Of the "big four", division is likely to regarded by many learners as "the odd one out", "the difficult one", "the one that is complicated", or "the scary one". It seems to have been that way "for ever", in the perception of many who have trodden the learning pathways through the world of…

Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

This article is the first in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation." The Nuffield report is soundly based on research about how children learn some of the concepts involved in mathematics. In this series of articles the author takes key…

The supposed pre-eminence of an external examination can exert a disproportionate influence on a curriculum and the associated learning and teaching. Teaching can easily subordinate learning and understanding to curriculum coverage if the society develops a culture that appears to make such demands. This study focuses on Tanzania and provides the…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

Ever since "mental arithmetic" was updated to "mental calculation," official documents have succeeded in perpetuating several basic misconceptions and misunderstandings about this topic. This situation does not augur well for the successful teaching of mental calculation strategies to young children. In this article, the author…

The Williams Review (Dept. for Children, Schools and Families, 2008) is significantly important to all early years and primary educationalists, including those who are involved in teaching mathematics to the next generation of primary school teachers. The report, compiled as a result of this review, sets out the ways that children in primary…

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

An attitude survey and arithmetic tests were given to samples of students in order to quantify the benefit obtained from their use of calculators. Results showed that the use of the calculators does improve students' arithmetic performance with the less able students showing about twice the improvement of the more able. (MN)