It would not be possible in the short time allotted to me for this paper to discuss any scheme of Educational Reconstruction which might appear to me as ideal. Indeed it is doubtful, notwithstanding the constant use which is made of the term, whether any reconstruction of our educational system, in the full sense of the word, is probable or even possible. But many reforms, some of them fundamental and far-reaching in their effects, are both possible and probable. It is with certain of these which, directly or indirectly, will materially affect the position of mathematics, that I propose to deal as far my limited time allows.