The last ten years have witnessed many changes in the methods employed in the teaching of arithmetic, which to a very considerable degree are the direct product of the activity and exertions of this Association. Two signal benefits may be mentioned ; firstly, uniformity of method in elementary processes has been secured ; and, secondly, the educational value of practical applications to mensuration, physics, etc., has received due recognition. The object of this paper is to raise for discussion a question of quite a different character.