The main object of this address is not so much to express my own views on the matter, as to stimulate discussion among the many experienced teachers here, which may encourage the inexperienced, or timid, teacher to loose his grim grip on the printed examination syllabus, and refresh himself and his pupils by occasional profitable digressions from the printed path.

By “ anticipating the work of the Sixth Form ” I am assuming that we mean providing the pupil with such mathematical training in the main school that he reaches the Sixth Form with a mind which is eager, alert, and inquisitive, and with a sufficient equipment of mathematical knowledge to enable him to explore some of the mathematical realms which are awaiting his attention.