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The Culture of the Mathematics Classroom: An Unknown Quantity?

Chapter
Part of the Mathematics Education Library book series (MELI, volume 14)

Abstract

The whole notion of a ‘culture of the mathematics classroom’ implies an acceptance of the idea that mathematics exerts a unique influence on the context of classrooms in which the subject is being taught and learned. This is a relatively recent departure from traditional concerns in mathematics education and is one of the outcomes of shifts in perspectives within the field that have, in turn, given rise to some changes of emphasis in related research. A book such as this is in itself indicative of the importance given to new considerations of this kind. The aim of this chapter is to provide a theoretical setting for the chapters that follow which are concerned, in one way or another, with issues related to this change. In attempting to provide this setting, changes will be viewed from three broad perspectives: (a) those related to the nature of mathematics as a discipline; (b) those concerned with research about teachers and the teaching of mathematics, and (c) those concerning pupil perspectives.

Keywords

Mathematics Education Mathematics Teacher Mathematical Knowledge Mathematical Learning Mathematics Curriculum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alderson, J.: 1988, Parental involvement in children’s mathematics Unpublished master’s thesis, Essex Institute of Higher Education, Brentwood, U.K.Google Scholar
  2. Anderson, L. M.: 1981, Student responses to seatwork: Implications for the study of students’ cognitive processes (Research Series No. 102 ). East Lansing, MI: Institute for Research on Teaching, Michigan State University.Google Scholar
  3. Ashton, P., Kneen, P., Davies, F. and Holley, B.: 1975, The aims of primary education: A study of teachers’ opinions. London: Macmillan Education Ltd.Google Scholar
  4. Bassham, H.: 1962, Teacher understanding and pupil efficiency in mathematics–a study of relationship. Arithmetic Teacher 9, 383–387.Google Scholar
  5. Begle, E. G.: 1979, Critical variables in mathematics education. Washington, DC: Mathematics Association of America and the National Council of Teachers of Mathematics.Google Scholar
  6. Bell, A., Fischbein, E., and Greer, B.: 1984, Choice of operation in arithmetic problems: The effects of number size, problem structure and context Educational Studies in Mathematics. 15, 129–147.CrossRefGoogle Scholar
  7. Bennett, N.: 1976, Teaching styles and pupil progress London:Open Books. Berliner, D. C.: 1986 In pursuit of the expert pedagogue. Educational Researcher 15. 5–13.Google Scholar
  8. Berliner, D. C., Stein, P., Sabers, D., Clarridge, P., Cushing, K., and Pinnegar, S.: 1988, Implications of research on pedagogical expertise and experience for mathematics teaching. In D. A. Grouws, T. Cooney, and D. Jones, (Eds.), Effective perspectives on research on teaching (pp. 67–95 ). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  9. Biggs, J. B.: 1967, Mathematics and conditions of learning Slough, U.K.: National Foundation for Educational Research (NFER).Google Scholar
  10. Bishop, A. J. and Nickson, M.: 1983, The social context of mathematics education: A review of research in mathematical education (Part B), Windsor, U.K.: NFER-Nelson.Google Scholar
  11. Bloor, D.: 1976, Knowledge and Social Imagery London: Routledge Kegan Paul.Google Scholar
  12. Brown, C. A., and Cooney, T. J.: 1982, Research on teacher education: A philosophical orientation, Journal of Research and Development in Education, 15 (4) 13–18.Google Scholar
  13. Brown, M.: 1986, Developing a model to describe the mathematical progress of secondary school students (11–16 years): Findings of the graded assessment in mathematics project. In Proceedings of the Tenth International Conference for the Psychology of Mathematics Education (pp. 135–140 ). London, U.K.Google Scholar
  14. Brown, S. I., Cooney, T. J., and Jones, D.: 1990, Mathematics teacher education. In W R Houston (Ed.), Handbook of Research on Teacher Education (pp. 639–656 ). New York: Macmillan.Google Scholar
  15. Carpenter, T. P., and Moser, J. M.: 1983, The acquisition of addition and subtraction: A cognitive perspective. In R. Lesh M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 7–44 ), New York: Academic Press.Google Scholar
