Chapter 10: Calculation

Book chapter


Harris, A. 2014. Chapter 10: Calculation. in: Taylor, H. and Harris, A. (ed.) Learning and Teaching Mathematics 0-8 London SAGE Publications. pp. 145-163
AuthorsHarris, A.
EditorsTaylor, H. and Harris, A.
Abstract

In this chapter you can read about:
•Different forms of addition, subtraction, multiplication and division which children encounter
•How children progress from counting to calculating
•The different mental and written calculation strategies used by children
•Resources and models for supporting understanding of calculation
•The importance of understanding, reliability, efficiency and fluency in calculation.

KeywordsMathematics; Learning and teaching; Primary school
Page range145-163
Year2014
Book titleLearning and Teaching Mathematics 0-8
PublisherSAGE Publications
Output statusPublished
Place of publicationLondon
ISBN9781446296417
Publication dates
PrintNov 2013
Publication process dates
Deposited19 Feb 2025
Digital Object Identifier (DOI)https://doi.org/10.4135/9781526401601.n10
Official URLhttps://uk.sagepub.com/en-gb/eur/learning-and-teaching-mathematics-0-8/book239011
References

Anghileri, J. (2001) Development of Division Strategies for Year 5 Pupils in Ten English Schools, British Educational Research Journal, 27(1), pp. 85-103
Anghileri, J. (2008) Uses of counting in multiplication and division. In Thompson, I. (ed.) Teaching and Learning Early Number. Maidenhead: Open University Press
Askew, M. Bibby, T. and Brown, M. (2001) Raising attainment in primary number sense: from counting to strategy. London: Beam Education
Barmby, P., Bilsborough, L., Harries, T and Higgins, S. (2009) Primary Mathematics: Teaching for Understanding. Maidenhead: Open University Press
Baroody, A., Bajwa, N. and Eiland, M. (2009) Why can't Johnny remember the basic facts? Developmental Disabilities Research Reviews, 15 (1) pp. 69-79 (available at http://dx.doi.org/10.1002/ddrr.45)
Carpenter, T. P. and Moser, J. M. (1983) The acquisition of addition and subtraction concepts. In Lesh, R. and Landau, M. (eds.) Acquistion of Mathematical Concepts and Processes. New York: Academic Press
Carpenter, T.P. and Moser, J. M. (1984) The acquisition of addition and subtraction concepts in grades one through three, Journal for Research into Mathematics Education, 15(3) 179-202
Downton, A. (2010). Challenging multiplicative problems can elicit sophisticated strategies. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, pp. 169-176). Fremantle, Western Australia: MERGA Inc.
Ell, F., Irwin, K., & McNaughton, S. (2004) Two pathways to multiplicative thinking. In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics education for the third Millennium, towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Townsville pp. 199-206). Sydney: MERGA

Foxman, D. and Beishuizen, M. (2002) Mental calculation methods used by 11 year olds in different attainment bands: A reanalysis of data from the 1987 APU survey in the UK, Educational Studies in Mathematics, 51 (1/2), 41-69
Fischbein, E., Deri, M., Nello, M.S., & Marino, M.S. (1985) The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17

Greer, B. (1992) Multiplication and division as models of situations. In Grouws, D. (ed.) Handbook of Research on Mathematics Teaching and Learning. New York: Macmillan
Heirdsfield, A. M., Cooper, T. J., Mulligan, J., & Irons, C.J. (1999). Children’s mental multiplication and division strategies. In Zaslavsky, O. (Ed.), Proceedings of the 23rd Psychology of Mathematics Education Conference (Vol.3, pp. 89-96). Haifa, Israel: PME

Kouba, V. L. (1989) Children’s Solution Strategies for Equivalent Set Multiplication and Division Word Problems. Journal for Research in Mathematics Education, 20(2), pp.147-158
Hughes, M. (1986) Children and Number: Difficulties in Learning Mathematics. Oxford: Blackwell
Maclellan, E. (2012) Number Sense: The Underpinning Understanding for Early Quantitative Literacy, Numeracy: Vol. 5: Iss. 2, Article 3 (available at http://dx.doi.org/10.5038/1936-4660.5.2.3) [accessed 2 January 2013]
Mansergh, J. (2009) Tables with a Number Stick, Derby: Association of Teachers of Mathematics (available at http://www.youtube.com/watch?v=yXdHGBfoqfw) [accessed 2 January 2013]
Mulligan, J. and Mitchelmore, M. (1997) Young children's intuitive models of multiplication and division, Journal for Research in Mathematics Education, 28 (3) pp. 309-330

Nunes, T., Bryant, P. and Watson, A. (2009) Key Understandings in Mathematics Learning. London: Nuffield Foundation.

Pulley-Sayre, A. and Sayre, J. (2003) One is a Snail, Ten is a Crab. London: Walker Books Limited

Thompson, I. (2000) Mental calculation strategies for addition and subtraction - Part 2, Mathematics in School, January 2000, pp.24-26

Thompson, I. (2008) From counting to deriving number facts, In Thompson, I. (ed.) Teaching and Learning Early Number, 2nd edn. Maidenhead: Open University Press
Thompson, I. (2010) Getting your head around mental calculation, In Thompson, I. (ed.) Issues in Teaching Numeracy in Primary Schools, 2nd edn. Maidenhead: Open University Press
Threlfall, J (2002) Flexible mental calculation, Educational Studies in Mathematics, 50, pp. 29-42

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