Observations on the Study and Teaching oF Mathematics

Abstract

I have chosen for the subject of my discussion this evening the rather broad topic “The Study and the Teaching of Mathematics.” Doubtless some of you will think that either of these subjects is too broad to be covered in one evening's discussion, and that I should at least confine myself to one of them. But the two things are so closely intertwined that I do not wish to separate them. The study and teachmg of mathematics go hand in hand. Most of us who study mathematics do so under the direction and guidance of some more experienced person who has been along that way himself and who is, or should be, fully acquainted, not only with the pitfalls and the difficult spots in the path, but with the beautiful scenery on all sides which we can enjoy provided only it be pointed out to us. It is true that there are notable exceptions to this rule, the best known of which is perhaps that of Blaise Pascal. But not many of us are Pascals. In our study of mathematics the difficulties in our path would be so great and we would be so busily engaged in getting over them that we would scarcely have the time, even if we had the ability, to see the beauties that lie all around us. Hence we need a guide. For that reason I have had the temerity to include both the study and teaching of mathematics in the title of this discusion tonight.