Is the Average Secondary School Pupil able to Acquire a Thorough Knowledge of all the Mathematics Ordinarily Given in these Schools?

Abstract

Before taking up the subject of our discussion, I ought to state that it has always been with the greatest reluctance that I have felt constrained to criticise the teaching of mathematics in the elementary and secondary schools. The reason for my reluctance is the inequity of the situation. We college teachers have an opportunity to test the knowledge of many who have been taught in the elementary and secondary schools, and on the results of this test, our favorable or unfavorable criticism is based. But the inequity exists because we college teachers constitute ourselves a court of last resort, so to speak. True enough, the college student will be judged by the mental capabilities which he possesses, but very few of them will have to show how much actual knowledge of mathematics they have gained while under our instruction. If we college teachers are unsuccessful with the student, we have the defense that he came to us not fully prepared and that the foundation of his mathematical knowledge was not strong enough to put the superstructure on. However, I feel that there is as much need for improvement in the course of study and the method of teaching of college mathematics as there is of the elementary and secondary mathematics.