Over the past three years this author has spent a good deal of time in primary classrooms, working with teachers on problem solving approaches to the teaching and learning of mathematics. He has also worked part-time on an initial teacher training course and an NCETM/Yorkshire Forward funded project entitled "Inspiring Mathematics Champions". Thus…

A discussion of what constitutes proof is given. Methods of teaching proof in a more intuitive and informal way than is usually done are suggested. (MK)

The author advocates a return to the teaching of logic in the public schools. Methods of lessening student difficulties in learning are highlighted and current school projects are discussed. (MP)

The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)

An example of an unrealistic "real world" problem from the National Assessment of Educational Progress highlights a comparison of school and "folk" mathematics. The failures of typical problems taught in school and some suggested remedies are featured. (MP) Aspect of National Assessment (NAEP) dealt with in this document:…

A description is given of materials produced by the Schools Council Project on Statistical Education. (MK)

The current state of computers in mathematics education is discussed. Aspects of new technology available to mathematics teachers include high resolution color graphics, the potential for making computer films, and the use of computers in working out or helping in problem solving. (MP)