N. M. (2005). Issues of methods and theory in the study of mathematics teachers' professed and attributed beliefs. Educational Studies in Mathematics, 58, 361–391.CrossRefGoogle Scholar
  29. Speer, N. M. (2008). Connecting beliefs and practices: A fine-grained analysis of a college mathematics teacher's collections of beliefs and their relationship to his instructional practices. Cognition and Instruction, 26, 218–267.CrossRefGoogle Scholar
  30. Sullivan, P., & Mousley, J. (2001). Thinking teaching: Seeing mathematics teachers as active decision makers. In F.-L. Lin & T. J. Cooney (Eds.), Making Sense of Mathematics Teacher Education (pp. 147–163). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  31. Thompson, A. G. (1984). The relationship between teachers' conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105–127.CrossRefGoogle Scholar
  32. 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 Publishing Company.Google Scholar
  33. Van Zoest, L. R., Jones, G. A., & Thornton, C. A. (1994). Beliefs about mathematics teaching held by pre-service teachers involved in a first grade mentorship program. Mathematics Education Research Journal, 6(1), 37–55.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of TasmaniaLauncestonAustralia

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