Mathematics–algebra, geometry, and the more advanced kinds of arithmetic–will now enter into the syllabus and take its place as what it really is: not a separate “subject” but a sub- department of Logic. It is neither more nor less than the rule of the syllogism in its particular application to number and measurement, and should be taught as such, instead of being, for some, a dark mystery, and, for others, a special revelation, neither illuminating nor illuminated by any other part of knowledge.
History, aided by a simple system of ethics derived from the grammar of theology, will provide much suitable material for discussion: Was the behavior of this statesman justified? What was the effect of such an enactment? What are the arguments for and against this or that form of government? We shall thus get an introduction to constitutional history–a subject meaningless to the young child, but of absorbing interest to those who are prepared to argue and debate. Theology itself will furnish material for argument about conduct and morals; and should have its scope extended by a simplified course of dogmatic theology (i.e., the rational structure of Christian thought), clarifying the relations between the dogma and the ethics, and lending itself to that application of ethical principles in particular instances which is properly called casuistry. Geography and the Sciences will likewise provide material for Dialectic.
But above all, we must not neglect the material which is so abundant in the pupils’ own daily life.
There is a delightful passage in Leslie Paul’s “The Living Hedge” which tells how a number of small boys enjoyed themselves for days arguing about an extraordinary shower of rain which had fallen in their town–a shower so localized that it left one half of the main street wet and the other dry. Could one, they argued, properly say that it had rained that day on or over the town or only in the town? How many drops of water were required to constitute rain? And so on. Argument about this led on to a host of similar problems about rest and motion, sleep and waking, est and non est, and the infinitesimal division of time. The whole passage is an admirable example of the spontaneous development of the ratiocinative faculty and the natural and proper thirst of the awakening reason for the definition of terms and exactness of statement. All events are food for such an appetite.