ABSTRACT
Debates over the nature of good mathematics teaching are as old as teaching itself and, in spite of government pronouncements to have found the philosopher’s stone of perfect school organization and classroom pedagogy, are likely to continue for as long as schools exist. This is partly because there is no consensus about what it means to be a mathematically educated adult and partly because of the very nature of teaching and learning. Teachers and learners are individuals with their own backgrounds, personalities, and ambitions. Methods which work well for one teacher sometimes fail for another. The preferred style of learning for one pupil may be different from that of another. An approach which works well with most of a class may fail totally for a significant minority. Good teachers cater for the needs of individuals as well as groups by continuously modifying their approaches in response to the feedback they are receiving from learners.
