Prologue

Our panel's topic is one of the hotly discussed national issues: K-12 mathematics instruction. Mathematics is an important thinking tool, being

• • a way of looking at and making sense of the world;

• • a way of, for example, checking out the validity of claims made by advertisers or politicians; • a way of reasoning.

Certain mental habits, observable in young children, should be cultivated in school rather than inhibited or allowed to atrophy.

Mathematics is particularly well suited for exercising mental muscles. Even those who do not achieve virtuosity can find that the psychological rewards of feeling mentally fit and gaining control of one's reasoning powers are just as great as the rewards of physical fitness and control of one's body.

Classroom teachers, always considered essential in the education of our children, are now expected to play even more crucial roles. Reformers eager to save public education see teachers as “agents of change”. Advocates of children who see so many deprived of functioning families want teachers to act in loco parentis. Future employers have discovered that they no longer need human robots but flexible thinkers who can work in teams to solve problems with tools appropriate to the task. They are joining educators (who want to build communities of future adults able to cope with the demands of the next century) in viewing teachers as coaches in the acquisition of skills, and as guides in discussions of conjectures and verifications of results. Our demands on teachers are overwhelming indeed.