Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references.…

Two alternatives are given to the decomposition and equal addition subtraction algorithms. (MK)

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)

The author presents and elaborates on a division algorithm devised by his 9-year-old son. (MK)

The importance of place value is discussed. Examples illustrating place value in addition and subtraction are given. (MK)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)

Basic computational problems admit several different solution algorithms. A student's choice of method may be related to personal characteristics which also bear on his ability to learn other mathematical techniques and theories. (SD)

Describes activities in a mathematics class for six-year-olds. The article makes several points, including: working independently is very absorbing; investigative work is as important as algorithms; and children working in groups can achieve more than even the brightest child working alone. (PK)

The first aim in school might be to help children become more aware of the algorithmic processes they use; then, ensure that they can devise algorithms and define them. Many examples of how these aims can be met are given, including the use of calculators and computers. (MNS)