The Emergence of Ability

  • Fiona Walls


This chapter looks at the ways in which work, performance under pressure and right/ wrong answering were combined in classroom practice to define and recognise mathematical ability. The chapter uses the examples of three children to show how “bottom”, “middle” and “top” were constructed as subject positions in the learning of mathematics and how children were grouped according to these categories. The chapter uses teacher, parent and child talk to demonstrate how this system of classification was naturalised and seen as an expression of children’s innate and fixed mathematical qualities. Despite growing evidence that grouping for instruction by ability in mathematics is of dubious benefit, teachers were convinced that they could not effectively cater for students’ needs if they did not teach in this manner. The children were made as subjects in the discourse of ability as mathematically able or not.


Mathematical Learning Mathematical Achievement Extension Group Mathematical Ability Ability Group 
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.


  1. Becker H (1963) Outsiders. Free Press, OxfordGoogle Scholar
  2. Berger P, Luckmann T (1966) The social construction of reality: a treatise in the sociology of knowledge. Penguin, LondonGoogle Scholar
  3. Berger T, Keynes H (1995) Everybody counts/everybody else. In: Fisher N, Keynes H, Wagreich P (eds) Changing the culture: mathematics education in the research community. Issues in ­mathematics education, vol 5. Conference Board of the Mathematical Sciences, Washington, DC, pp 89–110Google Scholar
  4. Boaler J (1997a) Experiencing school mathematics: teaching styles, sex and setting. Open University Press, BuckinghamGoogle Scholar
  5. Boaler J (1997c) When even the winners are losers: evaluating the experiences of top set students. J Curriculum Stud 29(2):165–182CrossRefGoogle Scholar
  6. Boaler J, Wiliam D (2001) ‘We’ve still got to learn!’ Students’ perspectives on ability grouping and mathematics achievement. In: Gates P (ed) Issues in mathematics teaching RoutledgeFalmer, London, pp 77–92Google Scholar
  7. Brownell W (1938) Two kinds of learning in arithmetic. J Educ Res 31(9):656–664Google Scholar
  8. Burton L (1989) Images of mathematics. In Ernest P (ed) Mathematics teaching: the state of the art. Falmer, New York, 180–187Google Scholar
  9. César M (1995) Pupils’ ideas about mathematics. In: Meira L, Carraher D (eds) Proceedings of the 19th Conference of the International Group for the Psychology of Mathematics Education, vol 1, pp 198–206Google Scholar
  10. Cotton T (2004) What can I say, and what can I do? Archaeology, narrative and assessment. In Walshaw M (ed) Mathematics education within the postmodern. Information Age, Greenwich, CT, 219–237Google Scholar
  11. Cross L, Hynes M (1994) Assessing mathematics learning for students with learning differences. Arith Teach 41(7):371–377Google Scholar
  12. Donlan C, Hutt E (1991) Teaching maths to young children with language disorders. In: Durkin K, Shire B (eds) Language in mathematical education: research and practice. Open University Press, Buckingham, pp 198–207Google Scholar
  13. Dowling P (1998) The sociology of mathematics education: Mathematical myths/pedagogic texts. London: The Falmer PressGoogle Scholar
  14. Drew D (1996) Aptitude revisited: rethinking math and science education for America’s next century. The John Hopkins University Press, BaltimoreGoogle Scholar
  15. Foucault M (1977) Discipline and punish: the birth of the prison. Penguin, LondonGoogle Scholar
  16. Gallagher S (1992) Hermeneutics and education. State University of New York Press, Albany, NYGoogle Scholar
  17. Goldman S, Hasselbring T (1997) Achieving meaningful mathematics literacy for students with learning disabilities. J Learn Disabil 30(2):198208CrossRefGoogle Scholar
  18. Hallam S, Toutounji I (1996) What do we know about the grouping of pupils by ability?: a research review. Institute of Education, University of London, LondonGoogle Scholar