  16. Carraher, T. N.: 1989, Negotiating the results of mathematical computations. International Journal of Educational Research, 13 (6), 637–646.CrossRefGoogle Scholar
  17. Cobb, P.: 1986, Contexts, goals, beliefs and learning mathematics For the Learning of Mathematics, 6 (2), 2–9.Google Scholar
  18. Cobb, P.: 1987, An investigation of young children’s academic arithmetic contexts Educational Studies in Mathematics, 18, 109–124.CrossRefGoogle Scholar
  19. Cohen, L., Manion, L.: 1980, Research methods in education, London: Croom Helm.Google Scholar
  20. Confrey, J.: 1980, Conceptual change analysis: Implications for mathematics and curriculum inquiry East Lansing, MI: Institute for Research on Teaching, Science-Mathematics Teaching Center, Michigan State University.Google Scholar
  21. Cooney, T. J.,Goffree, F., Stephens, M., and Nickson, M.: 1985, The professional life of teachers For the Learning of Mathematics,5(2), 24–30.Google Scholar
  22. D’Ambrosio, U.: 1985, Ethnomathematics and its place in the history and pedagogy for mathematics For the Learning of Mathematics, 5(1), 44–48.Google Scholar
  23. Davies, W. B.: 1983, The sociology of education In P. Hirst (Ed.), Eductional theory and its foundation disciplines (pp. 100–137 ), London: Routledge Kegan Paul.Google Scholar
  24. Delamont, S.: 1981, All too familiar? A decade of classroom research Educational Analysis, 3 (1), 47–68.Google Scholar
  25. Department of Education and Science: 1978, Primary Education in England A survey by H. M. Inspectors of Schools London: Her Majesty’ s Stationery Office. Department of Education and Science: 1979, Aspects of secondary education in England London: Her Majesty’s Stationery Office.Google Scholar
  26. Department of Education and Science: 1985, GCSE: The national criteria for mathematics London: Her Majesty’s Stationary Office.Google Scholar
  27. Desforges, C.: 1985, Matching tasks for children. In S. N. Bennett and C. Desforges, (Eds.) Recent advances in classroom research (pp 92–104) London:Constable. Desforges, C., and Cockburn, A.: 1987, Understanding the mathematics teacher: A study of practice in first schools. London: The Falmer Press.Google Scholar
  28. Donaldson, M. C.: 1978, Children’s minds. London: Croom Helm.Google Scholar
  29. Eisenhart, M. A.: 1988, The ethnographic research tradition and mathematics education research Journal for Research in Mathematics Education, 19 (2), 99–114.CrossRefGoogle Scholar
  30. Fasheh, M.: 1982, Mathematics. culture and authority For the Learning of Mathematics, 3 (2), 2–8.Google Scholar
  31. Feiman-Nemser, S., and Floden, R. E.: 1986, The cultures of teaching. In M. C. Wittrock (Ed.), Handbook of research in teaching ( 3rd edition, pp. 505–526 ). London: Collier-Macmillan.Google Scholar
  32. Galton, M., Simon, B., and Croll, P.: 1980, Inside the primary classroom London:Routledge Kegan Paul.Google Scholar
  33. Gelman, R.: 1969, Conservation acquisition: A problem of learning to attend to relevant attributes, Journal of Experimental Child Psychology, 7, 167–187.CrossRefGoogle Scholar
  34. Good, T., and Biddle, B. J.: 1988, Research and improvement of mathematics instruction: The need for observational resources. In D. A. Grouws, T. J. Cooney, D. Jones (Eds.), Perspectives on research on effective mathematics teaching (Vol. I, pp. 114–142 ) Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  35. Good, T., and Brophy, J.: 1978, Looking in classrooms New York: Harper Row.Google Scholar
  36. Good, T., Grouws, D., and Ebmeier, H.: 1983, Active mathematics teaching New York:Longman.Google Scholar
  37. Hamlyn, D. W.: 1970, The theory of knowledge London:Macmillan Press.Google Scholar
  38. Herscovitz, R., and Vinner, S.: 1984, Children’s concepts in elementary geometry–a reflection of teachers’ concepts. In B. Southwell et al. (Eds.), Proceedings of the Eighth International Conference for the Psychology of Mathematics Education (pp. 28–34 ) Darlinghurst, Australia.Google Scholar
  39. Hersh, R.: 1979, Some proposals for revising the philosophy of mathematics Advances in Mathematics, 31 (1), 31–50.CrossRefGoogle Scholar
  40. Jaworski, B.: 1989, To inculcate versus to elicit knowledge Actes de la 13e conference internationale, Psychology of Mathematics Education, Paris.Google Scholar
  41. Joseph, G.: 1990, April, The politics of anti-racist mathematics. Paper presented at a conference on the Political Dimensions of Mathematics Education, Institute of Education, University of London, U.K.Google Scholar
