cial life of
the student so that the analysis of these may lead the student to
formulate many of the generalizations that are given early in a
textbook course?

Should college mathematics be presented as a series of subjects,
e.g., algebra (advanced), solid geometry, trigonometry,
analytical geometry, calculus, etc.? Would it be better to
present the subject as a single and unified whole in two or three
semesters?

Should a student study his mathematics as it is developed in his
book,--viz., as an intellectual product of a matured mind
familiar with the subject,--or should the subject grow gradually
in a more or less unorganized form from a series of mechanical,
engineering, building, nautical, surveying, and structural
problems that can be found in the life and environment of the
student?

V. Moot Questions in the Teaching of this Subject.

VI. How judge whether the subject has been of worth to the student?

How test whether the aims of this subject have been realized?

How test how much the student has carried away? What means,
methods, and indices exist aside from the traditional
examination?

VII. Bibliography on the Pedagogy of this Subject as Far as It Applies
to College Teaching. The aim of the bibliography
should be to give worth-while contributions that present
elaborations of what is here presented or points of view and
modes of procedure that differ from those here set forth.

PAUL KLAPPER
_The College of the City of New York_

CONTENTS
PAGE

INTRODUCTION xiii

By NICHOLAS MURRAY BUTLER, Ph.D., LL.D. President of Columbia
University. Author of _The Meaning of Education_, _True and False
Democracy_, etc. Editor of _Educational Review_

PART ONE--THE INTRODUCTORY STUDIES

CHAPTER

I HISTORY AND PRESENT TENDENCIES OF THE AMERICAN COLLEGE 3
By STEPHEN PIERCE DUGGAN, Ph.D. Professor of Education, The
College of the City of New York. Author of _A Student's
History of Education_

II PROFESSIONAL TRAINING FOR COLLEGE TEACHING 31
By SIDNEY E. MEZES, Ph.D., LL.D. President of The College of
the City of New York. Formerly Pr