My part in this symposium is to deal with the introduction of the fundamental ideas of algebra, as far as the stage usually known as the “Certificate stage”. As I shall attempt to show later, this is an extremely vague phrase, but it will be sufficient for the present to note that I am speaking of that part of algebra which is a compulsory subject for the great majority of secondary school pupils and that it is no part of my plan to deal with the needs of universities or any specialised developments of the subject. These needs, in my opinion, should not be allowed to influence unduly teaching at the “compulsory” stage.