dren to purpose, to plan, and to accept responsibility; and we must recognize that with these opportunities there will also be greater possibilities of failing, so that the responsibility of the teachers is even greater under the plan here considered than in the old type of school. The new type of school must, therefore, demand greater freedom for the children to move about and a very much more elaborate apparatus of books and tools. Both of these mean greater demands upon the teacher. It is only under such a regime that we may expect to have an education that is, indeed, live, and an education characterized by "growth" and "leading on." THE EXAMINER'S CATECHISM* PHILOSOPHY OF EXAMINING Are there irreconcilable differences between examinations given as external tests to satisfy interested authority and examinations given as means of growth and development? Is it consistent with modern educational philosophy to continue traditional systems of examinations, as commonly employed as a basis of promotions in which pupils feel that they must pass set examinations at stated times or fail to maintain their places in the school? What philosophical considerations seem to determine the purposes of examinations? What are the most prominent motives that appeal to pupils who do their studying. primarily with reference to final examinations? What are some of the evil results of emphasis upon examinations as an incentive to study? Within what limits is it true that under present systems of examining, teachers cannot get at the things most highly prized educationally? e. g., the effect of teaching upon the development of social attitudes or upon the establishment of specific habits? Should examinations be made educative in the sense that they enable the pupil to test his own powers? What can be done in giving examinations to interest pupils more in beating their own. records than in beating the records of others? *The English Journal, 1919-1920. In what sense may examinations afford satisfaction to the thoughtful student who finds therein opportunity for new combinations of ideas? Should examinations be made educational in the sense that they make the pupil conscious of the growing process? To what extent may they serve as opportunities for encouragement and enthusiasm? Which is the more valid test, that of information or that of appreciation in examinations on literature? What are the most important moral effects, either good or bad, resulting from the traditional method of examining such as is commonly used as a basis of promotion in public schools and as a requirement for college entrance? PRACTICE Should specific tests be devised to measure power to organize? What can be done to break the habit common among teachers of writing out examination questions without due reflection. on their educational value? Is it necessary to depend upon examinations as a means of systematizing knowledge from a review of the whole field passed over in a course? Should examinations for review be associated largely with the critical conditions of term or course grading? TH ETHEL LUCCOCK Northwestern High School HE graph, like nature, speaks a various language. I always start the subject enthusiastically, for through the graph I find more natural points of contact with the pupil's life and interests than in ordinary work in mathematics. When the graph is being taught, the hard and fast lines between pupil and teacher are lost sight of in the mutual interchange of information and ideas. Not only do I acquire then a vast fund of information from the class; but I acquire a knowledge of my class. In the introductory work I am reminded of a device used by an 'instructor in freshman English in college. He would read us part of a story. Then, using that as an introduction, we would “make up" an ending. We reverse the process with our graphs, for, while the work always ends with the graph of the straight line and the quadratic curve, the beginning varies with the time and sea son. Last spring we were just ready to start the study of graphs on the Monday after Easter. The freakish behavior of the Easter temperature made an excellent starting point, giving a simple graph of timely interest. Another time we began with our scholarship report, just printed in the Northwestern Colt. Again some statistics showing what percentage of men listed in Who's Who had received training in college, high school, grammar school, or were "self made, gave us an introduction. interesting to note that while 71 were college trained about 2 percent were listed as self made. It was percent While we were making simple graphs, such as temperature graphs, based on the weather reports in the Free Press, the class was collecting graphs from newspapers and magazines. One, taken from the child welfare page of a women's magazine, excited a sympathetic response. The graph represented a child's variation in weight. The line progressed steadily upward except for one sharp decline. The explanation for this loss of weight was "school examinations." Another from The Detroit News showed the effect of a fifteen minute rest period in the afternoon in keeping the accuracy and efficiency of a force of stenographers up to standard until closing time. The teacher was much touched by one graph published by Wesleyan University, in its efforts to raise an endowment fund to increase the salaries of its professors. It showed how everything had been increased -the expense of operating the buildings and the janitors' salaries—the professors' salaries alone remaining unchanged. The search is valuable in that it shows how wide-spread is the use of the graph. An examination. of Graphic Methods of Presenting Facts by Brinton was also helpful in showing the different kinds of graphs as well as their varied uses. Each class had one problem to work out. One group made a graph of the reports of the tardiness contest between Northern and Northwestern high schools. On this, one notes that the high peaks always fell on Mondays. Another class worked out a graph comparing the scholarship record of the boys and the girls in Northwestern, since the opening of the school. We made, also, comparative graphs of the monthly markings by houses and by grades. Various statistics from the school office can be used, such as the percentage of failure in different subjects, and attendance records for the grade rooms. One class made a graph showing the percentage of distribution of classes in our school for that semester. Next of fuel shortage or trade conditions. One girl brought in a comparative record of the steam pressure in a duplex apartment, showing conclusively that the folks downstairs were getting all the heat. Another girl was absent for several days just after we began to study graphs. Her mother was ill with influenza, so the recently acquired knowledge was used in making a graph of the patient's fever record, which she brought with her on her return to school. Sometimes these graphs bore on very practical problems. Last November the scholarship committee from one of the grade rooms was most depressed. This grade room had been lowest in scholarship among Mr. Homer W. Anderson in his article on "The Size of High