ABSTRACT
The present chapter is offered as a synthesis of ideas that have been discussed previously in journal articles (Backhouse, 1978; Buxton, 1978b; Byers & Herscovics, 1977; Skemp, 1976; Tall, 1978) and at a meeting of the British Society for the Psychology of Learning Mathematics. I am much indebted to all of these contributors for their stimulating interchange of ideas.
