In this book we have set out to ask fundamental questions about school mathematics in the next decade, and about what mathematics educators in every country should be doing now to prepare for it. These questions are not asked as part of an academic game. Given careful discussion, backed by appropriate research and experimentation, answers relevant to particular countries and to particular educational systems may be found to many of them.

Just as important, many of the questions can be posed, and answered, within the context of an individual school or classroom. As we stressed in the last chapter, it is the ‘lighthouse’ teacher, the one who in his or her own classroom demonstrates what is possible, who can indicate the way for successful large-scale developments. Changes based on experience have a far greater chance of success than do those based on hypotheses and pipe dreams!

Certainly the answers to the questions we pose cannot be found in the literature. We have drawn attention to many references, for it is important that we are aware of what has been done in the past, and of the experience that has been accumulated. It is not the mathematics educator's job continually to reinvent the wheel. Yet, as we have stressed so often, the challenges facing us today are of a novel type: society has changed and with it both the demands made upon us as mathematics teachers and also the technology we can utilise in meeting those demands. New problems will demand new responses.