School Classes" in the December copy of The Detroit Journal of Education. Our attendance graphs showed very clearly that the greatest numbers of absences occur on Monday and Friday, and are, partly at least, avoidable. But it is in their original graphs, required from each pupil, that the greatest interest lies. Several made graphs showing the increase in prices during the last four years. Rents seemed to rise straight up; the price of sugar, once released, soared; potatoes made an interesting study as their graph showed the effect of the ban on potatoes last spring; motor stocks declined whenever the different companies were closed because 50 80 70 60 2 8 2 8 8 8 20 go 40 30 graphs. I always find some capable but indifferent pupils, who become interested because they see a practical use for their classroom work and make a big improvement through all the rest of the course. standard were discussed. A girl from the graphs. Other subjects were: attendance records for Sunday schools, missionary collections, the growth of a church building fund, the election returns by precincts on Municipal Ownership, the rate at which the railroad men were going out on strike and returning to work last spring, the increasing shortage of farm labor, statistics showing the relative per capita expenditure for education in different countries before the war, the effect of the war on language study in our high school-how, as German dropped out, French, Latin, and Spanish increased; the increase and decline in the price of Fords; the decline in real estate values last fall; the distribution of immigrants; and the relation of exports and imports. I will cite just one of these to show how a pupil's own idea often opens up other problems. One girl made a graph, showing the standings of three classes in History (2) Her record showed only the number of 1's, 2's, 3's, and 4's. At first glance it appeared that the afternoon class was lower than the others, thus leading her to see the necessity of turning it into percentages to show a proper comparison. Then she made a study of several other weeks to see whether the afternoon classes really fell below the others, and whether the best work usually occurred in the middle of the week, as it had that week. A comparison with other subjects might even be made. A writer in School Science and Mathematics last year suggested a good introduction to graphs showing the natural tendency people have always had to make a picture of any idea they wish to present. The best way to give anyone a clear idea of a square is to draw a picture of it. The system commonly used in counting votes is a graphic method. The printed note in music is really a graph of a musical tone. We locate points on a map with reference to two fixed axes, the north and south, and east and west lines. I even found recently in a novel entitled Pretty Michal, by Jokai, a list of thirty-three symbols used by the housewives of Northern Hungary, in about 1650, to add mystery and glamour to their humble cooking recipes. I remember vividly the system we used as children to record our changing heights. Once a year we lined up and each one in turn measured his height upon the kitchen door. There we had a composite graph, comparing not only the heights of the various members of our family, but each one's yearly record of growth. The record, unfortunately, was interrupted by the family's removal to a new home. But nearly everyone can recall some such simple record kept that will put the graphic idea in terms of his own experience. Our graphs were not elaborate, for we did not spend a great deal of time on the subject. Our object was to enable the pupils to read and interpret a graph and to apply it to simple cases within the range The pupils were interested in each other's of the pupils' own interests. THE SECRET OF THRIFT* THE CLIFFORD BREWSTER UPTON Associate Professor of Mathematics and Provost of Teachers College Columbia University INTRODUCTION FOR TEACHERS HE aim of this article is to present in a new light certain facts about systematic saving and investment, an important element of thrift. The article is addressed to boys and girls merely to suggest one possible way of making a somewhat difficult topic interesting to school children. It is expected that teachers will make many improvements upon this presentation in adapting it to the needs of their individual classes. The form in which thrift is here presented requires a knowledge of simple interest; consequently this presentation is limited, in general, to pupils in the seventh and eighth grades and in the high school. In some schools it can be given in the sixth grade. Children need some basic facts about saving. An appeal to patriotism as a reason for saving, to be effective, must always be supplemented by facts about the economics of thrift. It is the economic basis that this article seeks to give. Before taking up this treatment, the teacher should read to the pupils from the Arabian Nights the story of "Aladdin and the Wonderful Lamp," unless all the children are familiar with it. The material of this paper represents a number of lessons to be incorporated into the work of the arithmetic class. The teacher should devise enough supplementary problems to enable the pupils readily to understand each of the ideas that are to be brought out. To the Pupils of the 7th and 8th Grades and the High School: Do you know what to do with a quarter of a dollar to make it turn into a whole *Copyright, 1921, by C. B. Upton. dollar without your having to do any work whatever? Of course you know that you could invest this quarter in newspapers and make a profit by selling the papers. After selling papers every day for a week you might have a dollar by the end of that time; but this would require work on your part. What I want to know is this: How can you make a quarter grow into a dollar without your doing any work whatever? I hear one of you say that only a magician could do that. Well, it does sound like magic, doesn't it? Perhaps it seems to you to be a kind of magic as wonderful as Aladdin's lamp. You remember in the story of Aladdin that when Aladdin wanted gold, or precious jewels, or a beautiful palace, all he had to do was to rub a lamp and his wish was immediately granted. I am going to tell you about a lamp of another kind, a new Aladdin's lamp, which when rubbed will make $1 turn into $5, or into $6, or into as much as $10, or even more. This new lamp I shall call the Magic Thrift Lamp. If you rub or touch the Magic Thrift Lamp with a dollar, the dollar will begin to grow and will keep on growing just as long as the Magic Thrift Lamp touches it. As soon as you take the dollar away from the lamp, the dollar will stop growing. And, like Aladdin's lamp, this Magic Thrift Lamp has the power to do these wonderful things for every boy or girl who possesses it. Just think of this great magic that can turn a dollar into $5, or $6. or even $10! It is curious, too, that this Magic Thrift Lamp will do more for the young boys and girls than for the older ones. For the youngest boys and girls it will turn the dollar into $10; for those a little older it will turn the dollar into $7 or $8; for |