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Educational Studies in Mathematics

, Volume 58, Issue 3, pp 361–391 | Cite as

Issues of Methods and Theory in the Study of Mathematics Teachers’ Professed and Attributed Beliefs

  • Natasha M. Speer
Article

Abstract

In research on teachers’ beliefs, a distinction is often made between what teachers state (“professed beliefs”) and what is reflected in teachers’ practices (“attributed beliefs”). Researchers claim to have found both consistencies and inconsistencies between professed and attributed beliefs. In this paper, methods and research designs typically used in studies of teachers’ beliefs are examined. It is asserted that, in some cases, the perceived discrepancy between professed and attributed beliefs may actually be an artifact of the methods used to collect and analyze relevant data and the particular conceptualizations of beliefs implicit in the research designs. In particular, the apparent dichotomy can be the result of a lack of shared understanding between teachers and researchers of the meaning of terms used to describe beliefs and practices. In addition, it is asserted that it is inappropriate to classify any belief as entirely professed since researchers make various attributions to teachers through choices about data collection, theory, analysis of data, and presentation of findings. Moreover, the emphasis on classifying beliefs in this manner may be inhibiting researchers from developing a more comprehensive understanding of teachers’ beliefs. Traditional and alternative methods are described, a data example is provided to illustrate the claims, and implications for future research are discussed.

