or 441 x2 == 169 400+40;r r2. Hence x==lQ%. Therefore h === 212 7o56^=^ô r h = 6%. Hence the area == %.^%. 20 = 126.If we take a, b, c as the sides of the triangle we get the usual Heronian formula,One reason why beginning algebra often becomes uninteresting is that the teacher does not offer the student enough concrete illustrative material. It is hoped that the above simple applications will be of use to the teacher and will incite him to think up more problems of a simple nature.MATHEMATICAL EQUIPMENT AND ITS USES.
INTRODUCTIONIn the following course of study it is aimed so to reorganize the body of secondary-school mathematics as to fit the subject effectively to the needs of the students and to make it more productive for mental life and growth. Since 1903 the departments of mathematics of the University High School and the School of Education have been developing a solution of the problem of mathematical reorganization along the lines of correlation. By the bringing together of subjects that are closely related, each is reinforced by the aid of the others, and the entire work in these subjects is unified and vitalized. For example, algebra and geometry supplement each other. Both are used to express facts about quantity. The formula and the graph are only different ways of expressing the law of a group of numerical facts. Each states the facts in generalized form and thus makes the deduction of any number of particular cases possible. Moreover, when the two forms of thought are correlated in a single course of instruction the student's comprehension of quantity is at the same time deepened and simplified-deepened because of the more enduring impression made upon the mind; simplified because the double method of attack makes it easier to overcome difficulties by supplying always a strategic alternative.The student will see the advantages of having various modes of treating the facts of quantity. Thus, he is made to realize the value of algebra by seeing the superiority of algebraic methods in 648 This content downloaded from 034.213.178.048 on May 10, 2018 12:40:06 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). SECONDARY MATHEMATICS IN UNIVERSITY HIGH SCHOOL 649important respects as compared with arithmetic and geometric methods.When the various mathematical subjects are treated separately, each tends to take on the rigid form of the final science. This leads inevitably to a certain formalism in the mode of presentation. Such formalism is not the best method for the high-school pupil. Correlation helps to avoid excessive formalism. Rigor is not carried beyond the understanding of the pupil.Leading mathematicians and professors of the teaching of mathematics have long recognized the relationship between the various subjects of secondary mathematics, especially algebra and geometry, and have advocated the desirability of teaching them together. The details of a plan for this correlation are being worked out in the University High School and the content of the first-year course is now well organized and is given in First-Year Mathematics, a textbook published by the University of Chicago Press. The second-year course is contained in Second-Year Mathematics, also published by the University of Chicago Press. Work on the thirdand fourth-year courses is progressing and it is hoped to publish them in the near future. AIMS AND VALUESAmong the purposes of secondary mathematics the following are emphasized:I. A knowledge of the fundamental facts and principles ...
SCHOOL SCIENCE A N D MATHEMATICSflight of the bullet between the discs. To measure this angle, the motor is stopped and the shaft rotated till the hole in the first disc is in line with the bore of the rifle, as determined by sighting through the open breech. The point where the line of sight meets the second disc is then read on the graduated circle.The speed of the motor may be determined directly with stopwatch and revolution counter, or more accurately, by the "method of slip," described in any laboratory book which deals with the induction motor.Using a .22 caliber army rifle, and a motor having a synchronous speed of 1200 revolutions per minute, the angle of lag is about sixty degrees. This angle can be measured to an accuracy of 1-2 degree. The velocity determined is about 1000 feet per second. The results obtained by different students differ by two or three per cent, and the results obtained by this method differ from those obtained by the ballistic pendulum by about the same amount. This probably represents, not experimental m o r , but actual differences in the velocities of different bullets.
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