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-could be carried over to the acquirement of a better technique through practice on a miscellaneous content.
Thus far we have dealt with the results of teaching the symbols and modes of expression as ends to the neglect of the content, although in doing so we were obliged also to criticise the logical classifications in which the tendency to isolate forms usually ends. The situation of arithmetic in the public schools to-day is however an instance where a content study is suffering from injurious classification. First the quantitative aspect of objects was rigidly isolated from the qualitative. Counting was seen to be the fundamental operation, and nearly all the other numerical processes were “devices for speed," of which the chief ones were the multiplication and decimal methods of grouping. These “ devices for speed” were arranged in a series of increasing complexity, the later using the earlier in combination. The principle is a well-known pedagogical principle. It is psychological as well as logical. But the classification was carried out so minutely that the content became miscellaneous even within a single ten minutes in many cases. It led to an arrangement of topics in which the increasing complexity is often purely imaginary. Twos are the topic for the second grade, first quarter; threes, for the second quarter; fours, for the third ; and fives, for the fourth quarter; and this is only typical of what may be found in other grades. The result of this extreme classification is that the teacher is left too little latitude for the introduction of continuous and interesting content. A principal of one of the Chicago public schools recently said to me, “I have been seriously thinking of teaching seventh and eighth grade arithmetic through a grain elevator. Do you know of anything which in its construction and management brings in more of the arithmetic topics of these grades?” There are of course practical difficulties here—the need of simplification, and how enough first-hand experience can be furnishedof which constructive work carried on in the schools is a partial solution.
To point out the predominance of the logical classification and the resulting miscellaneous content in arithmetic merely emphasizes how severely-and by this is meant prematurely
the quantitative side of things has been isolated. In confirmation one needs only to observe the deplorably common attitude of public school children above the second grade towards arithmetic. They look upon it and their own lives outside the school as two different things. Hence their body of first-hand experience which we call common sense forsakes them in the arithmetic lesson, and they solve problems merely by rote. The transition from the undifferentiated qualitative and quantitative acts of persons in daily life to “ 34 of 17, 72 per cent of 914
is what number?” is too abrupt. The place of logical classifications of subject-matter in elementary school instruction has been much misunderstood. It would be interesting to trace out the purposes for which the current classifications in the various content and symbol studies and modes of expression were originally devised. We should find that many of them were not devised for pedagogical purposes, but for the use of adults. They were introduced into the material and process of instruction because they were the shape in which the teacher's knowledge finally existed. But we can only point out the general place of classifications in the elementary school.
The primary use of classification is to sum up one's experience in a form readily accessible to the owner. All topical reviews are classifications of this kind. To get the real benefit the children themselves should classify their experience periodically, aided by the teacher in selecting the basis of classification likely to prove most serviceable.
Secondly, classifications have a use in suggesting short cuts in the experience of others. These short cuts are, however, available in the elementary school in subordination to the nature of mental activity and to the order of mental development. We have tried to point out that the use made in the public schools of the classifications of the forms in writing, spelling, and grammar, and of the groupings to facilitate counting in arithmetic, does violence to the nature of the child's mental processes, because only under certain circumstances, defined above, is he interested in the miscellaneous content which inevitably results from such classifications.
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Our criticism thus far has suggested only general directions of change. The question of importance is with regard to the specific changes advised, and as to their practicability with the present average expenditure per pupil.
I should say that the abandonment of reading as a separate study and with it the present composite readers is practicable. History and geography in very simple form, yet of coherent and progressive content, should be introduced also into the earlier grades, even the first. Reading would then be taught in connection with them, and with nature study and literature. In some public schools reading by the children of their own compositions has been found to have advantages over textbooks in the first two or three grades, although text-books were not given up. This should meet with considerable favor, because if geography and nature study are ever to become successful in the lowest grades, they must become mainly the working over of class and individual observations at first hand. This would insure to the reading of written exercises a prominent place in reading work of the lowest grades.
