What the Schools Teach and Might Teach

by John Franklin Bobbitt

MATHEMATICS

To arithmetic, the Cleveland schools are devoting a somewhat larger proportion of time than the average of cities.

TABLE 7.—TIME GIVEN TO ARITHMETIC
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| Hours per year | Per cent of grade time|
Grade |———————————————————————-
| Cleveland | 50 cities| Cleveland | 50 cities |
—————————————————————————————-
1 | 38 | 60 | 5.2 | 6.9 |
2 | 136 | 96 | 15.5 | 10.7 |
3 | 142 | 131 | 16.3 | 14.4 |
4 | 152 | 149 | 17.2 | 15.4 |
5 | 142 | 144 | 17.1 | 14.9 |
6 | 155 | 146 | 17.5 | 15.0 |
7 | 142 | 140 | 16.1 | 14.4 |
8 | 158 | 142 | 17.9 | 14.1 |
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Total | 1065 | 1008 | 15.5 | 13.3 |
—————————————————————————————-

That everybody should be well grounded in the fundamental operations of arithmetic is so obvious as to require no discussion. Beyond this point, however, difficult problems arise. The probabilities are that the social and vocational conditions of the coming generation will require that everybody be more mathematical-minded than at present.

The content of mathematics courses is to be determined by human needs. One of the fundamental needs of the age upon which we are now entering is accurate quantitative thinking in the fields of one's vocation, in the supervision of our many co-operative governmental labors, in our economic thinking with reference to taxation, expenditures, insurance, public utilities, civic improvements, pensions, corporations, and the multitude of other civic and vocational matters.

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.