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The Standard Mathematical Service is an organized enterprise, the first of its kind, attempting to provide adequate teaching tools for assisting in the mathematics teacher's four-fold professional task: "teach-practice-measure-remedy." The Standard Service Series of Arithmetics, of which the present volume is Book I, is a main unit of this Service. The Series consists of four books, one each for the third and fourth grades, one for the fifth and sixth grades, and one for the seventh and eighth grades.
The Standard Service Arithmetics are a conscious and consistent attempt to apply the known facts about child-learning to arithmetic teaching. These facts have been drawn from the classroom experience of hundreds of teachers and from careful experimentation, carried out over a period of several years. The material and organization of all books of the series have been tried out and digested into final form after classroom use by pupils drawn from all parts of the United States.
Book I of the Standard Service Series, which is for the third grade, employs important principles of learning through the following seven features which appear consistently throughout the year's work:
(1) Gradual, detailed development of new topics, with careful regard to the vocabulary, illustrations, and explanations used.
(2) Scrupulously calculated distribution of drill and review (a) to insure proper amounts of periodic practice on the basic number facts and processes, and (b) to prevent the forgetting of what has been previously learned.
(3) The systematic use of motivating devices such as: (a) games, races, puzzles, pictures, etc., that make an appeal to the third-grade child; (b) legitimate appeal to the spirit of competition
with the pupil's own past records and with the standards achieved in tests and races by thousands of other third-grade children; (c) consistent employment of the principle of "awareness of success or failure at the time of learning" through the agency of Self-Testing Drills, Problem Scales, and self-measuring exercises; and (d) prevention of initial discouragement through easy mastery by a leisurely, step-by-step unfolding of topics.
(4) Provisions for securing an active, critical, social, and selfreliant attitude toward the learning of arithmetic.
(5) Explicit lessons to give children an insight into problem analysis and problem study, with detailed guidance in habits of estimating and judging intelligently.
(6) The systematic measurement of achievement with the attendant recognition of individual differences through SelfTesting Drills, Problem Scales, and other standardized material, the units of which are carefully correlated with the general subject-matter and distributed throughout the year.
(7) The consistent training of the pupil in good habits of using his book as a learning tool. In the body of the text and in the Self-Help Practice Lessons, the pupil is taught how to help himself with the precise difficulties on which he finds he needs restudy and repractice. The reading simplicity of this book is such as to raise it above the customary reference-book type of text to the plane of a real learning instrument for a third-grade pupil. Good habits of using such a text will contribute powerfully toward good study habits in general, as well as toward early self-reliance.
One out-standing point of departure of The Standard Service Series of arithmetics is that an entire book is given to each of the third and fourth grades. A single book is provided for the fifth and sixth grades and a single book for the seventh and eighth grades. The greater maturity of the pupil permits of greater compression and progress by longer strides, making a single book feasible for two years' work in these upper grades.
This organization of the material is again the result of careful experimentation and deliberate determination by the authors.
The impelling reason for a four-book series lies in the fact that to give a genuinely modern treatment of third- and fourthgrade arithmetic, based on the scientific findings of the last decade, demands leisurely and expansive treatment. When the authors had proved to themselves, literally through years of patient, intensive experimental study, that the irreducible minimum scope for a genuinely pedagogical treatment of the arithmetic for these lower grades demanded a space of more than 700 pages, they decided to publish each year's work in a separate book. There would be no thought of trimming the final product to the dimensions and character of the customary reference-book type of text, thereby discarding the results of careful investigations made over a period of years. The decision was simply forced by the necessities of the undertaking. The main items of space that required separate volumes for each of these grades fall into three groups:
I. Definite pedagogical undertakings that demand expansive treatments. (1) Development, step by step, of scientifically itemized stages of difficulty in new arithmetical processes. and topics, by advances so gradual and so copiously illustrated, exemplified, and practiced on as to be easily within the grasp of the child.
(2) Numerous silent-reading exercises in chatty and informal language for child appeal. These lessons, oftentimes with pictorial and diagrammatic aids, provide stimulating instruments for self-teaching.
(3) Carefully devised lessons which assist the learner in problem-solving, with problem settings drawn from real life. These units also train the pupil in estimating results and in the technique of checking. The instructions and sample treatments given in these units have, through the ordeal of varied and crucial experimentation, proved their worth.