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Entered according to Act of Congress, in the year 1847, by
WILLIAM J. REYNOLDS, in the Clerk's Office of the District Court of the District of Massachusetts.
ADVERTISEMENT TO THE REVISED EDITION.
The character of Colburn's First Lessons is too widely and thoroughly known to make it necessary to give, in this edition, any extended statement of its principles and method. Ideas which were new at the first publication of this work have now, through the great change” that has taken place in elementary instruction in Arithmetic, through its influence, become the common possession of all intelligent teachers.
The careful revision of the work which has now been made has suggested very few points in which any change seemed to be required. It has been thought that a more easy and gradual introduction would render the work more useful to the most youthful beginners.*
The use of the book with beginners demands of the teacher considerable labor in the way of proposing original questions, and devising modes of illustration; and a short course of Introductory Lessons is prefixed, which the teacher may use as materials and hints in the first steps of the study.
* In the city of Lowell, where this book has been used from its first publication, the School Committee passed a vote in December, 1846, excluding all other Arithmetics in their Primary Schools ; thus showing, in the opinion of intelligent men who acted upon their experience, that Colburn's First Lessons is sufficiently easy for the most juvenile scholar.
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clem GENERAL VIEW OF THE PLAN.
EVERY combination commences with practical examples. Care has been taken to select such as will aptly illustrate the combination, and assist the imagination of the pupil in performing it. In most instances, immediately after the practical, abstract examples are placed, containing the same numbers and the same operations, that the pupil may the more easily observe the connection. The instructer should be careful to make the pupil observe the connection. After these are a few abstract examples, and then practical questions again.
The numbers are small, and the questions so simple, that almost any child of five or six years old is capable of understanding more than half the book, and those of seven or eight years old can understand the whole of it.
The examples are to be performed in the mind, or by means of sensible objects, such as beans, nuts, &c. The pupil should first perform the examamples in his own way, and then be made to observe and tell how he did them, and why he did them so." *
Several examples in each section are performed in the Key, to show the method of solving them. No answers are given in the book, except where
It is remarkable, that a child, although he is able to perform a variety of examples which involve addition, subtraction, multiplication, and division, recognizes no operation but addition. Indeed, if we analyze these operations when we perform them in our minds, we shall find that they all reduce themselves to addition. They are only different ways of applying the same principle. And it is only when we use an artificial method of performing them, that they take a different form.
If the following questions were proposed to a child, his answers would be, in substance, like those annexed to the questions. How much is five less than eight? Ans. Three. Why? Because five and three are eight. What is the difference between five and eight? Ans. Three. Why? Because five and three are eight. If you divide eight into two parts, such that one of the parts may be five, what will the other be? Ang. Three. Why? Because five and three are eight.
How much must you give for four apples at two cents apiece? Ans. Eight cents. Why? because two and two are four, and two are six, and two are eight.
How many apples, at two cents apiece, can you buy for eight cents ? Ans. Four. Why? Because two and two are four, and two are six, and two are eight.
We shall be further convinced of this, if we observe that the same table serves for addition and subtraction; and another table which is formed by addition, serves both for multiplication and division. In this treatise the same plate serves for the four operations.
This remark shows the necessity of making the pupil attend to his manner of performing the examples, and of explaining to him the differenco between them.