Overview

In collaboration with Leiden University

Children find division the hardest operation to use for problem solving.

This project collected evidence of children's strategies for division and compared their ways of working with those of Dutch children taught using the Realistic Mathematics Education (RME) approach.

Findings include:

• There is a gap between pupils' mental methods and the standard written methods they are taught.
• The traditional algorithm which is widely used by the English pupils results in less progress than the Dutch approach using written methods based explicitly on repeated subtraction with'chunking' to achieve efficiency.
• Flexibility in choice of strategies is more important than the exclusive use of one sophisticated strategy. This flexibility is impaired by the early introduction of the written algorithm.
• English pupils are generally very poor at using written recording to help them to keep track of their methods.

Related Publications

Books:

Anghileri, J. (ed.) (2001) Principles and Practice in Arithmetic Teaching: Buckingham: Open University Press

Anghileri, J. (2000) Teaching Number Sense London: Continuum

Related articles, chapters and other book contributions:

Anghileri, J., Beishuizen, M. and van Putten, K. (in press) From Informal Strategies to Structured Procedures: mind the gap! Educational Studies in Mathematics

Anghileri, J. (2001) 'A Study of Progression in Written Calculation Strategies for Division' Support for Learning 16 (1) 17-23

Anghileri, J. (2001) 'Development of Division Strategies for Year 5 Pupils in Ten English Schools' British Education Research Journal 27 (1) 85-103

Anghileri, J. (2001) Mental and Written Calculations Methods for Multiplication and Division. In Askew, M. and Brown, M. Teaching and Learning Primary Numeracy: Policy, Practice and Effectiveness. A Review of British research for the British Educational Research Association in conjunction with the British Society for Research in the Learning of Mathematics Notts: BERA

Anghileri, J. (2000) 'Multiplication and division' in QCA Teaching Mental Calculation Strategies: Guidance for Teachers at Key stage 1 and Key Stage 2. London: QCA

Anghileri, J. (2000) 'Division with Year 5' in M. Askew (ed.) Numeracy Lessons (2) London: BEAM

Anghileri, J. (1999) 'Issues in teaching multiplication and division' - Chapter 15 in Ian Thompson (ed.) Issues in Teaching Primary Number Buckingham: Open University Press

Anghileri, J.(1999) 'Language, Arithmetic and the Negotiation of Meaning' In DfEE National Numeracy Strategy: Guide for your professional development: Book 3 London: DfEE

Beishuizen, M. and Anghileri, J. (1998) 'Which mental strategies in the early number curriculum? A comparison of British ideas and Dutch experiences' in British Education Research Journal. 24 (5) 519-538

Anghileri, J. (1997) 'Using Counting in Multiplication and Division' in Ian Thompson (ed.) Teaching and Learning Early Number Buckingham: Open University Press

Anghileri, J.(1991) 'The language of multiplication and division' in Durkin K. and Shire B. (eds) Language in Mathematical Education Buckingham: Open University Press

Anghileri, J. (1989) 'An Investigation of Young Children's Understanding of Multiplication', Educational Studies in Mathematics 20:367-385.

Further Publications - conference proceedings, professional journals etc.:

Anghileri, J. (2001) 'What are we trying to achieve in teaching standard calculating procedures'. In van den Heuvel-Panhuizen (ed.) Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (PME25) Vol 2 pp41- 49 Utrecht: Freudenthal Institute

Anghileri, J., Beishuizen, M., Van Putten, K. and Snijders, P (1999) 'A comparison of English and Dutch year 5 pupils' calculation strategies for division'. Proceedings of the 4th British Congress on Mathematics Education Northampton

Anghileri, J. and Beishuizen, M. (1998) 'Counting, Chunking and the Division Algorithm' Mathematics in School 27(1) pp2-4 January 1998

Anghileri, J. and Askew. M. (1998) National Numeracy Project Training Manual : Written Calculations: Multiplication and Division London: DfEE

Anghileri, J. (1998) 'A discussion of different approaches to arithmetic teaching'. In Olivier, A. and Newstead, K. Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (PME22) Stellenbosch South Africa :University of Stellenbosch

Anghileri, J. (1996) 'Negotiating Meanings for Division' Mathematics in School 24,3

Anghileri, J. (1996) 'Language and Strategies in Children's Solution of Division Problems' Proceedings of the BSRLM Conference, Sheffield

Anghileri, J. (1995) 'Division and the role of language in the development of solution strategies' Proceedings of the British Congress of Mathematical Education - BCME3 Conference, Manchester Business School 13-16 July 1995. (pp8)

Anghileri, J. (1995) 'Children's Finger Methods for Multiplication' Mathematics in School 24,1

Anghileri, J.(1995) 'Language, Arithmetic and the Negotiation of Meaning' For the Learning of Mathematics 21,3 10-14

Anghileri, J.(1994) 'Language and the Role of the Teacher' in Proceedings of the Joint Conference: British Society for Research into Learning Mathematics/Association of Mathematics Education Tutors Northampton 13th-14th May 1994 pp1-6

Anghileri, J.(1991) 'Division' Proceedings of the 2nd British Congress on Mathematics Education (BCME2) Conference Loughborough.

Anghileri, J. (1986) 'Children's Difficulties with Multiplication'. Proceedings of the BSRLM Conference, Exeter, Sept. 1986

Anghileri, J. (1985) 'Young Children's Understanding of Multiplication'. Proceedings of the British Society for Research into Learning Mathematics, Canterbury, Nov. 1985

Anghileri, J. (1985) 'Should we say times?' Mathematics in Schools May 1985.

Project Directors

Julia Anghileri - jea28@cam.ac.uk

Additional Publications

Anghileri J, & Baron, S. (1999) Playing with the Materials of Study: Poleidoblocs, Education 3 - 13 27,2: 57-64

Anghileri, J. and Baron, S. (1998) Learning with 3-D Shapes, Child Education February 1998

Anghileri, J. and Baron, S. (1997) Playing and learning with Poleidoblocs, Mathematics Teaching 161: 48-51 Dec 1997 ATM

Coltman, P., Anghileri, J. & Petyaeva, D. (2002) Scaffolding learning through meaningful tasks and adult interaction. Early Years 22 (1) 39-49