The Fibonacci series has been studied since it was first described by Leonardo of Pisa--Fibonacci--in 1202. It begins with the sequence 1, 1, 2, 3, 5, 8... Each succeeding number is the sum of the previous two. In number theory courses, students are introduced to the concept of modulo arithmetic, sometimes called "clock" arithmetic. In modulo…

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…

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…

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…

In this article, the author explores the concept of "moving one place to the left." A recent investigation by Thompson and Bramald explored the relationship between young children's understanding of place value and their ability to add two-digit numbers. The study took the form of a series of one-to-one interviews with a sample of 144 children…

Operations with zero and concepts associated with the use of zero are examined in some detail. Historical practices concerning zero are discussed. (CT)

Evaluates the National Numeracy Strategy (NNS) as a successful framework for promoting confidence and competence with numbers and measures, an understanding of the number system, a repertoire of computational skills, and the ability to solve number problems in a variety of school contexts. Suggests taking steps to change children's mathematical…

A series of puzzle-type activities combining arithmetic reasoning and geometric figures is described and illustrated. (SD)

Some proposals on how children may learn the basic multiplication facts through practical activities based on the rectangle. (MM)

After noting that accurate calculation is not the only reason for teaching arithmetic, innovative activities providing practice with basic facts, pattern spotting,'' and exploration are presented. (MS)

Beginning with peg manipulation the author sets up a different multiplication system and set of primes. (JM)