Excerpt from The Teaching of Mathematics, in the Elementary and the Secondary School
I Should have been untrue to my profound conviction of the need of pedagogic preparation antecedent to entrance upon the actual work of teaching mathematics if I had not kept prospective teachers of mathematics in mind throughout the preparation of this book; I should have ignored the patent fact that it is experienced teachers who feel most keenly the problems of teaching and the need for their study if I had addressed myself to the inexperienced exclusively. As a consequence, unity of treatment and homogeneity of style have been in a measure sacrificed in what follows; the experienced teacher will, according to his experience, find this or that trite and superfluous; the inexperienced aspirant will occasionally feel the lack of the perspective of experience.
I appreciate deeply the importance of the historical aspect of the teaching of mathematics, but in view of its genial treatment in the excellent and well-known work of Smith, I have felt at liberty not to touch upon it. Some writers on methods in mathematics discuss more or less extensive topics of subject matter, in the form either of presentations to pupils or of a more Intensive study from the teacher's viewpoint. Such work is important - an essential element of progress, indeed; but I have found it advisable here strictly to confine myself to illustrative use only of subject matter. Within the bounds of the field thus limited I have further restricted myself, in the main, to conditions as they exist in the United States.
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