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mathematical knowledge. Arithmetic is reviewed mainly through applications found within the domain of child life, through wide experiences in many situations. Thus, the arithmetic has changed from the formal drill process used in the lower grades to a process of assimilation through application.

The following are some of the important features of this text:

The material is organized in pedagogical units, rather than in logical units, i.e., material has been put together which is most economically and effectively learned together. Instead of learning a number of isolated facts or lessons, the pupil sees the relations of a compact body of facts closely related to one another and to the major topic. He will therefore not only master the unit with economy of effort, but will retain it more permanently than when facts are studied separately.

The method of approach is inductive.' This is the method of the beginner. The main object is thorough understanding of the concepts to be derived from numerous instances familiar to the pupil by means of examining, contrasting, and comparing. Formal statements, defining the new term or stating the principle, are always the last step in the development.

New terms are introduced when they are needed, and not earlier. Moreover, invariably such explanations are given in the text as are necessary to let both the teacher and the pupil understand the reason for bringing in new terms. Each new topic is started with a real problem impressing the pupil with the usefulness of the subject to be studied.

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The book contains a great many type examples, illustrating both the method and the arrangement of a solution. Neat and clean-cut written work in mathematics is an important factor in clean-cut thinking. Hence this feature is stressed throughout.

The language of the book is precise, but the sentences are simple so that the pupil can read and understand them. Problems are arranged in order of difficulty determined from actual pupil-performance. There is not a problem in the book which has not been worked by pupils.

In the process of finding the solutions of a problem and in the interpretation of the solutions, it is important that the pupil understand the meaning of approximated measures. Lack of appreciation of the degree of precision causes not only misleading impressions, but also useless effort and waste of time. Since measurement plays an important part in this course and since many data are necessarily approximations, the pupil must learn to determine the degree of precision in the results determined from these data. Hence, considerable attention is given to this matter.

The author wishes to express his appreciation to Director Chas. H. Judd and to Professor H. C. Morrison and the late Professor S. C. Parker of the School of Education, the University of Chicago, for work on the manuscript and for their constant advice and inspiration during the process of development of this course, and to Professor W. C. Reavis, whose interest and support as principal of the University High School has greatly facilitated experimentation in junior high school classes.

The studies which contributed to the refinement of the material used in the course presented in this book were aided by a grant from the Commonwealth Fund.

E. R. BRESLICH.

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