Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-11T21:01:24.120Z Has data issue: false hasContentIssue false
  • English
  • Français

Reasoning as a mathematical habit of mind

Published online by Cambridge University Press:  02 March 2020

Mike Askew
Mike Askew*
Affiliation:
University of Witwatersrand, Johannesburg
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper I look at different aspects of mathematical reasoning, and argue that we need to make sure students of all ages engage in a range of mathematical reasoning, particularly given the evidence that teaching for reasoning is a powerful complement to teaching that is more focused on skills and procedures.

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 559 , March 2020 , pp. 1 - 11
Copyright
© Mathematical Association 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kilpatrick, J., Swafford, J. & Findell, B. (Eds.), Adding it up: Helping children learn mathematics, Washington DC: National Academy Press (2001).Google Scholar
Department for Education, The national curriculum in England: Key stages 1 and 2 framework document, London: DfE (2013).Google Scholar
Whitehead, A. N., The aims of education and other essays, New York: The Free Press (1929).Google Scholar
Nunes, T., Bryant, P., Sylva, K., Barros, R., Development of maths capabilities and confidence in primary school [Research report], London: Department for Children, Schools and Families (DCSF).Google Scholar
Nunes, T., Bryant, P., Barros, R., Sylva, K., The relative importance of two different mathematical abilities to mathematical achievement. British Journal of Educational Psychology, 82(1) (2012) pp. 136–156. https://doi.org/10.nn/j.2044-8279.2011.02033.xCrossRefGoogle ScholarPubMed
Arcavi, A., Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3) (1994) pp. 24–35.Google Scholar
English, L. & Sriraman, B., Problem Solving for the 21st Century. In Sriraman, B. & English, L. (eds.), Theories of Mathematics Education pp. 263–290). Retrieved from http://link.springer.com/chapter/10.1007/978-3-642-00742-2_27Google Scholar
Carpenter, T., Fennema, E., Franke, M. L., Levi, L. & Empson, S. B., Children’s Mathematics: Cognitively Guided Instruction, Portsmouth, NH:Heinemann (1999).Google Scholar
Lamon, Susan, Teaching Fractions and Ratios for Understanding, Taylor and Francis (2005).Google Scholar
Henningsen, M. & Stein, M. K., Mathematical tasks and student cognition: classroom-based factors that support and inhibit high-level mathematical thinking and reasoning, Journal for Research in Mathematics Education 28(5) (1997) p. 524. https://doi.org/10.2307/749690CrossRefGoogle Scholar
Kahneman, D., Thinking, fast and slow, London: Allen Lane (2011).Google Scholar
Marton, F. & Booth, S., Learning and awareness, Mahwah NJ: Lawrence Erlbaum Associates (1997).Google Scholar
Al Cuoco, Paul Goldenburg and Mark, June, Habits of Mind: An Organizing Principle for Mathematics Curricula, Journal of Mathematical Behavior 15 (1996) pp. 375–402.CrossRefGoogle Scholar
Fosnot, C. T. & Dolk, M., Young Mathematicians at Work: Constructing Fractions, Decimals and Percents, Portsmouth, NH: Heinemann (2002).Google Scholar
Dewey, J., How we think: A restatement of the relation of reflective thinking to the educative process,Boston; New York: D. C. Heath and Company (1933).Google Scholar