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MYERS ARITHMETIC

BOOK II

BY

GEORGE WILLIAM MYERS

PROFESSOR OF THE TEACHING OF MATHEMATICS AND ASTRONOMY
COLLEGE OF EDUCATION, THE UNIVERSITY OF CHICAGO

CHICAGO

SCOTT, FORESMAN AND COMPANY

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PREFACE

The work of Book I of the MYERS ARITHMETICS is for the third and fourth grades. It aims, first, to furnish clear concepts of number, and of the four fundamental arithmetical processes as tools for all sorts of measuring, and, second, to secure fairly good control of the necessary tabular machinery, including the facts of the addition and multiplication tables, the correlative subtraction and division truths, and the most useful facts and relations of denominate numbers. This is accomplished, partly by direct formal teaching of the tables, and partly by indirect uses in interesting problems, drawn from natural sources, suitably graded, and organized to impress the number lessons to be taught.

The broader educational aim of the work of Book II is to strengthen the grasp of arithmetic that is already secured, to give a measure of control of connected thinking, of inference-making, and to add appreciably to the pupil's ability to work independently. More particularly, this book seeks to expand the child's horizon of number to include fractional number, and to extend his control of the four fundamental operations to fractional number, both common and decimal. Long division, with its complicated technique, is thoroughly taught in Part I. Considerable systematizing of the pupil's knowledge of common fractions, together with a reconnoitre of decimals, and a forecast of percentage are also included in this Part.

Part II gives a topical first-treatment of addition, subtraction, multiplication, and division of whole and fractional number. It strengthens the hold on denominate numbers, on scale-drawing and mensuration, on bills and

accounts, and on percentage, and opens the attack upon interest. A little practical work on graphing is given. This constitutes Part II of the book, an arithmetic in itself. The first part of Book II is predominantly, not exclusively, spiral in treatment; the second part is predominantly, not exclusively, topical in its treatment.

The plan of these books recognizes the following important truths:

In the primary grades, children are too immature to profit by the study of topical unities, that call for much concentration. Unities, indeed, there must be; but they must be small enough to furnish immediate ends, and to lead to speedy successes. Arithmetical methods in the primary school must accordingly be characterized by variety, and by small topical unities. The spiral plan is well adapted to these grades.

In the grammar school, if work is to hold the interest, it must call for greater concentration. The pupil is now too mature either to enjoy or to profit by the practice of flitting from topic to topic at the beck of book or teacher. Unities of subject-matter must be larger and more complete than in the preceding grades. Pupils now work profitably and pleasurably under ends more remote, and successes may come a little more tardily. Gratuitous hopping from topic to topic, abiding nowhere long enough to make an appreciable point, is the sure road to failure in the grammar grades. The spiral plan is too lax, too centrifugal in its effects upon attention. The topical plan is best here. Grammar grade pupils crave the feeling that things are being completed as one subject is being left for another. Their standards of completeness may be unsophisticated. They are, however, aone the less real. Under-concentration in the grammar school is as disastrous to interest as is over-concentration in the primary school.

In the intermediate grades, the pupil's mental attitude is transitional. His mode of working is something be

tween the highly varied mode of the primary school and the more concentrative mode of the grammar school. The treatment best adapted to fifth and sixth grade pupils is a spiro-topical plan. Changes from topic to topic in these grades, particularly in the sixth, should be made at natural breaking points of subjects, or where minor or partial unities are completed. It is through the connectedness of these partial unities of topics that the child aids the natural drift of his mental faculties from the verbal to the rational type. This transition means much for arithmetic work, and good arithmetic work here will do much to promote the transition.

The destruction of interest in elementary school mathematics is nowhere so serious today as it is in the fifth and sixth grades. This is due, in good degree, at least, to the failure of arithmetical methodology to make practical recognition of the transitional type of mind found in these grades. Whether this book overcomes this difficulty or not, it, at least, assumes its reality and struggles with it.

Summaries of Parts I and II are given at the end of the book. These summaries serve (1) to assist the teacher to take an inventory of the results accomplished by the work of a year, and (2) to test the work with a view to guaranteeing a definite outcome. Furthermore, the teacher will welcome the summary of the work of a preceding grade as an aid in determining where and how to begin her work. The summaries will tend to reduce the waste due to "lost motion" from grade to grade in arithmetic. The acknowledgments rendered in the preface of Book I deserve to be repeated here.

Mr. F. W. Buchholz's energy, vigilance, and patience with the manuscript and proofs have increased as the work on the series has advanced.

Chicago, June, 1908.

THE AUTHOR.

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