Three Major Difficulties in the Learning of Demonstrative Geometry

Abstract

Efficient and successful teaching of demonstrative geometry in the senior high school requires on the part of the teacher much more than a knowledge of the subject matter. The young person who goes into the geometry classroom after leaving college with honors in mathematics is not necessarily a good teacher. Unless he has been forewarned in one way or another, he is likely to resort to the lecture method which his professors have used in college and then find to his surprise that his pupils have learned little. He may have taken courses in which he studied the general laws of learning as applied to pupils of high school age, but even so he will have difficulty in translating his knowledge to fit the specific requirements of the classroom. Part of his training may have been to observe the work of a highly efficient, successful, and artistic teacher whom he may try to imitate. He will find, however, that he has not been keen enough to grasp the meaning and purpose of many of the techniques. Not knowing beforehand how a group of pupils will react to a given situation, he fails to see when and how the experienced teacher has avoided pitfalls by introducing many details of development not necessarily needed in the finished product but indispensable to the learning process. Before he can become adept in preparing a course of study or planning his everyday lessons, he needs to know what difficulties pupils will have with the many component tasks which when integrated fulfill the desired aim. A teacher can plan a skillful development only when he has reached a point where he can predict within reasonable limits what the reactions of a group of pupils will be.