Key words

mathematics teacher cognition research methods teacher beliefs teacher practices 

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References

  1. Aguirre, J.M. and Speer, N.M.: 1999, ‘Examining the relationship between beliefs and goals in teacher practice’, Journal for Mathematical Behavior 18(3).Google Scholar
  2. Ball, D.L., Lubienski, S. and Mewborn, D.S.: 2001, ‘Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge’, in V. Richardson (ed.), Handbook of Research on Teaching, American Educational Research Association, Washington, DC, pp. 433–456.Google Scholar
  3. Barwell, R.: 2003, ‘Discursive psychology and mathematics education: Possibilities and challenges’, Zentralblatt für Didaktik der Mathematik 35(5), 201–207.Google Scholar
  4. Begle, E.G.: 1979, Critical variables in mathematics education: Findings from a survey of the empirical literature, Mathematical Association of American and National Council of Teachers of Mathematics, Washington, DC.Google Scholar
  5. Borko, H. and Putnam, R.T.: 1996, ‘Learning to teach’, in D.C. Berliner and R.C. Calfee (eds.), Handbook of Educational Psychology, Macmillan Library Reference USA, Simon and Schuster Macmillan, New York, pp. 673–708.Google Scholar
  6. Bullough, R.V., Knowles, J.G. and Crow, N.A.: 1991, Emerging as a Teacher, Routledge, London.Google Scholar
  7. Calderhead, J.: 1996, ‘Teachers: Beliefs and knowledge’, in D.C. Berliner and R.C. Calfee (eds.), Handbook of Educational Psychology, Macmillan Library Reference USA: Simon and Schuster Macmillan, New York, pp. 709–725.Google Scholar
  8. Calderhead, J. and Robson, M.: 1991, ‘Images of teaching: Student teachers’ early conceptions of classroom practice’, Teaching and Teacher Education 7, 1–7.CrossRefGoogle Scholar
  9. Clark, C.M. and Peterson, P.L.: 1986, ‘Teachers’ thought processes’, in M.C. Wittrock (ed.), Handbook of Research on Teaching, 3rd ed., Macmillan, New York, pp. 255–296.Google Scholar
  10. Cohen, D.K.: 1990, ‘A revolution in one classroom: The case of Mrs. Oublier’, Educational Evaluation and Policy Analysis 12(3), 327–345.Google Scholar
  11. Cooney, T.: 1985, ‘A beginning teacher’s view of problem solving’, Journal for Research in Mathematics Education 16(5), 324–336.Google Scholar
  12. Dick, B.: 2000, ‘Grounded theory: A thumbnail sketch, http://www.scu.edu.au/schools/gcm/ar/arp/grounded.html.
  13. Ernest, P.: 1985, ‘The philosophy of mathematics and mathematics education”, International Journal of Mathematics Education, Science, and Technology 16(5), 603–612.Google Scholar
  14. Ernest, P.: 1988, ‘The impact of beliefs on the teaching of mathematics’, in Paper presented at the ICME VI, Budapest, Hungary.Google Scholar
  15. Ernest, P.: 1989, ‘The knowledge, beliefs and attitudes of the mathematics teacher: A model’, Journal of Education for Teaching 15(1), 13–33.Google Scholar
  16. Ernest, P.: 1991, The Philosophy of Mathematics Education, The Falmer Press, London.Google Scholar
  17. Frederiksen, J.R., Sipusic, M., Sherin, M.G. and Wolfe, E.: 1998, ‘Video portfolio assessment: Creating a framework for viewing the functions of teaching’, Educational Assessment 5(4), 225–297.Google Scholar
  18. Furinghetti, F. and Pehkonen, E.: 2002, ‘Rethinking characterizations of beliefs’, in G.C. Leder, E. Pehkonen and G. Torner (eds.), Beliefs: A Hidden Variable in Mathematics Education?, Vol. 31, Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 39–58.Google Scholar
  19. Gellert, U.: 2001, ‘Research on attitudes in mathematics education: A discursive perspective”, in Paper presented at the 25th meeting of the International Group for the Psychology of Mathematics Education (PME-XXV), Utrecht, pp. 33–40.Google Scholar
  20. Hoyles, C.: 1992, ‘Mathematics teaching and mathematics teachers: A meta-case study’, For the Learning of Mathematics 12(3), 32–44.Google Scholar
  21. Kuhs, T.M. and Ball, D.: 1986, Approaches to teaching mathematics: Mapping the domains of knowledge, skills, and dispositions, Michigan State University, Center on Teacher Education, East Lansing, MI.Google Scholar
  22. Leder, G.C. and Forgasz, H.J.: 2002, ‘Measuring mathematical beliefs and their impact on the learning of mathematics: A new approach’, in G.C. Leder, E. Pehkonen and G. Torner (eds.), Beliefs: A Hidden Variable in Mathematics Education?, Vol. 31, Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 95–114.Google Scholar
  23. Leder, G.C., Pehkonen, E. and Torner, G. (eds.). 2002, Beliefs: A Hidden Variable in Mathematics Education?, Vol. 31, Kluwer Academic Publishers, Dordrecht/Boston/London.Google Scholar
  24. Lerman, S.: 1990, ‘Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics”, British Educational Research Journal 16(1), 53–61.Google Scholar
  25. McLeod, D. and McLeod, S.: 2002, ‘Synthesis – Beliefs and mathematics education: Implications for learning, teaching, and research’, in G.C. Leder, E. Pehkonen and G. Torner (eds.), Beliefs: A Hidden Variable in Mathematics Education?, Vol. 31, Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 115–126.Google Scholar
  26. Nathan, M.J., Knuth, E. and Elliot, R.: 1998, ‘Analytic and social scaffolding in the mathematics classroom: One teacher’s changing practices’, in Paper presented at the Annual Meeting of the American Educational Research Association, San Diego, 1998.Google Scholar
  27. Nespor, J.: 1987, ‘The role of beliefs in the practice of teaching’, Journal of Curriculum Studies 19(4), 317–328.Google Scholar
  28. Pajares, M.F.: 1992, ‘Teachers’ beliefs and educational research: Cleaning up a messy construct’, Review of Educational Research 62(3), 307–332.Google Scholar
  29. Prawat, R.: 1992, ‘Teachers’ beliefs about teaching and learning a constructivist perspective’, American Journal of Education 100(3), 354–395.Google Scholar
  30. Putnam, R. and Borko, H.: 2000, ‘What do new views of knowledge and thinking have to say about research on teacher learning’, Educational Researcher 29(1), 4– 15.Google Scholar
  31. Richardson, V.: 1996, ‘The role of attitudes and beliefs in learning to teach’, in D.C. Berliner and R.C. Calfee (eds.), Handbook of Educational Psychology, Macmillan Library Reference USA, Simon and Schuster Macmillan, New York.Google Scholar
  32. Sherin, M.: 1996, The nature and dynamics of teachers’ content knowledge, Doctoral Dissertation, University of California, Berkeley, Berkeley, CA.Google Scholar
  33. Sherin, M.: 2002, ‘When teaching becomes learning’, Cognition and Instruction 20(2), 119–150.CrossRefGoogle Scholar
  34. Skott, J.: 2001a, ‘The emerging practices of a novice teacher: The roles of his school mathematics images’, Journal of Mathematics Teacher Education 4(1), 3–28.CrossRefGoogle Scholar
  35. Skott, J.: 2001b, ‘Why belief research raises the right question but provides the wrong type of answer’, in Proceedings of The Third Nordic Conference on Mathematics Education, Högskolan Kristianstad.Google Scholar
  36. Speer, N.M.: 2000, ‘Examining how beliefs shape instruction: Case studies of teaching assistants in calculus’, in Paper presented at the 22nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ.Google Scholar
  37. Speer, N.M.: 2001, Connecting beliefs and teaching practices: A study of teaching assistants in collegiate reform calculus courses, Doctoral Dissertation, University of California, Berkeley, Berkeley, CA.Google Scholar
  38. Thompson, A.: 1984, ‘The relationship of teachers’ conceptions of mathematics teaching to instructional practice’, Educational Studies in Mathematics 15, 105– 127.CrossRefGoogle Scholar
  39. Thompson, A.: 1985, ‘Teachers conceptions of mathematics and the teaching of problem solving’, in E. Silver (ed.), Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Lawrence Erlbaum Associates, Hillsdale, pp. 281– 294.Google Scholar
  40. Thompson, A.: 1992, ‘Teachers’ beliefs and conceptions: A synthesis of the research’, in D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 127–146.Google Scholar
  41. Torner, G.: 2002, ‘Mathematical beliefs – A search for a common ground: Some theoretical considerations on structuring beliefs, some research questions, and some phenomenological observations’, in G.C. Leder, E. Pehkonen and G. Torner (eds.), Beliefs: A Hidden Variable in Mathematics Education?, Vol. 31, Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 73–94.Google Scholar
  42. Wilson, M.S. and Cooney, T.J.: 2002, ‘Mathematics teacher change and development. The role of beliefs’, in G.C. Leder, E. Pehkonen and G. Torner (eds.), Beliefs: A Hidden Variable in Mathematics Education?, Vol. 31, Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 127–148.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Michigan State UniversityEast LansingU.S.A.

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