The Teaching of Mathematics in the Elementary and the Secondary School

During recent years there has developed in this country a very real interest in the teaching of mathematics, as evidenced by the formation of numerous associations of teachers of mathematics. This interest may be traced to two principal sources. The great mathematical revival finding its expression in the rapid and healthy growth of the American Mathematical Society has had naturally a reactionary effect upon collegiate and then upon secondary instruction. This effect is seen in the effort to put upon a scientific basis the elementary parts of mathematics in their relation to the subject as a whole. At the same time, modern pedagogy holds as its principal thesis that both subject matter and manner of presentation must be arranged with reference to a psychological study of the pupil. Hence a further rearrangement of mathematical material is required with the express object of obtaining and retaining the student’s interest. These two courses of the demand for improvement in mathematical instruction call for two lines of preparation on the part of the teacher, mathematical and peciagogical. A man may have studied a wide range of mathematical topics and yet have so poor a notion of how to present his ideas that it takes several years’ experience to learn to teach; and in the meantime many of his pupils may discover, or believe that they have discovered, that they are so mentally deficient as to be unable to grasp mathematics. On the other hand, a man may learn something of the technique of teaching and be so ignorant of the principles of the science that his students do not obtain any idea of the spirit of mathematical studies. Such ignorance may be partially pardoned in the man who is forced to teach many different subjects; but it is, even at present, no novelty to find a teacher of mathematics only, who thinks that he requires his students to give a complete reason for every step in a geometrical demonstration. It is generally conceded that the normal schools have been unable to afford proper mathematical training for the high school teacher, and it is gratifying that the colleges are beginning to offer courses in mathematics arranged especially for those intending to enter the field of secondary instruction. Such courses should touch on many topics having an immediate bearing on elementary algebra and geometry and not ordinarily included in the courses usually offered to undergraduates, as well as some discussion of pedagogical principle. The proper person to conduct them has been aptly described by a well-known mathematician as “a mathematician sufficiently interested in his subject to publish occasional investigations, and who has the pedagogic instinct.”