Concretizing the Teaching of Arithmetic
The entire curriculum of the elementary school has been undergoing a complete revision, and arithmetic, which has always held a central place in the curriculum, is still a subject which arouses great interest. Arithmetic has been taught and studied throughout the ages for many reasons. For some of the early people - Hindus, Arabians, and Egyptians — the subject was studied because of its practical values. Although the Greeks recognized the practical value, it was the cultural worth that made the big appeal. The primary appeal for the Romans was the utilitarian one. The nineteenth century added the supposed disciplinary value of Arithmetic. The practical and social values of arithmetic have always been considered valid reasons for retaining arithmetic in the school course, and are, no doubt, largely responsible for the commanding place the subject still holds. What has become of the doctrine of Formal Discipline, which taught that training in the study of a particular subject will aid in the comprehension of other subjects, and in the general development of mental strength and ability? The new psychology, based largely on the results of experimentation has tended to overthrow the earlier arguments for Arithmetic as mental discipline . The new psychology opposes the doctrine of transfer of ability. We now hold that mental power developed in one subject is not transferred to all other experiences, but only to those situations that are similar in subject matter, or in method of learning or procedure, or where the experience has been raised to the level of an ideal. Children may be trained to neatness of papers in penmanship, but there will be no "carry over" to papers in arithmetic, until "neatness" in and of itself, has become an ideal; until it has been generalized into a concept. Professors Bagley and Ruediger have conducted educational experiments, the findings of which have proved the validity of the above mentioned argument. Formal discipline is now looked upon as a defense for all the useless material included in the early arithmetics.
Drew, Mary L, "Concretizing the Teaching of Arithmetic" (1928). ETD Collection for Fordham University. AAI30557710.