Chapter 3

Just as the thought involved in physics, astronomy, or engineering needs to be put in mathematical terms in order that it may be used effectively, so must it be with effective vocational, civic, and economic thinking in general. Our chief need is not so much the ability to do calculations as it is the ability to think in figures and the habit of thinking in figures. Calculations, while indispensable, are incidental to more important matters.

Naturally before one is prepared to use mathematical forms of thought in considering the many social and vocational problems, he must have mastered the fundamentals. The elementary school, at as early an age as practicable, should certainly give the necessary preliminary knowledge of and practice in the fundamental operations of arithmetic. This should be done with a high degree of thoroughness, but it should always be kept in mind that this is only a preliminary mastery of the alphabet of mathematical thinking. The other part of our problem is a development of the quantitative aspects of the vocational, economic, and civic subjects. One finds clear recognition of this in Cleveland in the new arithmetic manual. The following quotations are typical:

"The important problem of the seventh and eighth grades is to enable the pupils to understand and deal intelligently with the most important social institutions with which arithmetical processes are associated."

In discussing the teaching of the mathematical aspect of insurance, we find this statement: "Owing to the important place this subject holds in life, we should emphasize its informational value rather than its mathematical content."

Under taxation and revenue: "If the general features of this subject are presented from the standpoint of civics, the pupils should have no difficulty in solving the problems as no new principle is introduced."

Under stocks and bonds: "Pupils should be taught to know what a corporation is, its chief officers, how it is organized, what stocks and bonds are, and how dividends are declared and paid, in so far as such knowledge is needed by the general public."

These statements indicate a recognition of the most important principle that should control in the development of all of the mathematics, elementary and secondary, beyond the preliminary training needed for accuracy and rapidity in the fundamental operations.

When this principle is carried through to its logical conclusion, it will be observed that most of these developments will not take place within the arithmetic class, but in the various other subjects. Arithmetic teaching, like the teaching of penmanship, etc., is for the purpose of giving tools that are to be used in matters that lie beyond. The full development will take place within these various other fields. For the present, it probably will be well for the schools to develop the matters both within the arithmetic classes and in the other classes. Neither being complete at present, each will tend to complete the other.

On the side of the preliminary training in the fundamental operations, the present arithmetic course of study is on the whole of a superior character. It provides for much drill, and for a great variety of drill. It emphasizes rapidity, accuracy, and the confidence that comes to pupils from checking up their results. It holds fast to fundamentals, dispensing with most of the things of little practical use. It provides easy advances from the simple to the complicated. The field of number is explored in a great variety of directions so that pupils are made to feel at home in the subject. One large defect is the lack of printed exercise materials, the use of which would result in greatly increased effectiveness. Such printed materials ought to be furnished in great abundance.

ALGEBRA

In the report of the Educational Commission of Cleveland, 1906, we find the following very significant sentences relative to the course of study for the proposed high school of commerce:

"An entirely new course of study should be made out for this school. Subjects which have been considered necessary in a high school, because they tend to develop the mind, should not for this reason only be placed in a commercial course. Subjects should not be given because they strengthen the mind, but the subjects which are necessary in this course should be given in such a way as to strengthen the mind. The mathematics in this school should consist of business arithmetic and mensuration. We can see no reason for giving these students either algebra or geometry. But they should be taught short and practical methods of working business problems."

We find here a recommendation since carried out that indicates a clear recognition of the principle of adaptation of the course of study to actual needs. Carried out to its logical conclusion, and applied to the entire city system, it raises questions as to the advisability of requiring algebra of girls in any of the high school courses; or of requiring it of that large number of boys looking forward to vocations that do not involve the generalized mathematics of algebra. Now either the commercial students do need algebra or a large proportion of these others do not need it. It seems advisable here to do nothing more than to present the question as one which the city needs to investigate. The present practice, in Cleveland as elsewhere, reveals inconsistency. In one or the other of the schools a wrong course is probably being followed. The current tendency in public education is toward agreement with the principle enunciated by the Cleveland Educational Commission, and toward a growing and consistent application of it.

Differentiation in the mathematics of different classes of pupils is necessary. The public schools ought to give the same mathematics to all up to that level where the need is common to all. Beyond that point, mathematics needs to be adapted to the probable future activities of the individual. There are those who will need to reach the higher levels of mathematical ability. Others will have no such need.