The teaching of writing, spelling, and elementary grammar through composition and occasional dictation based on the content studies is, I believe, the most natural way to give these studies a connected and interesting content, and at the same time adequately motivate their study. This also obviates the difficulty, often experienced under the other method, of getting the children to apply their knowledge. When it is learned apart from their own expression, it often remains isolated. This means first the discontinuance of the so-called copy books: A composition book in which the children copy some of their written exercises after correction might be used. Models of correct penmanship are of course retained for convenient reference. Secondly, it means that spelling is taught chiefly by correction of the children's mistakes in their written exercises. The advantages of this method over the use of the graded word list are economy of time and preservation in the children of the natural motive for learning to spell, viz., ready and accurate communication of thought. Some children learn to spell a word much sooner than others do. By having all the chil
dren spell all the words the same length of time, much time is wasted, and the need and value of the study are not brought home to the child.
That part of the classified spellers which is based on phonetic analogies of words is, owing to the peculiar character of the English language, in clear violation of the psychology of association and should be discontinued entirely. Details cannot be given here.
Thirdly, to teach writing, spelling, and elementary grammar in connection with composition means that in grammar the logical classification of grammatical forms does not determine the order of topics. This, however, does not mean dissipation of energy. The order of topics is determined by the children's natural need in composition as it develops under the teacher's guidance. By suitable emphasis the teacher concentrates his efforts on certain of the most common errors, ignoring the rest, until these are usually absent. But he has the logical classification of forms clearly in mind, and is alert to the occurrence of good opportunities to introdnce new topics even to single pupils. A two years' course in advanced grammar in the upper grades would form a recapitulation and classification of the usages treated in the elementary course.
The changes in writing, spelling, and grammar are the easiest to make since they involve no additions to equipment, and no unmanageable change in the amount of activity of the pupils in the schoolroom, and consequently practically no decrease in the number of pupils per teacher. Many public school systems have already made these changes partly or wholly, varying in details from the plan described, but agreeing in principle. The Rochester schools and the Washington School in Chicago are examples.
To remedy the isolation and over-classification in arithmetic is a far more difficult problem. A quite successful solution of it has been worked out in the University of Chicago Elementary School by subordinating arithmetic to the actual demands for it in school life, except with the children nine years old and over, who have periods of drill in number work to gain facility. Construction work has a far more prominent place in this school
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than in the public schools. Cooking, woodworking, and science experimentation (especially applied physics) are found to be the modes of construction most fruitful of arithmetical opportunities. I do not mean that on this plan the complexity of the numerical processes is disregarded. No doubt it is reduced to what is really essential. Then the construction work, school accounts, etc., are so selected as to conform to this minimum, and still present to the child a connected, progressive content adapted to call forth his interest and effort.
That part of this method which concerns the subordination of arithmetic to the need for it in the constructive work of the school is impracticable in the public schools without a considerable increase in the present average expenditure per pupil. But all of the arithmetical processes except mensuration (including involution and evolution) are used as much in commercial transactions as in cooking, woodworking, and science. For this reason with no increase in expenditure much can be done to give arithmetic a more continuous and less abstract content; first by reducing the classification according to complexity to what are really important differences. The four processes with integers, and with fractions not involving formal factoring, and the decimal system through three or four places should precede long multiplication and long. division. But the former need not be faultless before the latter are begun, since the latter give much practice in the former. All in these two groups should precede those fractions which necessitate formal factoring, nearly all () of decimal fractions and percentage. Powers and roots and their application in mensuration form a fourth group in time.
in time. Ratio and proportion belong to all the groups. Among the several topics which form any one of these groups there is no precedence of any consequence. They may well be taught together much of the time. Yet the first group covers a little less than one-half of the whole course in arithmetic, the second a few weeks, and the third about three-eighths.
After unnecessary classification is eliminated it becomes for 1. Supt. J. M. Greenwood in Rept. Com. Fifteen, Educational Review, '95, Vol. IX, p. 290.