Julia Anghileri

Which Mental Strategies in the Early Number Curriculum? A Comparison of British Ideas and Dutch Views

Abstract Mental arithmetic has recently gained a higher profile in primary mathematics. The question then arises whether mental strategies should be left to spontaneous development or should be taught in some didactic order? In reaction to a School Curriculum and Assessment Authority (SCAA) discussion paper and other publications a comparison is made between British ideas and Dutch views. In the Netherlands the Realistic Mathematics Education theory has, since the 1980s, inspired textbook design and teaching practice, but also discussions on mental mathematics. Better balancing between ‘mental recall and mental strategies’ led to an improved National Programme (1990) and a second generation of revised textbooks. A great difference is the radical choice for postponing (formal) place value and written algorithms and building first on pupils’ (informal) mental strategies. This principle of ‘progressive mathematisation’ is developed further with the empty number line as a new model for mental strategies up to...

From Informal Strategies to Structured Procedures: mind the gap!

This paper explores written calculation methods for division used by pupils in England (n = 276) and the Netherlands (n = 259) at two points in the same school year. Informal strategies are analysed and progression identified towards more structured procedures that result from different teaching approaches. Comparison of the methods used by year 5 (Group 6) pupils in the two countries shows greater success in the Dutch approach, which is based on careful progression from informal strategies to more structured and efficient procedures. This success is particularly not able for the girls in the sample. For the English pupils, whose written solutions largely involved the traditional algorithm, the discontinuity between the formal computation procedure and informal solution strategies presents difficulties.

Development of Division Strategies for Year 5 Pupils in Ten English Schools

A division test involving both context and bare problems was taken by year 5 pupils in 10 different schools at two points in the school year to identify changes in approach as the standard algorithm was introduced. Increase in the use of the standard algorithm led to many errors and only half of the attempts to use this strategy in the second test were successful. More successful were efficient informal strategies although difficulties in structuring a written record of such strategies were evident. Overall 52% of pupils gained a higher score in the second test while 48% remained the same or performed less well. In comparing context and bare problems, development of a successful strategy was most marked in problems that were given a context. In both tests girls performed better than boys with better improvements over the two tests.

A study of the impact of reform on students' written calculation methods after five years' implementation of the National Numeracy Strategy in England

The National Numeracy Strategy was introduced in England in 1998 to reform mathematics teaching in all primary schools. The strategy has been widely implemented and this paper investigates some of the changes that are evident after the first five years. Reporting a comparison between studies in 1998 and 2003 of pupils’ calculating strategies for division, this study shows a small improvement overall but lack of the uniformity that may be expected from a national Strategy. Structured written recording, progressively developed from more intuitive understanding, was not evident in much of the pupils’ work. In some schools there was success with the new ‘chunking’ written method, identified in the Framework as ‘informal’, while in less successful schools, pupils continued to use various informal and inefficient strategies. While in 1998 success of boys and girls was not significantly different, in 2003 the boys were more successful. The boys made more use of informal working and mental strategies, while the girls relied on more structured written methods and in the schools where girls did better they used mostly the chunking algorithm.

A study of progression in written calculation strategies for division

Many readers will relate, not only as teachers, but also from their own memories of childhood and the rules by which pupils were then taught, to the challenge Julia Anghileri discusses in this article. Her research on effective and ineffective strategies for division sheds light on the problem of how to develop ‘number sense’ in pupils and a thorough understanding of the calculation methods they use.

Playing with the materials of study: Poleidoblocs

Young children learn through practical experiences. The building bricks known as Poleidoblocs present opportunities to use and characterise a set of related 3-D mathematics shapes. This study identifies ways in which geometric awareness develops through free play and structured tasks, but points to limitations in learning without teacher interaction.

iPRISM — Interactively promoting research in mathematics

If children are to benefit from research in Mathematics Education then dissemination needs to reach their teachers. It is undoubtedly valuable to have peer reviewed articles in academic journals but the nature of such publications often makes them inaccessible, or at least inconvenient, for these teachers. This report identifies an innovative approach to dissemination of research through an interactive CD-rom and an initial evaluation by practitioners.