There is a growing belief that even for those who are in need of algebra the subject is not at present organized in desirable ways. It is thought that, on the one hand, it should be knit up in far larger measure with practical matters, and on the other, it should be developed in connection with geometry and trigonometry. The technical high schools of Cleveland have adopted this form of organization. Their mathematics is probably greatly in advance of that of the academic schools.

GEOMETRY

Form study should begin in the kindergarten, and it should develop through the grades and high school in ways similar to the arithmetic, and in conjunction with the arithmetic, drawing, and construction work. Since geometrical forms involve numerical relations, they supply good materials to use in making number relations concrete and clear. This is now done in developing ideas of fractions, multiplication, division, ratio, per cent, etc. It should be done much more fully and variously than at present and for the double purpose of practising the form-ideas as well as the number-ideas. Arithmetic study and form-study can well grow up together, gradually merging into the combined algebra and geometry so far as students need to reach the higher levels of mathematical generalization.

At the same time that this is being developed in the mathematics classes, development should also be going on in the classes of drawing, design, and construction. The alphabet of form-study will thus be taught in several of the studies. The application will be made in practical design, in mechanical and free-hand drawing, in constructive labor, in the graphical representation of social, economic, and other facts of life. The application comes not so much in the development of practical problems in the mathematics classes as in the development of the form aspect of those other activities that involve form.

We have here pointed to what appears to be in progressive schools a growing program of work. Everywhere it is yet somewhat vague and inchoate. In connection with the arithmetic, the drawing, the construction and art work, and the mathematics of the technical high schools, it appears to be developing in Cleveland in a vigorous and healthy manner.

HISTORY

The curriculum makers for elementary education do not seem to have placed a high valuation upon history. Apparently it has not been considered an essential study of high worth, like reading, writing, spelling, grammar, and arithmetic. To history are allotted but 290 hours in Cleveland, as against 496 hours in the average of 50 progressive American cities. This discrepancy should give the city pause and concern. If a mistake is being made, it is more likely to be on the part of an individual city than upon that of 50 cities. The probability is that Cleveland is giving too little time to this subject.

TABLE 8.--TIME GIVEN TO HISTORY =========================================================== | Hours per year | Per cent of grade time| Grade |----------------------------------------------- | Cleveland | 50 cities| Cleveland | 50 cities | ----------------------------------------------------------- 1 | 0 | 27 | 0.0 | 3.1 | 2 | 0 | 31 | 0.0 | 3.4 | 3 | 19 | 35 | 2.1 | 3.8 | 4 | 25 | 57 | 2.9 | 5.8 | 5 | 25 | 67 | 2.9 | 6.9 | 6 | 51 | 71 | 5.7 | 7.3 | 7 | 85 | 91 | 9.7 | 9.2 | 8 | 85 | 117 | 9.7 | 11.6 | =========================================================== Total | 290 | 496 | 4.2 | 6.5 | -----------------------------------------------------------

The treatment in the course of study manual indicates that it is a neglected subject. Of the 108 pages, it receives an aggregate of less than two. The perfunctory assignment of work for the seventh grade is typical:

"UNITED STATES HISTORY

"B Assignment. Mace's History, pp. 1-124 inclusive. Questions and suggested collateral reading found in Appendix may be used as teacher directs.

"A Assignment. Mace's History, pp. 125-197. Make use of questions and suggested collateral reading at your own option."

For fifth and sixth grades there is assigned a small history text of 200 pages for one or two lessons per week. The two years of the seventh and eighth grades are devoted to the mastery of about 500 pages of text. While there is incidental reference to collateral reading, as a matter of fact the schools are not supplied with the necessary materials for this collateral reading in the grammar grades. The true character of the work is really indicated by the last sentence of the eighth-grade history assignment: "The text of our book should be thoroughly mastered."

In discussing the situation, the first thing to which we must call attention is the great value of history for an understanding of the multitude of complicated social problems met with by all people in a democracy. In a country where all people are the rulers, all need a good understanding of the social, political, economic, industrial, and other problems with which we are continually confronted. It is true the thing needed is an understanding of present conditions, but there is no better key to a right understanding of our present conditions than history furnishes. One comes to understand a present situation by observing how it has come to be. History is one of the most important methods of social analysis.

