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establish working contact with all organizations of teachers and others interested in its problems and to secure their active assistance. Nearly 100 such organizations have taken part in this work. A list of these organizations will be found in the appendix to this report (p. 632). Provisional reports on various phases of the problem were submitted to these coöperating organizations in advance of publication, and criticisms, comments, and suggestions for improvement were invited from individuals and special coöperating committees. The reports previously published for the committee by the United States Bureau of Education and in The Mathematics Teachers and designated as "preliminary” are the result of this kind of coöperation. The value of such assistance can hardly be overestimated and the committee desires to express to all individuals, organizations, and educational journals that have taken part its hearty appreciation and thanks. The committee believes it is safe to say, in view of the methods used in formulating them, that the recommendations of this final report have the approval of the great majority of progressive teachers throughout the country.

No attempt has been made in this report to trace the origin and history of the various proposals and movements for reform nor to give credit either to individuals or organizations for initiating them. A convenient starting point for the history of the modern movement in this country may be found in E. H. Moore's presidential address before the American Mathematical Society in 1902.6 But the movement here is only one manifestation of a movement that is world-wide and in which very many individuals and organizations have played a prominent part. The student interested in this phase of the subject is referred to the extensive publications of the International Commission on the Teaching of Mathematics, to the Bibliography of the Teaching of Mathematics, 1900-1912, by D. E. Smith and C. Goldziher (U. S. Bureau of Education, Bulletin, 1912, No. 29) and to the bibliography (since 1912) to be found in this report (Chap. XVI, p. 539f).

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* The Reorganization of the First Courses in Secondary School Mathematics, U. S. Bureau of Education, Secondary School Circular, No. 5, February, 1920. 11pp. Junior High School Mathematics, U. S. Bureau of Education, Secondary School Circular, No. 6, July, 1920.

The Function Concept in Secondary School Mathematics, Secondary School Circular, No. 8, June, 1921.

3 Terms and Symbols in Elementary Mathematics, The Mathematics Teacher, Vol. 14 (March, 1921), pp. 107-118. Elective Courses in Mathematics for Secondary Schools. The Mathematics Teacher, vol. 14 (April, 1921), pp. 161-170. College Entrance Re. quirements in Mathematics. The Mathematics Teacher, vol. 14 (May, 1921), pp. 224245.

* E. H. Moore : On the Foundations of Mathematics, Bulletin of the American Mathematical Society, vol. 9 (1902-3), p. 402; Science, vol. 17, p. 401.

The National Committee expects to maintain its office, with a certain amount of clerical help, during the year 1922-23 and perhaps for a longer period. It is hoped that in this way it may continue to serve as a clearing house for all activities looking to the improvement of the teaching of mathematics in this country, and to assist in bringing about the effective adoption in practice of the recommendations made in the following report, with such modifications of them as continued study and experimentation may show to be desirable.

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PART I

GENERAL PRINCIPLES AND RECOMMENDATIONS

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