  42. Kilpatrick, J.: 1988, Editorial, Journal for Research in Mathematics Education, 19 (2), 98.Google Scholar
  43. Kuhn, T.: 1970, The structure of scientific revolutions (2nd ed.). Chicago: The University of Chicago Press.Google Scholar
  44. Lakatos, I.: 1976, Proofs and refutations. Cambridge, U.K.: Cambridge University Press.CrossRefGoogle Scholar
  45. Lampert, M.: 1985 How do teachers manage to teach? Harvard Educational Review 55 (2), 178–194.Google Scholar
  46. Leinhart, G.: 1988, Expertise in instructional lessons: An example from fractions In D. A. Grouws, T. J. Cooney, D. Jones (Eds.), Perspectives on Research on Effective Mathematics Teaching (pp. 47–66). Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  47. Lerman, S.: 1986, Alternative views of the nature of mathematics and their possible influence on the teaching of mathematics. Unpublished doctoral dissertation, Centre for Educational Studies, King’s College, University of London, U.K.Google Scholar
  48. Lerman, S.: 1990, Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics, British Educational Research Journal, 16 (1), 15–61.CrossRefGoogle Scholar
  49. Levitas, M.: 1974, Marxist perspectives in the sociology of education London: Routledge Kegan Paul.Google Scholar
  50. Lortie, D. C.: 1975 Schoolteacher: A sociological study Chicago:The University of Chicago Press.Google Scholar
  51. Malle, G.: 1988 The question of meaning in teacher education. Paper presented at the Sixth International Congress on Mathematical Education, Budapest, Hungary.Google Scholar
  52. McGrath, J. E.: 1988, Looking for a common denominator: A study of underachievement in the primary mathematics classroom. Unpublished master’s thesis, Essex Institute of Higher Education, Brentwood, U.K.Google Scholar
  53. McLeod, D. B., Carpenter, T. P., McCormack, R. L., and Skvarcius, R.: 1978, Cognitive style and mathematics learning: The interaction of field independence and instructional treatment in numeration systems Journal for Research in Mathematical Education, 9, 163–174.CrossRefGoogle Scholar
  54. Mellin-Olsen, S.: 1987, The politics of mathematics education. Dordrecht, Holland: D. Reidel..Google Scholar
  55. Nash, R.: 1974, Pupils’ expectations of their teachers Research in Education, 47–61. National Committee of Excellence in Education: 1983, A nation at risk: The imperative for educational reform. Washington, DC: National Institute of Education.Google Scholar
  56. National Committee of Inquiry into the Teaching of Mathematics in Schools: 1982, Mathematics counts (The Cockcroft report). London: Her Majesty’s Stationery Office.Google Scholar
  57. National Curriculum Council: 1989, Mathematics in the National Curriculum London:Her Majesty’s Stationary Office.Google Scholar
  58. Nickson, M.: 1981, Social foundations of the mathematics curriculum: A rationale for change. Unpublished doctoral dissertation, Institute of Education, University of London, U.K.Google Scholar
  59. Nickson, M.: 1988a, Pervasive themes and some departure points for research into effective mathematics teaching. In D. A. Grouws, T. J. Cooney, and D. Jones (Eds.), Perspectives on research on effective mathematics teaching Vol. 1, pp. 245–252, Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  60. Nickson, M.: 1988b, What is multicultural mathematics? In P. Ernest (Ed.), Mathematics teaching: The state of the art pp. 236–241, Lewes, Sussex: Falmer Press.Google Scholar
  61. Noss, R.: 1988, The computer as a cultural influence in mathematical learning Educational Studies in Mathematics, 19, 251–268.CrossRefGoogle Scholar
  62. Orton, R. E.: 1988, Two theories of ‘theory’ in mathematics education: Using Kuhn and Lakatos to examine four foundational issues For the Learning of Mathematics, 8 (1), 36–43.Google Scholar
  63. Peterson, P. L., Swing, S. R., Stark, K. D., and Waas, G. A: 1984, Students’ cognition and time on task during mathematics instruction American Educational Research Journal, 21 (3), 487–515.Google Scholar
  64. Pimm, D.: 1982, Why the history and philosophy of mathematics should not be rated X. For the Learning of Mathematics, 3 (1), 12–15.Google Scholar
  65. Pimm, D.: 1990 April, Mathematical versus political awareness: Some political dangers inherent in the teaching of mathematics Paper presented at a conference on the Political Dimensions Mathematics Education, Institute of Education, University London, U.K.Google Scholar
