Algebra in the Elementary Schools
I have never yet heard of a high school teacher’s being satisfied with the first-year pupil’s knowledge of common fractions, and the other day a I. A. girl frankly admitted that she could not multiply 12⅔ by 15¾ because she had skipped one grade, had then had algebra and geometry, and the review didn’t touch on mixed numbers. Of course, this was not the fault of any teacher, but the fault of a system which is trying to crowd too many things into too small a space. The real efficiency of the schools does not depend upon their being housed in million-dollar buildings, under a well-organized administrative force, excellent equipment, etc.; it depends upon two things,—what is taught, and how it is taught; and more especially upon the latter; for every teacher of mathematics knows that a pupil can derive as much permanent good from the study of a very few topics or theorems, so presented as to be pleasing to the pupil, or at least interesting, and at the same time make him think, as he can from ten times the amount of material “rammed home” with the sole object of being reproduced at examinations. The policy of standardizing everything by examinations is doing our expensive school system an untold injury; the report of the city superintendent compares the schools according to the number of their pupils who pass the examinations, and the principal warns the teacher that he is rated according to the number of his pupils that pass, and this pressure is passed on to the pupil. Until some method of close class-room observation and supervision is introduced with a view to allowing free rein to a teacher’s individuality and originality even at the expense of his pupil’s failing the conventional examinations, it is hardly worth while suggesting other changes.