teach two years of algebra before we know the definition of an angle or how to handle ordinary geometric facts which occur simultaneously with the algebra? Try as we may, we cannot find an industry or an applied science where mathematics stands out in definite factors as we teach it in the school. Do we not find in this fact sufficient reason for the inability of the student to recognize fundamental elements? On the other hand, we cannot cast aside all mathematical sequence and merely proceed with the solution of problems. For a number of years, books of shop problems and applied mathematics have been coming into the market every few months; these books have in general gone too far to the other extreme and have ignored all mathematical sequence. This, again, causes confusion on the part of the student, because of introducing problems before he is ready for them. Our object must be, then, to formulate a sequence of mathematics and applied problems, so as to develop the subject in a rational way. The following lantern slides will, to some extent, give an idea of the outline of mathematics as it is being taught at the Cass Technical High School and in several high schools of similar type. A series of textbooks has been published recently, which have in general been followed in carrying out this course of study. A large amount of supplementary material has, however, been introduced, in order to meet our own particular problem. Incidentally, the writer believes that this supplementary work, in all courses, is one of the most worthwhile features. of reorganized education at the present time. MATHEMATICS I FIRST TEN WEEKS 1. Solution of simple equations. 2. Evaluation of algebraic expressions. 3. Angles. a) The use of the protractor. b) Definitions and equations involving supplementary, complementary, vertical angles, and the angles of a triangle. 4. Positive and negative numbers. By this arrangement of mathematics, we have in no way disarranged the mathematical sequence, and have paralleled the work in mechanical drawing and the shops. The knowledge of angles which the student has gained in the mathematics department makes it possible for those teaching mechanical drawing to omit geometric drawing and devote themselves entirely to their own subject. MATHEMATICS I SECOND TEN WEEKS 1. Addition, subtraction, multiplication, and division. 2. Evaluation of formulae. 3. Lever problems. 4. Graphing data. Problems similar to the following are given under this group: 1. The area of a triangle is expressed with a formula A=ba. Find A, if b=82R.D. 2. Evaluate 2ab+4bc-5cm. If A = 5, b=3, c=10, m=4. 3. Find the time of vibration of a pendulum 8 feet long. T=TL/G. Where = and G=32. 4. Find the area of a triangle whose sides are 5′, 12′, and 13′ if A=s(s—a) (s—b) (s-c). The sides are a, b, and c. s= abc 2 5. A wheelbarrow is loaded with 45 bricks, averaging 6 pounds each. What force will be required to lift the load, if the wheel is 4 feet from the end of the handles and 2 feet from the center of the load? Added to the work indicated in the problems shown above, from two to three weeks at the close of the semester are devoted to proportions. 1. If gunpowder were composed of 4 parts by weight of saltpeter, 2 parts of sulphur, and 3 parts of charcoal, how many pounds of each would there be in 200 pounds of gunpowder? 2. What percentage of evaporation is necessary to change a 6 per cent solution to an 8 per cent solution? 3. A motor running at 875 R.P.M. has a 10" driving pulley. What must be the size of the lineshaft pulley if it is driven at 180 R.P.M.? Let x=diameter of lineshaft pulley. (The speeds of two belted pulleys are inversely proportional to their 1. The diagonal of a square is 12". Find its perimeter. 2. The side of an equilateral triangle is 10 inches. Find its area. 3. The side of a regular hexagon is a. Find its area. This arrangement of problems and mathematical facts not only establishes fundamental facts of mathematics, but gives the information which is required by mechanics in all building and metal trades and lays a foundation for the mathematics of the science courses. If at the end of the first year of school a student is compelled to drop out, he will find that he is prepared to handle quickly and intelligently all the ordinary problems of the machine shop, the plumbing shop, sheet metal work, and the building trades. This is a decided advantage even aside from the fact that the mathematics parallels his school work. At the beginning of the second year, the student in the technical high school begins his work in chemistry. The instructor in the chemical laboratory assumes that the student can handle proportions. If he cannot, then the student is sent to the mathematical department to obtain the required information. Relieved, as they are, from the necessity of teaching mathematics with the chemistry, considerable more work can be done in the laboratories. The writer well remembers his own laboratory instructors who complained that they could not teach physics to any advantage because they were compelled to teach the subject of mathematics. MATHEMATICS III FIRST TEN WEEKS 1. Problems involving three unknown quantities. 2. Fractions. 3. Factoring and its applications. 4. Quadratic equations and their graphs. MATHEMATICS III SECOND TEN WEEKS 1. Radicals. 2. Square root. 3. Applications of square root. 4. Dimensions and areas of polygons. MATHEMATICS IV TWENTY WEEKS 1. Congruency of rectilinear figures and circles. 2. Ratio, proportion, similar triangles. 