The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

In a recent edition of "Mathematics Teaching" Midge Pasternack argued the case for the use of the 0-99 square with young children rather than the ubiquitous 1-100 square. In this article, the author would like to take the opportunity to mount a defence in favour of the much maligned 1-100 square. His main criticism of the 0-99 square (apart from…

A square lattice is used to generate classroom activities, such as counting the number of squares in a lattice of a given size. (MP)

Procedures using calculators are described for determining the recurring sequence of digits in the decimal representation of numbers of the form 1/n. (MN)

After stating that almost any topic could be generalized, the author was challenged to generalize the topic of polyominoes. His response is presented in this article. (SD)

With the advent of computers and electronic calculators, the role of logarithms in the curriculum is changing. An intuitive approach to logarithms, stressing the notion of isomorphism, is discussed. (SD)

Described are results obtained by students investigating double-diagrams, including discoveries of properties and accompanying proofs. (MP)

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (SD)

The use of dice and dominoes in the classroom is discussed as leading from counting activities to pattern recognition and discovery learning. (MP)

Four categories of abuses are discussed: calculations, games and puzzles; mystical button pushing; and checking answers. Useful activities are illustrated for the categories of calculations, patterns, exploration, applications, and new content. (MP)

Using the overhead projector, or overlays on an original pattern, a variety of tessellations can be generated. Several illustrations are included. (SD)

Examples of CLOPAK Networks, an approach to covering the plane with symmetrically arranged, close-packed geometric shapes, are given. Implications for the place of networks in geometry instruction are discussed. (MN)