  19. Hoffer T (1992) Middle school ability grouping and student achievement in science and mathematics. Educ Eval Policy Anal 14(3):205–227Google Scholar
  20. Ireson J, Hallam S (1999) Raising standards: is ability grouping the answer? Oxford Rev Educ 25(3):343–358CrossRefGoogle Scholar
  21. Lemert E (1951) Social pathology. McGraw-Hill, MaidenheadGoogle Scholar
  22. Linchevski L, Kutscher B (1998) Tell me with whom you are learning, and I’ll tell you how much you’ve learned: mixed-ability versus same-ability grouping in mathematics. J Res Math Educ 29(5):533–554CrossRefGoogle Scholar
  23. McDonald G (1993) Ages, stages and evaluation: the demography of the classroom. Eval Res Educ 7(3):143–154CrossRefGoogle Scholar
  24. Meighan R, Siraj-Blatchford I (1997) A sociology of educating. Third Edition. London: CassellGoogle Scholar
  25. Oakes J, Wells A, Jones M, Datnow A (1997) Detracking: the social construction of ability, cultural politics, and resistance to reform. Teachers Coll Rec 98(3):482–510Google Scholar
  26. Parks A (2007) Rethinking equity in mathematics education: a postmodern perspective. In: Lamberg T, Wiest L (eds) Proceedings of the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics EducationGoogle Scholar
  27. Pollard A, Triggs P, Broadfoot P, McNess E, Osborn M (2000) What pupils say: changing policy and practice in primary education. Continuum, LondonGoogle Scholar
  28. Postman N (1996) The end of education: redefining the value of school. Vintage, New YorkGoogle Scholar
  29. Ruthven K (1987) Ability stereotyping in mathematics. Educ Stud Math 18:243–253CrossRefGoogle Scholar
  30. Slavin R (1990) Achievement effects of ability grouping in secondary schools: a best evidence synthesis. Rev Educ Res 60(3):471–499Google Scholar
  31. Sukhnandan L, Lee B (1998) Streaming, setting and grouping by ability: a review of the literature. National Foundation for Educational Research, BerkshireGoogle Scholar
  32. Thorndike E (1922) The psychology of arithmetic. Macmillan, New YorkCrossRefGoogle Scholar
  33. Vanyan M, White N, Yuen P, Teper M (1997) Beliefs and attitudes toward mathematics among third and fifth-grade students: a descriptive study. School Sci Math 97(7):345–351CrossRefGoogle Scholar
  34. Zevenbergen R (2001) Language, social class and underachievement in school mathematics. In: Gates P (ed) Issues in mathematics teaching. RoutledgeFalmer, London, pp 38–50Google Scholar
  35. Zevenbergen R (2002) Streaming in school mathematics: a Bourdieuian analysis. Proceedings of the Third International Mathematics and Education Conference, part 2, pp 512–521Google Scholar
  36. Ministry of Education (1992) Mathematics in the New Zealand Curriculum. Learning Media, Wellington, New ZealandGoogle Scholar
  37. Ministry of Education (2001b) Curriculum update 45, February 2001. Learning Media, Wellington, New ZealandGoogle Scholar
  38. Ministry of Education (1994) English in the New Zealand curriculum. Learning Media, Wellington, New ZealandGoogle Scholar
  39. Ministry of Education (1996) Development band mathematics. Learning Media, Wellington, New ZealandGoogle Scholar
  40. Department for Education and Employment (1999) The National numeracy strategy: framework for teaching mathematics from reception to year 6. Cambridge University Press, CambridgeGoogle Scholar
  41. National Council of Teachers of Mathematics (2000) Principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston, VAGoogle Scholar
  42. Meighan R, Siraj-Blatchford I (1998) A sociology of educating, 3rd edn. Cassell, LondonGoogle Scholar
  43. Lim CS, Ernest P (2000) A survey of public images of mathematics. In: Rowland T, Morgan C (eds) Research in mathematics education: papers of the British Society for research in learning mathematics, vol 2. British Society for Research into Learning Mathematics, London, pp 193–206Google Scholar
  44. Lakoff G, Johnson M (1980) Metaphors we live by. The University of Chicago Press, ChicagoGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.James Cook UniversityTownsvilleAustralia

Personalised recommendations