Describes the results of part of a study into mathematical problem solving in secondary schools. Concludes that positive results were achieved, in part, as a consequence of the time that was spent in problem-solving lessons which allowed students to practice reading and working with word problems and working on basic material, particularly…

Suggests six characteristics of mathematical play. Analyzes the problem-solving process for the Six Circles and observations of students solving calculator and integration problems in relation to theories of play and cognitive gain. Discusses some difficulties of implementing a 'play' approach in the classroom and proposes further research…

In a future that is likely to be increasingly dominated by new technology, it is important to consider what mathematics is and how it might be taught. This article discusses these and related issues in the context of both universities and schools.