The history should be so taught that it will have a demonstrably practical purpose. In drawing up courses of study in the subject for the grammar grades and the high school, the first task should be an analysis of present-day social conditions, the proper understanding of which requires historical background. Once having discovered the list of social topics, it is possible to find historical readings which will show how present conditions have grown up out of earlier ones. Looked at from a practical point of view, the history should be developed on the basis of topics, a great abundance of reading being provided for each of the topics. We have in mind such topics as the following:

Sociological Aspects of War Territorial Expansion Race Problems Tariff and Free Trade Transportation Money Systems Our Insular Possessions Growth of Population Trusts Banks and Banking Immigration Capital and Labor Education Inventions Suffrage Centralization of Government Strikes and Lockouts Panics and Business Depressions Commerce Taxation Manufacturing Labor Unions Foreign Commerce Agriculture Postal Service Army Government Control of Corporations Municipal Government Navy Factory Labor Wages Courts of Law Charities Crime Fire Protection Roads and Road Transportation Newspapers and Magazines National Defense Conservation of Natural Resources Liquor Problems Parks and Playgrounds Housing Conditions Mining Health, Sanitation, etc. Pensions Unemployment Child Labor Women in Industry Cost of Living Pure Food Control Savings Banks Water Supply of Cities Prisons Recreations and Amusements Co-operative Buying and Selling Insurance Hospitals

After drawing up such lists of topics for study, they should be assigned to grammar grades and high school according to the degree of maturity necessary for their comprehension. Naturally as much as possible should be covered in the grammar grades. Such as cannot be covered there should be covered as early as practicable in the high school, since so large a number of students drop out, and all need the work. Of course, this would involve a radical revision of the high school courses in history. It is not here recommended that any such changes be attempted abruptly. There are too many other conditions that require readjustment at the same time. It must all be a gradual growth.

Naturally, students must have some familiarity with the general time relations of history and the general chronological movements of affairs before they can understand the more or less specialized treatment of individual topics. Preliminary studies are therefore both necessary and desirable in the intermediate and grammar grades for the purpose of giving the general background. During these grades a great wealth of historical materials should be stored up. Pupils should acquire much familiarity with the history of the ancient oriental nations, Judea, Greece, Rome, the states of modern Europe and America. The purpose should be to give a general, and in the beginning a relatively superficial, overview of the world's history for the sake of perspective. The reading should be biographical, anecdotal, thrilling dramas of human achievement, rich with human interest. It should be at every stage of the work on the level with the understanding and degree of maturity of the pupils, so that much reading can be covered rapidly. Given the proper conditions--chiefly an abundance of the proper books supplied in sets large enough for classes--pupils can cover a large amount of ground, obtain a wealth of historical experience, and acquire a great quantity of useful information, the main outlines of which are remembered without much difficulty. They can in this manner lay a broad historical foundation for the study of the social topics that should begin by the seventh grade and continue throughout the high school.

The textbooks of the present type can be employed as a part of this preliminary training. Read in their entirety and read rapidly, they give one that perspective which comes from a comprehensive view of the entire field. But they are too brief, abstract, and barren to afford valuable concrete historical experience. They are excellent reference books for gaining and keeping historical perspective.

Reading of the character that we have here called preliminary should not cease as the other historical studies are taken up. The general studies should certainly continue for some portion of the time through the grammar grades and high school, but it probably should be mainly supervised reading of interesting materials rather than recitation and examination work.

We would recommend that the high schools give careful attention to the recommendation of the National Education Association Committee on the Reorganization of the Secondary Course of Study in History.

CIVICS

Civic training scarcely finds a place upon the elementary school program. The manual suggests that one-quarter of the history time--10 to 20 minutes per week--in the fifth and sixth grades should be given to a discussion of such civic topics as the department of public service, street cleaning, garbage disposal, health and sanitation, the city water supply, the mayor and the council, the treasurer, and the auditor. The topics are important, but the time allowed is inadequate and the pupils of these grades are so immature that no final treatment of such complicated matters is possible. For seventh and eighth grades, the manual makes no reference to civics. This is the more surprising because Cleveland is a city in which there has been no end of civic discussion and progressive human-welfare effort. The extraordinary value of civic education in the elementary school, as a means of furthering civic welfare, should have received more decided recognition.

The elementary teachers and principals of Cleveland might profitably make such a civic survey as that made in Cincinnati as the method of discovering the topics that should enter into a grammar grade course. The heavy emphasis upon this subject should be reserved for the later grades of the elementary school.

