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…

As part of an NCETM project, the author is involved with three local schools investigating how engaging in role play might aid children's mathematical development. The project embraces children ranging from part-time Reception to Y4. In this extract, two Reception-age girls, Rachel and Connie, are playing in their classroom spacecraft, and need a…

One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…

This article reports on work undertaken by schools as part of Qualifications and Curriculum Authority's (QCA's) "Engaging mathematics for all learners" project. The goal was to use in the classroom, materials and approaches from a Royal Institution (Ri) Year 10 master-class, "Number Sense", which was inspired by examples from…

Activities that are helpful for teachers and pupils alike in getting the feel for how big a million really is are suggested. (DT)

Counting and dividing activities for 5- and 6-year-old children, using base ten multibase arithmetic blocks, are described. (DT)

A discussion of intuition, doubt, and surprise in mathematics arising from a problem involving rational points and lines. (RS)

Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

A method is discussed for learning the multiplication tables that avoid repeating tables everyday or memorizing a large body of facts at the same time. (MN)

Children's responses to a discovery learning exercise are discussed. (DT)

Discusses numeracy strategy. Focuses on gaining insight into student understanding of number. Discusses the benefits of this long-overdue numeracy strategy. (ASK)

An activity providing practice with whole number addition and subtraction, as well as enlarging on the idea of numeration systems, is described. (DT)

The representation of equivalent fractions is traditionally illustrated by diagrams showing division of units into parts. A second approach using linear graphs is suggested. (SD)

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

A collection of brief articles on mathematics and teaching mathematics. (FL)