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PREFACE.

THE leading propositions in the science of Arithmetic are here presented in accordance with the methods in use in the classes of the Brothers of the Christian Schools. Those methods are the result of the united experience flowing from two centuries of teaching. Their chief merit is this: that they dispense with the old way of simply getting the rules by rote and then applying them; in the stead, they speak to the child's intelligence, and lead him up gradually to the understanding of the principles upon which the rules are based. Knowing both the rule and the reason for it, the child no longer labors in the dark, and the teaching of Arithmetic ceases to be mere machine-work. He may afterwards forget the rule; but having learned to reason the problem out independently of a set form of words, he finds no difficulty in reaching the solution of any ordinary case to which he may apply himself.

Indeed, there is no other efficient method of teaching Arithmetic than this of appealing to the child's intelligence. The correct solution of every problem is

an exercise of judgment. It is therefore a good means of mental discipline. Mere memory-work will not produce the same result; it will rather cramp and impede the other faculties. It is not the method of nature. From the moment the child has learned to speak he seeks to know the why and wherefore of things, and ceases to ask questions only when he becomes discouraged by the unsatisfactory answers of inconsiderate parents or incompetent teachers.

All practical life is rooted in number and calculation. Business is transacted upon a basis of counting. Hence the importance of teaching this subject according to approved and practical methods. For this reason, our SCHOOL'S GOVERNMENT lays special stress upon accurate rather than rapid calculation. It says: "In teaching Arithmetic it is of less importance to teach the pupil to calculate rapidly than to do so accurately." It furthermore insists, as a means of acquir ing habits of accurate thinking, that precise language be used in all explanations and calculations: "The pupils should be taught to make use of the correct terms, and never in their work to employ a useless expression." And again it says: "We should insist on the pupils being very exact in the recitation of definitions and principles." Finally, it counsels the exercise of the pupil's judgment in words to which nothing can be added: "After having read the problem to be solved, and written on the blackboard the conditions

it contains, the pupils should be required to give an account, first, of what is asked of them, or what they have to find out; second, of what they know in reference to it; third, of the operations required by the nature of the problem."

The following pages will be found to embrace these principles in every respect. The language is adapted to the young minds for which it is intended. The explanations aim at being simple. The solutions given are strictly in accordance with the definitions and principles laid down. But the teacher need not confine himself to the forms here given. After the pupil understands these, he may be shown other methods with profit.