AbstractIn recent years much has been written concerning the widening gap between the newer developments in mathematics and the traditional mathematics taught in secondary' schools. Not unnaturally, leading scholars in mathematics have looked at the school programmes and found them wanting. These people have considered that mathematics curricula should be reformed so as to bring the subject matter in line with recent developments. Professional educators, many of whom are prepared to take an active part in shaping the future policies of school programmes in mathematics, find themselves faced with the problem of translating the suggested reforms into action within classrooms. Thus, while it is recognized that the mathematicians are in the best position to determine the structure of the discipline, it is the professional educators' responsibility to prepare good school programmes in mathematics.