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PREFACE.

The Werner Arithmetics present the following characteristic features:

1. Strict Classification is Made Subordinate to Gradation.

Proper sequence with reference to the pupil has been constantly in the thought of the author in his selection and arrangement of matter. In the first two books of the series (grades 3 to 6 inclusive) the attempt has been made to give the student a body of knowledge which later he may classify as a working basis for his advancement into the higher mathematics. In the third book, more attention is given to classification, and the elements of algebra and geometry are presented.

2. They are Emphatically “ Mental Arithmetics." They are also “

Complete Arithmetics” in the sense that they provide or suggest the work neccessary for a complete primary, intermediate and grammar school course in arithmetic.

Very many problems similar to those usually found in the so-called Mental Arithmetics appear, but in such close relation to problems in which larger numbers are employed, that the pupil passes from one to the other without obtaining the false notion that there are two kinds of arithmetic, namely, “mental ” and “written." See first book, pages 132, 142, 167, 172, 179, 189, etc.

3. The Pupil is Introduced in the Beginning to the Five

Fundamental Processes. The first five lines of this book (page 9) present problems in addition, subtraction, multiplication, division noting the number of groups, and division noting the number in each group. Then, by a kind of spiral advancement, the pupil moves around this circle and upward through all the intricacies of combination, separation and comparison of numbers.

4. In the Lower Grades the Pupil is Made Familiar with New

Terms by Means of Oral Instruction and Frequent Use of the Terms Employed.

(See first book, pages 53, 63, 73, 188, 218, etc.) Many years ago Col. Francis W. Parker said, substantially, that the arithmetic of the future would contain neither rules, definitions nor explanations. These books are, in part, a fulfillment of that prophecy. In the first two books of the series definitions are introduced after the pupils are familiar with the terms defined. Formal rules are omitted entirely, and the uniform direction to the teacher is, “If the child cannot solve the problem presented, do not explain, but give him problems that he can solve and so lead up to and over the difficulty."

5. The Arrangement of Topics is Unique and Convenient.

In this book, measurement problems appear on pages 43, 53, 63, 73, etc.; a certain class of fraction problems, on pages 45, 55, 65, 75, etc.; facts of addition, subtraction, multiplication and division, on pages 41, 51, 61, 71, etc. This decimal arrangement of subjects makes the books almost as convenient for reference as are the books that are made on the strict classification plan, while the frequent recurrence of similar matter insures thorough review.

F. H. H. WAUKEGAN, ILL., March, 1896.

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