Teaching Pupils How to Study Mathematics

Abstract

Of all the considerations connected with the study of mathematics, and indeed with the study of any subject, the most important is the mastery of the art of study itself. No topic has been so generally overlooked and neglected heretofore. This neglect is the source of many of our difficulties in teaching, and of many of the criticisms that have been heaped upon the various studies. A supervisor of the high schools of one of our states recently made a general outline for the reorganization of the courses in mathematics for the state. The matter of teaching pupils how to study had been entirely overlooked. His attention was called to the matter, and, realizing its importance, he made it a part of the program. After all, this is the chief thing to be gained from our schools. The pupil must leam the “how.” The “what” is not of so great importance. The “what” frequently changes. The “how” is relatively constant. In other words, the pupil should learn how to attack a problem with economy of time and effort, and with the greatest efficiency. The information he gains in the process is incidental, and illustrative of what he ought to expect as a result of his efforts after he has been trained. It is this sort of training that gives the educated man a measure of his powers, and ability to use these powers in the most effective manner in the various problems which he meets in his daily living. If education fails in this it fails utterly; indeed, it is then not education at all, it is a farce, and the school is a failure. Yet this is the point at which the schools do fail most lamentably. No subject in the high school curriculum is equal to mathematics in its opportunit ies for teaching the art of study. Geometry is especially valuable for this purpose.