In the majority of our public schools nine years are devoted to the study of arithmetic. Notwithstanding this fact, the majority of these students who have had this amount of training are unable to add a column of figures rapidly and accurately. They are unable to perform mentally the simplest operations in relation to business. The business world has deplored this condition of things for many decades. Is it not time for the teachers of this country to investigate the causes of these meager results? All who have given the question serious consideration agree that too much time is already devoted to the subject; all agree that the fault lies in the method employed in teaching numbers; this view is in the main correct. After all, may there not be another reason for the poor results? Every teacher who has had a few years' experience must have occasionally met the backward pupil, twelve or fifteen years of age, who has begun arithmetic, as hi called it, and in one year accomplished as much as his seatmate who has studied numbers for four or five years. In some instances these backward students have surpassed those of their own age who have had for years the routine drills of the school. If it is a fact that the majority of these backward students accomplish this work in so short a time, is it not conclusive evidence that we begin pure number work altogether too early? May it not be true that the child's mind is not sufficiently developed for this kind of training when he begins school at the age of five or six years? It is not implied here that in elementary science and language that numbers are to be ruled out, but that they are to be taught incidentally.
If pure number work could be delayed even a year or two and then be presented in a proper way, a great deal would be gained. The second reason for failure is also deserving of serious consideration. All teachers agree that, in teaching little folks numbers, objects should be employed until these objects can be readily pictured in the mind. They agree that the combinations, whether in addition, subtraction, multiplication or division, should be given by the child without conscious effort, in other words, the process of number teaching should secure for the child a storing up of concepts to be used forever afterwards without hesitation and with unvarying accuracy. This result is not secured, for the simple reason that early in the child's work the graphic representation of number is taught. For example, in learning the number four, under the pretext of busy work, the little fellow is asked to solve on his slate such examples as the following- 2 and 2 = ? ; 2 x 2 =?; 4-2=?.
If the child has had these combinations in relations to objects, if the child has committed to memory the results, how much time will the child consume in writing the results on his slate? The truth of the matter is, he does not write the result without hesitation. Without any reference to the teacher, he introduces new mental factors into his work. These factors have no relation whatever to the mental operations provided by the child in the presence of the objects. In this way two methods of computation are established in the child's mind.
As he progresses in the study of numbers he has less to do with the mental. When he enters the fifth or sixth grade, he is a slave to his written work and continues a slave during the remainder of his school life.
Graphic work in numbers in the first, second, and third grades of our public schools, not only has no value in itself, but is positively detrimental. Again we say that there can be no objection to using the language of number where it becomes a part of their written science or language exercises. Let the number work be purely oral during the first three years of the child's school life and thereafter use no graphic work except where large numbers are involved in addition, subtraction, multiplication and division. The time that is usually wasted in slate work, in busy work, could be devoted to reading, literature and elementary science. The operations in numbers would all be performed in the class under the guidance of the skillful teacher. The first three years of the child's work in numbers would enable him to acquire a power in mental arithmetic that the average high school graduate rarely possesses. The work of learning arithmetic would be revolutionized.