It is commonly said at the present time that the opening of the twentieth century is a period of unusual advancement in all that has to do with the school. It would be pleasant to feel that we are living in such an age, but it is doubtful if the future historian of education will find this to be the case, or that biographers will rank the leaders of our generation relatively as high as many who have passed away, or that any great movements of the present will be found that measure up to certain ones that the world now recognizes as epoch-making. Every generation since the invention of printing has been a period of agitation in educational matters, but out of all the noise and self-assertion, out of all the pretense of the chronic revolutionist, out of all the sham that leads to dogmatism, so little is remembered that we are apt to feel that the past had no problems and was content simply to accept its inheritance. In one sense it is not a misfortune thus to be blinded by the dust of present agitation and to be deafened by the noisy clamor of the agitator, since it stirs us to action at finding ourselves in the midst of the skirmish; but in another sense it is detrimental to our progress, since we thereby tend to lose the idea of perspective, and the coin comes to appear to our vision as large as the moon. In considering a question like the teaching of geometry, we at once find ourselves in the midst of a skirmish of this nature. If we join thoughtlessly in the noise, we may easily persuade ourselves that we are waging a mighty battle, fighting for some stupendous principle, doing deeds of great valor and of personal sacrifice. If, on the other hand, we stand aloof and think of the present movement as merely a chronic effervescence, fostered by the professional educator at the expense of the practical teacher, we are equally shortsighted. Sir Conan Doyle expressed this sentiment most delightfully in these words: The dead are such good company that one may come to think too little of the living. It is a real and pressing danger with many of us that we should never find our own thoughts and our own souls, but be ever obsessed by the dead. In every generation it behooves the open-minded, earnest, progressive teacher to seek for the best in the way of improvement, to endeavor to sift the few grains of gold out of the common dust, to weigh the values of proposed reforms, and to put forth his efforts to know and to use the best that the science of education has to offer. This has been the attitude of mind of the real leaders in the school life of the past, and it will be that of the leaders of the future. With these remarks to guide us, it is now proposed to take up the issues of the present day in the teaching of geometry, in order that we may consider them calmly and dispassionately, and may see where the opportunities for improvement lie.