  66. Pirie, S. E. B.: 1988, Understanding: Instrumental, relational, intuition, constructed, formalised…? How can we know? For the Learning of Mathematics 8 (3), 2–6.Google Scholar
  67. Plunkett, S.: 1981, Fundamental questions for teachers For the Learning of Mathematics, 2 (2), 46–48.Google Scholar
  68. Popkewitz, T. S.: 1988, Institutional Issues in the study of school mathematics: Curriculum research. In A. J. Bishop (Ed.), Mathematics education and culture pp. 221–249, Dordrecht, Holland: Kluwer Academic Publishers.CrossRefGoogle Scholar
  69. Popper, K.: 1972, Objective knowledge - an evolutionary approach Oxford:Oxford University Press.Google Scholar
  70. Porter, A., Floden, R., Freeman, D., Schmidt, W., and Schwille, J.: 1988 Content determinants in elementary school mathematics. In D. Grouws, T. J., Cooney and D. Jones (Eds.), Perspectives on research on effective mathematics teaching Vol. 1, pp. 96–114, Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  71. Reiss, V.: 1978, Socialization phenomena in the mathematics classroom: Their significance for interdisciplinary teaching. In Cooperation between science teachers and mathematics teachers pp. 392–417, IDM Bielefeld Materialen and Studien Ban 16 University of Bielefeld.Google Scholar
  72. Rutter, M., Maughan, B., Mortimore, P., and Ouston, J.: 1979, Fifteen thousand hours: secondary schools and their effects on children London:Open Books.Google Scholar
  73. Scheffler, I.: 1976, The language of education Springfield. IL: Charles C. Thomas.Google Scholar
  74. Shipman, M. D.: 1974, Inside a curriculum project London: Methuen.Google Scholar
  75. Shulman, L. S.: 1970, Psychology and mathematics education In E. Begle (Ed.), Mathematics Education pp. 23–71, 69th Yearbook of the National Society for the Study of Education, Chicago: University of Chicago Press.Google Scholar
  76. Smith, B. O., Stanley W. O., and Shores, J. H.: 1971, Cultural roots of the curriculum. In R. Hooper (Ed.), The curriculum: Context, design and development pp. 16–19, Edinburgh: Oliver Boyd.Google Scholar
  77. Spradley, J.: 1980, Participant observation. New York: Holt, Rinehart WinstonGoogle Scholar
  78. Steffe, L. P., and Killion, K.: 1986, Mathematics teaching: A specification in a constructionist frame of reference. In L. Burton and C. Boyles (Eds.), Proceedings of the Tenth International Conference for the Psychology of Mathematics Education, pp. 207–216, London: University of London, Institute of Education, U.K.Google Scholar
  79. Thom, R.: 1972, Modern mathematics: Does it really exist? In A. G. Howson (Ed.), Developments in mathematical education pp. 194–209, Cambridge, U.K.: Cambridge University Press.Google Scholar
  80. Thompson, A. G.: 1984, The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15 (2), 105–127.CrossRefGoogle Scholar
  81. Toulmin, S.: 1972, Human understanding Oxford: Clarendon Press.Google Scholar
  82. Trown, E. A., and Leith, G. O. M.: 1975, Decision rules for teaching strategies in primary schools: Personality–treatment interactions. British Journal of Educational Psychology, 45, 130–140.CrossRefGoogle Scholar
  83. von Glasersfeld, E.: 1981, An attentional model for the construction of units and number Journal for Research in Mathematical Education, 12 (2), 83–94.CrossRefGoogle Scholar
  84. Ward, M.: 1979, Mathematics and the 10-year-old Schools Council Working Paper No. 61. London: Evans-Methuen Educational.Google Scholar
  85. Wittman, E. C.: 1989, The mathematical training of teachers from the point of view of education Journal fur Mathematik—Didaktik, 10 (4), 291–308.Google Scholar
  86. Wolfson, P.: 1981, Philosophy enters the classroom For the Learning of Mathematics, 2 (1), 22–26.Google Scholar
  87. Yates, J.: 1978, Four mathematical classrooms: An inquiry into teaching method. Southampton, UK.: Faculty of Mathematical Studies, University of Southampton.Google Scholar
  88. Zaslaysky, C.: 1989, Integrating mathematics with the study of cultural traditions, In C. Keitel, P. Damerow, A. J. Bishop, and P. Gerdes (Eds.), Mathematics, education and society pp. 14–15, Paris: United Nations Educational, Scientific and Cultural Organisation (UNESCO).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  1. 1.Research and Evaluation DivisionUniversity of Cambridge Local Examinations SyndicateCambridgeUK

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