M THE IROQUOIS ARITHMETICS FOR SCHOOL AND LIFE BOOK THREE GRADES SEVEN AND EIGHT 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. THE IROQUOIS ARITHMETICS TWO BOOK SERIES ELEMENTARY, Grades Three, Four and Five Including a review of Grades One and Two ADVANCED, Grades Six, Seven and Eight THREE BOOK SERIES BOOK ONE, Grades Three and Four Including a review of Grades One and Two BOOK TWO, Grades Five and Six BOOK THREE, Grades Seven and Eight 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. The Third and Fourth Yearbooks of the 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 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. In the Fourth Year Book of the Department of Superintendence it says: "Modern psychology demands that in the teaching of arithmetic there should be, on the part of the child, a real feeling of need and clear vision of use and application,—in short, there should be as complete motivation as possible." The Iroquois Arithmetics have been built to meet this demand. BOOK THREE Book Three is for grades 7 and 8. Like Books One and Two it is a complete self-explanatory text. No teacher's manual is needed. Language. The language of Book Three, both in vocabulary and sentence structure, is slightly easier than standard reading material for the Seventh and Eighth Grades. Pupils are able to read material that they do not thoroughly understand; and, since scientific research has determined that from 30% to 50% of the errors in problem solving are due to the inability of the pupils to understand the language of the problems, the authors have carefully avoided bringing any language difficulties into either the process explanations or the problems. Scientific Drill on the 390 Number Combinations. In both the seventh and eighth grades a systematic review of the fundamental processes in whole numbers, fractions and decimals places special stress on this very important phase of arithmetic. As in the preceding grades, the 390 number combinations have been used with a frequency ratio in proportion to the difficulty of the combinations as established by recent scientific investigations. The ratio established gives the most difficult group of combinations four times as often as the easiest group. In this way adequate provision is made for scientific drill which has heretofore been lacking in basal texts, as recent investigations have shown. Tests in Measuring Individual Progress. A very complete series of mixed fundamental drills and tests is provided at frequent intervals to enable both teacher and pupil to measure the progress made. All these drills and tests are skillfully motivated so that the interest of the pupil may be maintained. The tests are diagnostic, remedial and self-rating. The self-rating scales by which a pupil measures his own progress should stimulate pupils to do their best. Furthermore, the instructions at the beginning of the tests are so worded that these tests may be utilized for drill purposes as well as testing. If the test makes it evident that some pupils need more drill, the teacher is immediately able to assign extra work. Thus a plan is provided for skillful teaching which is in harmony with the modern tendency to provide for individual differences. Fractions and Decimals. The work in fractions has been built to conform with business practice which calls for emphasis on fractions |