Advertisement

Teaching Mathematics to Adults: Integrating New and Old Knowledge

  • Mary Dodd
  • Jean Mathias
  • Sam J. Nolan
Chapter

Abstract

Adult students bring with them knowledge and experience which can adversely affect their learning of mathematics. This chapter develops the metaphor of building on a Brownfield site to highlight the difficulties they experience. It is demonstrated and addressed through two case studies, one to do with mental mathematics (to challenge the notion of “one best method”), and the second to do with misconceptions in applied mathematics (mechanics).

Keywords

Formal Method Proportional Reasoning Common Misconception Informal Method Threshold Concept 
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.

References

  1. Altorre, S., & Figueras, O. (2005). Proportional reasoning of adults with different levels of literacy. In M. Horne & B. Marr (Eds.), Connecting voices in adult mathematics and numeracy: practitioners, researchers and learners. Proceedings of the 12th international conference of Adults Learning Maths—A research forum, Melbourne, 42–47.Google Scholar
  2. Benn, R. (1997). Adults count too: Mathematics for empowerment. Leicester: NIACE.Google Scholar
  3. Carraher, T., Carraher, D., & Schliemann, A. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21–29.CrossRefGoogle Scholar
  4. Coben, D. (2000). Mathematics or common sense? Researching ‘invisible’ mathematics through adults’ life histories. In D. Coben, J. O’donoghue, & G. Fitzsimons (Eds.), Perspectives on adults learning mathematics: Research and practice. Dordrecht/Boston/London: Kluwer.Google Scholar
  5. Dodd, M. (2008). CURRENT REPORT: The mathematical competence of adults returning to learning on a university foundation programme: a selective comparison of performance with the CSMS study. In E. Nardi, T. Rowland, & L. Haggarty (Eds.), Research in mathematics education (Vol. 10, pp. 203–204). Oxford: Routledge.Google Scholar
  6. Dodd, M. (2012). The influence of previous understanding and relative confidence on adult maths learning: Building adult understanding on a brownfield site. Doctorate in Education thesis, Open University.Google Scholar
  7. Duffin, J., & Simpson, A. (2000). Understanding their thinking: The tension between the cognitive and the affective. In D. Coben, J. O’donoghue, & G. Fitzsimons (Eds.), Perspectives on adults learning mathematics research and practice. Dordrecht/Boston/London: Kluwer.Google Scholar
  8. Evans, J. (2000). Adults’ mathematical thinking and emotions: A study of numerate practice. London/New York: Routledge Falmer.Google Scholar
  9. Gagné, R. (1968). Presidential address of division 15 learning hierarchies. Educational Psychologist, 6(1), 1–9.CrossRefGoogle Scholar
  10. Gagné, R. (1969). The conditions of learning. London/New York/Sidney/Toronto: Holt, Rinehart and Winston.Google Scholar
  11. Gagné, R. (1985). The conditions of learning and theory of instruction (4th ed.). New York: Rinehart and Winston.Google Scholar
  12. Gilbert, J. K. (1982). Students’ conceptions of ideas in mechanics. Physics Education, 17(2), 62–66.CrossRefGoogle Scholar
  13. Greer, B. (1994). Extending the meaning of multiplication and division. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics. Albany: State University of New York Press.Google Scholar
  14. Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66, 64.CrossRefGoogle Scholar
  15. Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. The Physics Teacher, 30, 141–158.CrossRefGoogle Scholar
  16. Karsenty, R. (2002). What do adults remember from their high school mathematics? The case of linear functions. Educational Studies in Mathematics, 51, 117–144.CrossRefGoogle Scholar
  17. Knowles, M. (1980). The modern practice of adult education: From pedagogy to andragogy (2nd ed.). New York: Cambridge University Press.Google Scholar
  18. Land, R., Cousin, G., Meyer, J. H. F., & Davies, P. (2005). Threshold concepts and troublesome knowledge (3): Implications for course design and evaluation. In C. Rust (Ed.), Improving student learning: Diversity and inclusivity, proceedings of the 12th improving student learning conference (pp. 53–64). Oxford: Oxford Centre for Staff and Learning Development (OCSLD).Google Scholar
  19. Land, R., Meyer, J. H. F., & Baillie, C. (2010). Threshold concepts and transformational learning. Rotterdam: Sense.Google Scholar
  20. Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255–276.Google Scholar
  21. Meyer, J. H. F., & Land, R. (2003). Threshold concepts and troublesome knowledge 1: Linkages to ways of thinking and practising. In C. Rust (Ed.), Improving student learning: Theory and practice ten years on (pp. 412–424). Oxford: Oxford Centre for Staff and Learning Development (OCSLD).Google Scholar
  22. Meyer, J. H. F., & Land, R. (2005). Threshold concepts and troublesome knowledge (2): Epistemological considerations and a conceptual framework for teaching and learning. Higher Education, 49(3), 373–388.CrossRefGoogle Scholar
  23. Perkins, D. (2006). Constructivism and troublesome knowledge. In R. Land & J. H. F. Meyer (Eds.), Overcoming barriers to student understanding: Threshold concepts and troublesome knowledge (pp. 33–47). London/New York: Routledge/Taylor & Francis Group.Google Scholar
  24. Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.Google Scholar
  25. Skemp, R. (1979). The psychology of learning mathematics. Middlesex: Pelican Books.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Mary Dodd
    • 1
  • Jean Mathias
    • 1
  • Sam J. Nolan
    • 2
  1. 1.Foundation CentreUniversity of DurhamDurhamUK
  2. 2.Centre for AcademicResearcher and Organisation Development, Durham UniversityDurhamUK

Personalised recommendations