THE IROQUOIS ARITHMETICS: FOR SCHOOL AND LIFE BOOK ONE GRADES THREE AND FOUR BY HARRY DEW. DEGROAT PRINCIPAL OF THE STATE NORMAL SCHOOL SIDNEY G. FIRMAN SUPERINTENDENT OF SCHOOLS WILLIAM A. SMITH SUPERINTENDENT OF SCHOOLS IROQUOIS PUBLISHING COMPANY, INC. SYRACUSE, N. Y. To Teachers of Arithmetic: The Iroquois Arithmetics represent a distinct advance in arithmetic textbook achievement. They bring to pupil and teacher not only the experience of successful arithmetic teachers but also the results of modern researches and surveys. These investigations are demonstrating scientifically where the real difficulties lie and how to meet them. Three noteworthy investigations have been constantly before the authors: 1. Number Combinations, Their Relative Diffi- 2. Research in Constructing the Elementary 3. Summary of Educational Investigations The University of Wisconsin investigation clearly points out the relative difficulty of all number combinations and how arithmetic texts in the future should emphasize them. Utilizing these facts the authors give the pupils drill in proportion to the relative difficulty of the 390 number combinations in addition, subtraction, multiplication and division. In a similar manner the results of the other recognized investigations are utilized. Furthermore, the authors have carefully considered the latest and most generally accepted courses of study in the subject, including the New York State course of study, those for Baltimore County, Baltimore City and 397927 Minneapolis, as well as all State courses of study in arithmetic that have recently been issued, in order that this series might meet nationwide and present-day demands. THE IROQUOIS ARITHMETIC SERIES The Plan. To begin with, these books are built for the pupil, to create in the pupil's mind a desire to use numbers and to supply the means of satisfying that desire. With the watchword "teach only one difficulty at a time" a three-fold plan has been used. 1. By skillful use of child experience a need is created in the pupil's mind for each operation before introducing the procedure. 2. Each process or variation of each process is built upon a concrete situation of interest to a child-one in which the application of numbers unfolds a new interest. 3. The necessary graded drill in abstract number work is interspersed with problems of real child appeal which provide a reason for learning how to use numbers. Language and Illustrations. The language of these texts is noteworthy in its fitness to the pupil's stage of development. It is accurate and concise but never over the head of the pupil nor yet too childish. Each picture has a definite and real purpose. Reviews. The review features are skillfully handled by the accumulative method which constantly introduces, in new settings, the topics previously studied, thus avoiding what the pupil often regards as the monotony of review. Tests. Tests introduced at frequent intervals as well as at the end of each book provide a means for continuous measurement of attainment. These tests are devised to determine the needs of individual pupils, and to separate what the pupil knows from what he does not know, thereby determining specifically and accurately what drill is needed. Oral and Written Work. No sharp demarcation is made between oral work and written work. Ample material is available for both but, with the wide differences in capacity and attainments of classes, it is believed best to leave to the teacher the decision as to which shall be oral. Copying Minimized. Care has been taken in spacing abstract drill on the page to minimize unnecessary copying. With a folded answer paper as shown opposite page 1 the pupil works from the printed page and writes only his answers. BOOK ONE Book One is for Grades 3 and 4, but includes a review of the work of the first and second grades. This review, though brief, is so complete that it is in itself an admirable text for the second grade, and introduces the pupil very gradually to the larger field of the third grade. No teacher's manual is required. The text is a selfcontained course of study. It is self-explanatory and in language that a pupil can understand. Number Combinations. The modern practice of teaching addition and subtraction by means of number combinations whose sums have |