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distant schools, by extending the school curriculum and making it more elaborate, by adding the high school, by prohibiting child labor, the school has practically assumed the whole responsibility for the education of the young.

Is the modern school without the home doing for initiative, what the home with the old school did?

Is the child developing a civic sense in the isolation of the school which he developed in his intimate relation to the home and society?

I am not able to answer either of these two questions, positively, affirmatively. But there are few schools in which children are taught or allowed to go alone in their learning. The teacher goes before not merely to blaze a path but to build a boulevard. Many children are not only carried to school, but they are carried through school. Every lesson is developed in advance. Only the child is left undeveloped.

It is doubtful if the school is any more useful in awakening civic sense than in developing initiative. Civic sense is a late form of the general sense of social obligation.

It is rare to find in any school above the kindergarten any serious attempt to utilize the instinct of mutual aid. In the kindergarten the most severe reprimand that is used is to remind a child that he is not helping. But I have not been fortunate enough to have seen the principle applied among older children. From beginning to end the work is individual and the motives are individual.

It is from this standpoint that the isolation of the public school appears in the strongest light.

No one who thinks of the changes that have come

in public education during the last generation, can fail to see that with all the gains that have been made there have been some losses.

If we are wise, we shall not shut our eyes either to the gains or losses. If the gains are real and substantial, we want to keep them. If the losses are real, we ought to try to avoid them.

The practical question is: Can public education organize itself so as to develop the two great social forces, individual initiative and mutual aid? Some attempts are being made to do this. I have seen in a normal school, groups of students engaged in the mutual study of problems in psychology. I have seen in a primary school groups of children on their own initiative simulating the life of primitive peoples of whom they had read, providing by mutual labor shelter, clothing, implements and food.

I have seen grammar school children carrying on garden operations on the co-operative principle, and applying the same principle in their constructive work.

I have seen high school students conducting together analytical investigations in chemistry, constructive experiments in physics, and practical work in surveying

I have seen in a school for orphaned boys, a city organization, with city officers, cottages built by the boys, owned in shares, the shares dealt in in the market, the property taxed and protected by the city officials, these officials being periodically elected by the whole body of citizens.

I have seen at Tuskegee an immense brick school edifice being built by the co-operative labor of students,—the building like the cathedrals of old, a monu

ment to the brotherhood of labor, and to the individual initiative of Booker T. Washington.

When such cases cease to be sporadic and become general, we shall have extracted the fangs of the graded school.

But to make them general will be no easy task. To it must be brought the profoundest convictions, the most ardent enthusiasm, the most cordial and sympathetic co-operation, the most sagacious judgment and the most diligent and patient effort. To effect such a transformation of popular education would be a consummation worthy of the Twentieth Century and would be the supreme triumph of the two forces which have conditioned all social progress through the ages.

ARITHMETICA MISUSED AGENT IN EDU

CATION

LOUIS P. NASH, SUPERINTENDENT OF SCHOOLS, HOL

YOKE, MASS.

Arithmetic will always be, as it has always been, one of the fundamental, necessary, central subjects which must be first considered in education. It is quite the fashion to rail at arithmetic almost in terms of abuse, as though arithmetic were to blame for about all the unsatisfactory teaching in elementary grades. However, we need not be much troubled, this, too, will pass. I have put this word “misused" into my title for two reasons: First, because of this undiscriminating criticism, and secondly because it must be ad

mitted that the subject has not always been so well and wisely used by teachers as to develop all its value. What I have to say may be arranged under four headings :-

I. Present Status. Just now there is a very encouraging condition of inquiry and criticism upon this subject. The place and the value of arithmetic are being studied and we have a right to look for very important advancement in the near future. I wish to protest against the extravagant importance that is given to the "explanation" in certain schools. Explanation is good, but a cast-iron form of explanation may operate to keep the child from ever understanding the conditions of the problem. The work with littie children should deal with objects and with actual numbers. It is to be observed that the operation “five times two" or "five times three" includes the taking of a number of objects or a group of objects as a unit, and this is a much more difficult step than taking the single thing as the unit. In much of the primary work that is now being brought before us the early objective work is very clearly developed but the mind of the child is allowed to remain in that stage of purely objective thinking. The doctrine of the three stages of thought is not a new one, being as old as Plato, but it is one that ought to be known and that should guide the practice of every single teacher.

II. The Ends to be Gained. The results which we seek by arithmetic teaching are: First, useful knowledge, second, mental culture, third, moral uplift. We need a little elementary arithmetic for the affairs of common life, and arithmetic also is the gateway to all the higher sciences. Every carpenter and every other mechanic is using principles of geometry all the while though he may not be aware of the fact. Arithmetic naturally leads the mind forward from the lowest stages of thinking to the higher. It is impossible for us to visualize large numbers; we must use the concept and work with the symbol, and the advancement by which the mind moves forward from the apprehension of a simple number of objects to the working of large problems by the means of the figures and then in successive higher stages to algebra, calculus, logarithm, etc., is almost an exact parallel of the general evolution by which the mind advances from the merest sensory idea to the highest reaches of which human thought is capable. The third end, which includes moral evolution, is the general end of all education, and if arithmetic had nothing to offer on that side of life then it would not be a fit subject for the curriculum. The first moral requirement is to know and to tell the truth and mathematical study induces exactness of apprehension and of statement. There is a very noble sentence in the preface to McLellan and Dewey's “Psychology of Number” which I like to think of:

“As for the objection that number work is lacking in ethical substance and stimulus, much may be learned from the study of Greek civilization from the recognition of the part which Greek theory and practice assigned to the ideas of rhythm, of balance, of measure in moral and ästhetic culture.

Even upon its merely formal side a study which requires exactitude, continuity, patience, which automatically rejects all falsification of data, all slovenly manipulation, which sets up a controlling standard of balance

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