3. The trigonometry of the right triangle. Natural function. MATHEMATICS V TWENTY WEEKS Measurements of angles. Similarity and proportionality in circles. Inequalities. Areas of polygons. Regular polygons and circles. MATHEMATICS VI TWENTY WEEKS Solid geometry, plane trigonometry, logarithms. Problems involving: 1. Lateral area, total area, and volume of: a) Prisms. b) Pyramids. c) Cones. d) Frustums of pyramids and cones. 2. Areas of: a) Lunes. b) Zones. c) Spherical triangles. d) Spherical polygons. 3. Volumes of: a) Spherical wedges. c) Spherical segments. 4. Areas and volumes of spheres. THE RESPONSIBILITY OF THE TEACHER WITH REGARD TO THE TEACHING OF SEX HYGIENE RALPH E. BLOUNT, INSTRUCTOR IN PHYSIOLOGY, WALLER HIGH SCHOOL, CHICAGO, ILL. Every day the newspapers thrust before us tragedies whose plots turn on sex life. When we stop to think, we know that these tragedies are only a small fraction of the sad scenes with identical plots that are enacted on the stage of life with only private spectators. People young and old have need enough of guidance in matters of sex. The need has long been recognized. The effort to meet it is comparatively new and very inadequate. In fact, I know of no place where there is systematic, well-organized means of conveying the information and awakening the moral earnestness needed to bring mankind to a wholesome, happy sex life. The home has its part in this work, and the school has its part. Neither can take the place of the other. The fact is that parents and churches have always reserved this function to themselves-and have never performed it, and there is no hope that during the next generation at least they will adequately meet the need. Therefore the school must undertake the work, not to the exclusion of the parent, but filling in the blank left by the negligent parent, and supplementing the training given by the careful father and mother. The recent revelations of the magnitude and the horrors of the traffic which caters to the sex passion, and the discoveries of the prevalence of venereal diseases and their deep, race-destroying effect, have driven into our minds as nothing before ever did the urgency of action to save the life of the race. The danger which menaces the youth does not appeal to the parent as it does to the teacher. The parent, even if he knows how widespread the evil is, how inimical to every youth, says to himself: "Yet many escape. My son, my daughter will be one of these." This fatuous hope mollifies the feeling of urgency, and the parent lets the matter go. The impelling force that drives the teacher to action is the terror of disease and vice that threatens to destroy the children under his care. But the cry of warning against this evil is only a portion of his task. The teacher must establish in his pupils the right attitude of mind toward matters of sex-respectful but not prudish, candid but not flippant. He must give to them all the information that their natural curiosity or the needs of their life demand. He must hold before them the ideals of a clean and wholesome relation between boys and girls, young men and young women. He must present the ideals so skilfully that the pupils will accept them as controlling motives in their lives. He must repress the uncouth familiarities that mark the conduct of ill-bred boys and girls and explain to them the deep respect that lies at the foundation of more courteous behavior. He must teach his pupils that the reproductive function involves the most sacred duty to the whole human race present and future, that it should be used to produce only vigorous children, and that he whose condition precludes such has no right to children. This is the duty laid upon us. As I go on to outline the method by which the work is to be done, you will see that the parent, even he who is wise and skilful, is inadequate to the full task, and the ordinary parent is hardly able to make a beginning. Still less is the need met by two or three lectures, given under strained conditions, by a physician who is not a teacher-tho even this is better than nothing at all. The first principle of our school work in relation to sex is that it be not lugged in obtrusively. Everywhere it should fit naturally with the other work as a part that goes to make a perfect whole. For example, in history and geography the marriage customs and family life are discussed in connection with other customs. In biology and nature study the reproductive methods, egg-laying, care of young, etc., are given their place; and in regard to mankind the physiology and hygiene of the process of reproduction are part of the study of the human body and should come right along with other classwork. Another principle is that sex must not be made too prominent. The prevailing policy of avoiding all reference to sex calls attention unpleasantly to the omission. In the teacher's mind the subject will have to be unduly prominent for the present, because he is not accustomed to it and will have to make special preparation for it. But to the pupil, to whom all the facts of his lesson are discoveries, the wonders of reproduction come with the same ease and simplicity as the other wonders of an interesting world. - All thru the lower grades facts relating to reproduction and precepts for conduct in sex matters come up incidentally. The opportunities must be carefully utilized, not avoided. Sex is so much in evidence all thru life that there are plenty of occasions for its study without specially setting the stage. Please note that, altho intercourse between a male and a female is a sine qua non in most reproduction, this act plays but a small part in the drama of the renewal of life, at least in the mind of the uncorrupted child. And if we recognize the relation simply and then pass on to other parts of |