In the high schools, a little is being accomplished. In the academic high schools, those who take the classical course receive no civics whatever. It is not even elective for them. Those who take the scientific or English courses may take civics as a half-year elective. In the technical high schools it is required of all for a half-year. The course is offered only in the senior year, except in the High School of Commerce, where it is offered in the third. As a result of these various circumstances, the majority of students who enter and complete the course in the high schools of Cleveland receive no civic training whatever--not even the inadequate half-year of work that is available for a few.

Whether the deficiencies here pointed out are serious or not depends in large measure upon the character of the other social subjects, such as history and geography. If these are developed in full and concrete ways, they illumine large numbers of our difficult social problems. It is probable that the larger part of the informational portions of civic training should be imparted through these other social subjects. Whether very much of this is actually done at present is doubtful; for the history teaching, as has already been noted, is much underdeveloped, and while somewhat further advanced, geography work is still far from adequate at the time this report is written.

GEOGRAPHY

Geography in Cleveland is given the customary amount of time, though it is distributed over the grades in a somewhat unusual way. It is exceptionally heavy in the intermediate grades and correspondingly light in the grammar grades. As geography, like all other subjects, is more and more humanized and socialized in its reference, much more time will be called for in the last two grammar grades.

TABLE 9.---TIME GIVEN TO GEOGRAPHY =========================================================== | Hours per year | Per cent of grade time| Grade |----------------------------------------------- | Cleveland | 50 cities| Cleveland | 50 cities | ----------------------------------------------------------- 1 | 0 | 16 | 0.0 | 1.8 | 2 | 0 | 7 | 0.0 | 0.8 | 3 | 28 | 50 | 3.2 | 5.4 | 4 | 101 | 83 | 11.4 | 8.5 | 5 | 125 | 102 | 14.3 | 11.2 | 6 | 125 | 107 | 14.3 | 11.0 | 7 | 57 | 98 | 6.4 | 9.9 | 8 | 57 | 76 | 6.4 | 7.6 | =========================================================== Total | 493 | 539 | 7.2 | 7.1 | -----------------------------------------------------------

As laid out in the manual now superseded, and as observed in the regular classrooms, the work has been forbiddingly formal. In the main it has consisted of the teacher assigning to the pupils a certain number of paragraphs or pages in the textbook as the next lesson, and then questioning them next day to ascertain how much of this printed material they have remembered and how well. It has not consisted of stimulating and guiding the children toward intelligent inquisitiveness and inquiring interest as to the world, and the skies above, and waters round about, and the conditions of nature that limit and shape the development of mankind.

That the latter is the proper end of geographical teaching is being recognized in developing the new course of study in this subject. Industries, commerce, agriculture, and modes of living are becoming the centers about which geographic thought and experience are gathered. The best work now being done here is thoroughly modern. Unfortunately it is not yet great in amount in even the best of the schools, still less in the majority. But the direction of progress is unmistakable and unquestionably correct.

As in the reading, so in geography, right development of the course of study must depend in large measure upon the material equipment that is at the same time provided. It sounds like a legitimate evasion to say that education is a spiritual process, and that good teachers and willing, obedient, and industrious pupils are about all that is required. As a matter of fact, just as modern business has found it necessary to install one-hundred-dollar typewriters to take the place of the penny quill pens, so must education, to be efficient, develop and employ the elaborate tools needed by new and complex modern conditions, and set aside the tools that were adequate in a simpler age. The proper teaching of geography requires an abundance of reading materials of the type that will permit pupils to enter vividly into the varied experience of all classes of people in all parts of the world. In the supplementary books now furnished the schools, only a beginning has been made. The schools need 10 times as much geographical reading as that now found in the best equipped school.

It would be well to drop the term "supplementary." This reading should be the basic geographic experience, the fundamental instrument of the teaching. All else is supplementary. The textbook then becomes a reference book of maps, charts, summaries, and a treatment for the sake of perspective. Maps, globes, pictures, stereoscopes, stereopticon, moving-picture machine, models, diagrams, and museum materials, are all for the purpose of developing ideas and imagery of details. The reading should become and remain fundamental and central. The quantity required is so great as to make it necessary for the city to furnish the books. While the various other things enumerated are necessary for complete effectiveness, many of them could well wait until the reading materials are sufficiently supplied.