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SAMUEL HAMILTON, PH.D., LL.D.
THE “ Essentials of Arithmetic " consists of two books, which cover the arithmetical work from the second to the eighth year.
The two important ends sought in the teaching of arithmetic are (1) to give the pupil such a mastery of number combinations and processes as will enable him to perform with accuracy and speed all common numerical operations; and (2) to train him in the skillful application of these processes to the problems that he is likely to meet in his daily experiences. This series has aimed to lay equal stress on both these important phases of arithmetic.
The frequent drills in numbers in their abstract relations develop habits of accuracy and speed. The motivation of the drill work, especially in the earlier grades, is secured by means of interesting number games.
The problems have been framed with a view to the pupil's interests. At first they deal entirely with his life at home, at school, on the street, and in the playground; but gradually they reach out to include his contact with the larger spheres of social and industrial life. The problems are of two types, — first the isolated problems, which provide direct application of a principle to some need or experience of the pupil; and, second, groups of related problems, called “Everyday Use of Numbers,” which center about an idea or a situation in which the pupil feels a vital interest. These related problems serve as a review of various principles previously taught. The problems are all real because they are true to life. They carefully avoid impractical conditions and all questions that have no relation to common experience.
The pupil's self-activity is utilized in constructive work and in the framing of original problems. His initiative is exercised by leading him to discover many arithmetical truths for himself. The importance of the correct interpretation of problems and of the choice of the best methods for their solution is emphasized.
The “First Book” covers the work that is usually taught in the second, third, fourth, and fifth years, each chapter representing one half year's work. The second year's work, contained in Chapters I and II, may be used as review for classes that begin the use of a text-book in the third year. Chapters III and IV comprise the third year's work, Chapters V and VI, the fourth year's work, and Chapters VII and VIII, the fifth year's work.
The effort to follow prevailing prices has been limited by their rapid fluctuations and by their variation in different parts of the country.
Teachers should encourage pupils occasionally to substitute current local prices, thereby varying the problems in the book.