(b) To find the time when the principal, interest, and rate are given. (c) To find the rate when the principal, interest, and time are given. (d) To find the principal when the amount, rate, and time are given. Eighth Year. The work of this year will be outlined in detail hereafter. LOW EIGHTH. 1. Measurement of angles, lines, surfaces, solids, and capacity, using metric units. 2. Weights including specific gravity. 3. Construction of plane and solid figures, and development of surfaces of solids. 4. Building cubes and extraction of Cube Root. 5. Simple work in Concrete Geometry 6. Problems in Surveying. HIGH EIGHTH. 1. Use of letters in stating and solving problems. 2. Percentage and problems in Interest. 3. Longitude and Time. 4. Type problems. (a) Sawing wood. (b) Working problems. 5. Review. 58 COURSES IN MATHEMATICS. ARITHMETIC AND METHODS. The students who come to the Normal from the High School, as a rule, have not studied Arithmetic since leaving the grammar grades. They therefore need to study the subject from the standpoint of one who has a knowledge of Algebra and Elementary Geometry and who is able to comprehend the underlying principles. Methods are best learned through the study of the subject under a skillful teacher, and are useful only to the teacher who understands the subject. Hence, the course embraces a study of the subjectmatter of Arithmetic, a brief course in Concrete Geometry preparatory to teaching mensuration, and the discussion of methods. ADVANCED ARITHMETIC METHODS. Second Semester. This course includes a study of the history of Arithmetic and its evolution, and a study of the methods of the best authors and writers on the subject. A course of study is outlined for teaching different grades, and topics are worked out. Students who complete this course are prepared to supervise the teaching of Arithmetic. CONCRETE GEOMETRY. The course in Concrete Geometry includes:— 1. Measurements-Finding heights and distances of accessible and inaccessible objects, and drawing to scale. 2. Construction of geometric figures and deducing rules for areas. 3. Development of surfaces of simple solids and construction of solids, using cardboard. 4. Mensuration of surfaces and volumes of solids. The educational value of the subject will be emphasized. ADVANCED ALGEBRA. Second Semester. This course consists of the following: 1. Reviews: (a) Factoring, Factor Theorem, Remainder Theorem, Solution of Equations of Factoring; (b) Theory of Exponents and Radicals; (c) Quadratic Equations of one unknown, and of two or more unknowns. 2. Demonstration of principles and rules. 3. Ratio and Proportion, Variation, Progressions, Inequalities, Variables and Limits, Logarithms, and Undetermined Coefficients. SOLID GEOMETRY. 2 br. First Semester. This course is a study of straight lines and planes, polyhedrons, cylinder, cone, and sphere. The student is required to form clear conceptions of the various figures to master the proposition, and to be able to apply the principles in concrete examples. TRIGONOMETRY. 3 hr. First Semester. In Trigonometry the student is required to study the functions of any angle, of the sum and the difference of two angles, of multiple and half angles; to use natural and logarithmic functions; to solve plane triangles; and to measure height, distance, and area. The functions are studied as ratios, and are afterwards graphically represented in order to aid in the recognition of their signs and limiting values. The best forms are followed, and the formulas are SO arranged and studied that the student will be able to recall. them readily. Manual Training Training Department The aim of manual training in primary and grammar schools is to aid in the general educational development of the child, and, while it also has an economic value, this is, however, only a resultant of the child's broader education. The mental activity of the child is so wrapped up with, and so dependent upon, his physical activities, that a proper exercise of the body, and especially of the hand, is essential to his mental development. The education of man in general is a resultant of the activity of the human hand and mind working in conjunction. Neither of these factors has been of more or less importance than the other. The child, in his world of existence, is continually illustrating this important fact. It is a common saying that the child, without positive instruction, acquires more education during the first six years of his life than during any other period of the same length of time. This phenomenal development is wrought by bringing him into contact with the materials of the physical world, and with hands and mind he does the rest. The kindergarten aims to assist this natural development by bringing the child into touch with a larger world, and manual training aims to continue it by the same process. The burden of this work has fallen upon the school, because the child has been removed from participation in the industrial life of the race. Manual training has three separate functions in the education of the child. The first is to unfold his potential mind. The second is to humanize him. (60) The third is to train his hand technically. The first is the most important of the three, since it is fundamental to the others, and in fact to all mental development. As suggested above, the potential mind is the heritage of the race; it is the resultant of the racial activities of both hand and mind, and, therefore, its unfolding can be brought about only by the combined activity of hand and mind. The mechanical projects used in this unfolding process are immaterial, providing the child makes the work a part of his life work, and providing he does the mental part of it himself. Ideas can not be engrafted. The child can, however, be placed in a position to obtain them for himself. In fulfilling the first function the second function is to some extent incidentally covered. In the first four grades little or nothing results in a technical way from this work. The child, at this age, has neither the mental nor the physical development necessary to a technical training of the hand. In the latter part of the fourth or the earlier part of the fifth grades, however, we find that the child's control of the hand begins to develop more rapidly. He also begins to show more interest in the details of the work. From the standpoint of culture the second function is more important than the third, since it is the foundation necessary to a higher appreciation of the humanities. The child should be brought into contact with the home of the past and its industries, so that he may be able to understand our past history and appreciate such literature as may have a remote setting. As far as possible these experiences should be given the child before he is introduced to literature or history, otherwise the highest appreciation of these subjects will not be gained. To illustrate, the child will be very much interested in constructing a wigwam if he wishes to use it as a |