FOREWORD THE purpose of these bulletins is to give to the teachers of -- the various departments of the Normal School a comprehensive view of one another's work, which may serve as a basis of correlation to give our student-teachers and graduates a definite outline of the various subjects as taught in the Training Department, and to acquaint the public generally with the theory and practice of the school. Other bulletins will be issued from time to time, and will consist largely of outlines of the work actually being done in the Training Department, which has been arranged with special reference to the needs of the schools of the State. The succeeding numbers will treat of History and Geography, Reading and Literature, Drawing, Language, and Nature Study. This Bulletin will be mailed to any address on receipt of ten cents. Address, State Normal School, San Jose, California. 119992 OF THE UNIVERSITY OF CALIFORNIA Arithmetic If properly taught, arithmetic, besides fitting the boy or girl for performing the necessary calculations in the ordinary business relations, will also perform an important educational office. Besides the acquisition of knowledge, education should give three things: Mental attitude, mental strength, and good mental habits. To each of these arithmetic contributes no small share. It tends to give stability and balance, and a feeling of certainty; it trains in thinking and in the concentration of thought; and it aids in the formation of habits of neatness, conciseness, system, and investigation. It should rest on a basis of intelligence, and, as far as possible, should appeal to the understanding. This is possible to a much greater extent than is generally supposed. In arranging the course given below, the following points have been kept in mind: I. The How and the What It is one thing to be able to perform a given operation; it is quite another to determine in a given instance what operation should be performed. A pupil may be able to perform all the arithmetical operations, yet be helpless in an attempt to deal with a given problem. The how deals with the mechanics of number and may be mastered by rule. The what has to do with mind and can be mastered only as the mind grows. Any rule for this work would defeat the purpose of arithmetical study. Arithmetic does not need to wait on this growth. By well arranged exercises and proper methods it may and should minister to it. 5 2. Learning and Fixing Facts It is an easy matter to learn that 6 times 7 gives 42. This may be done with or without the aid of objects. Το fix this fact in the mind so that given 6 times 7, the 42 will immediately present itself, requires skilful teaching, and more or less frequent repetition. In order to be effective, this repetition should be methodical and should require the present active mind. It should require the use of the eye, the ear, and the vocal organs, and thus reach the mind through various avenues. It may be greatly aided by the proper use of rhythm. It should be accompanied by exercises requiring the immediate use of the knowledge obtained. 3. Accuracy, Skill, Speed, Independence No effort should be spared that the pupil shall get right results at first, for first impressions are apt to be deep, and if wrong, they are hard to overcome. Skill comes through practice in the use of good methods. The pupil is trained from the beginning in the best methods. Interested mental activity can be maintained without tiring, where dead repetition would result in fatigue. Where wise and economic methods are used, practice will produce speed. The wise teacher seeks to "liberate" her pupils-to make them self-reliant, and to lead them to a point where they can proceed without further assistance. When a pupil has grasped the law on which a process depends, he is ready to become his own master so far as that process is concerned. It is the teacher's duty to lead the child to discover the law, and to fix that law by appropriate exercises. 4. Avoiding Bad Habits Most bad habits in the handling of numbers are formed in early school years, and defy the efforts of later years to overcome them. The counting habit is formed because |