INTELLECTUAL ARITHMETIC, UPON THE INDUCTIVE METHOD OF INSTRUCTION. BY WARREN COLBURN, A.M. New Edition, Revised and Emproved. BOSTON: BROWN, TAGGARD & CHASE, SUCCESSORS TO W. J. REYNOLDS AND CO. No. 24 Cornhill. Samuel A. Green, M. D. a Boston. CHC.U. 1857. Entered TEMPERANCE C. COLBURN, Widow of Warren Colburn, Educ T Math=45771-11 415.47.7 ADVERTISEMENT TO THE REVISED EDITION. Frye J$18.56.305 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 publi cation, 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 LesBons is sufficiently easy for the most juvenile scholar. HARVARD COLLEGE LIBRARY INTRODUCTION. { THE first instructions given to the child in Arithmetic, are usually given on the supposition that the child is already able to count. This indeed seems a sufficiently low requisition; and if children were taught to count at home in a proper manner, they would have this power in a sufficient degree when they enter the primary school. But it will be found on trial that most children, when they begin to go to school, do not know well how to count. This may be proved by requiring them to count 20 beans or kernels of corn. Few of them will do it without mistake. The difficulty is they have been taught to repeat the numerical names, one, two, three, in order, without attaching ideas to them. They learn to count without counting things. This point then calls for the teacher's first attention to lead the child to apprehend the meaning of each numerical word by using it in connection with objects. The kind of objects to be employed as counters should, of course, be similar, as marks on the blackboard, beans, pieces of wood, or of cork, or the balls in numeration frame. Provided they are similar, and large enough to be seen without effort by all the class, it is of little consequence what they are: the simpler the better, and those which the teacher devises or makes, will, other things being equal, be best of all. Not more than ten should be used or exhibited to the children in the first few lessons. LESSON I. Let the class have their attention called to the teacher; and when he lays down a counter, when all can see it, let them say one; let the teacher lay down another, and the class say two; and So on up to ten. If any of the class become inattentive, let the teacher stop at once; and, after the attention is fully centred on him, let him begin again. After going through this addition a few times in this form, it may be varied thus. The teacher laying down the counters, one by one, as before, the class may be led to say, one and one are two, two and one are three, three and one are four, &c. The above mode of adding may be shortened by leading the class to say as follows: One and one are two, and one are three, and one are four, &c. At any time the word designating the counter may be used along with the number, as beans, balls, pieces, marks, or books, as the case may be. At times it will be well to give some fictitious designation to the counters, such as the teacher, or still better, such as some one of the class may choose, calling them men, sheep, horses, &c. Next to Addition, as illustrated above, should come Subtraction. Having counted ten, let the teacher take away one, and the class be made to say, one from ten leaves nine, one from nine leaves eight, &c. In Subtraction the same variations may be introduced as in Addition. No further illustrations of this operation need be given, as the teacher's discretion will supply all that is necessary. In connection with these exercises, let the pupil be taught to repeat in reversed order the numerical words they have employed, counting from one up to ten, and then in reverse order from ten to one. It is not to be supposed that the whole of the foregoing lesson can be learned at one exercise. It is only a small part of it that children will at first have sufficient power of attention to go over with profit. The same remark may be made respecting the following Introductory Lessons. LESSON II. 66 Let the teacher call the attention of the class, and require them to count, and then lay down, one by one, a small number of counters, say, for example, five; then let him separate them into two parts, as one and four, thus, ...., and say, one and four are five," and require the class to say the same. Then let him divide the number into different parts, as two and three, three and two, four and one, one and one and three, &c., requiring the class with each division to name the parts and make the addition. Let them always begin at the left end of the line of counters as they face them. Having exhausted the combinations of five, let the number six be taken, giving combinations like the following: ; • ·· ; &c. It may be found that a lower number. than five should be made the first step in this exercise. After the combinations of six have been exhausted, the number seven may be taken, and then successively, eight, nine, and ten. As a part of this Lesson, each question in addition should he converted into a question in subtraction; thus five and three are eight; then, having put the two parts together which make eight, remove the three, and lead the class to say, "three from eight leaves five." The following exercise is important in this connection. Let the teacher select some number, and give one part of it. and require the class as quick as possible to name the complementary part. Thus let six be the number, the exercise will be as follows. Teacher. "Now attend, six is the number; I am going to name one part of it; when you hear me name it, do you all name the other part as quick as you can; now be ready; five." Class; 66 One," Teacher: "Four." Class; "Troo." Teacher: "Three." Class: "Three." Teacher: "One." Class: "Five," &c. This exercise should not be pressed too fast, but carried on gradually as the pupil's strength of mind will allow. Special pains should be taken that the number ten be perfectly mastered in this form of combining its parts. This will give the pupil the most important aid in all his calculations in larger numbers. LESSON III. For a number of days after beginning the above exercises, the child should not have the book at all in his hands. If the child has the book in his possession, it will be well for the teacher to take it for a few days, and let the pupil employ himself at his seat in writing on a slate, or with other books. In this way the child has awakened within him the idea of calculation in numbers, without having become wearied with the reading of what excites no interest. After a few days, however, the book may be put into the pupil's hands, and he may be directed to get a lesson in Section I. In the meanwhile the Introductory Lessons should be continued, and form a part of each day's exercise till they are finished. In this way, the pupil, in studying his first lesson from the book, will already have learned the use of counters, and will naturally resort to them at his seat, using beans or marks on his slate for this purpose. It will be far better for him to come to the use of counters in this natural way, than to be enjoined to use them before he has been interested in witnessing their application. The pupil, in the preceding lessons, has become acquainted with all the numbers as far as ten, regarding them either as units, or as grouped into parts of a larger whole. The next step is to carry him through the numbers from ten to twenty. First, let the class count with the objects before them from one up to twenty; then, removing all but ten, let the ten be grouped in a pile or if they are marks on the board, let them be enclosed by a line drawn around them, and begin to count upward from ten, "One and ten are eleven; two and ten are twelve; three and ten are thirteen; "— here pause, and examine the composition of the word, thirteen three ten, or three and ten. Show how the three is spelt in thirteen, and also how the ten is spelt. Then proceed, "four and ten are fourteen," examining the word as in the former case; "five and ten are fifteen; six and ten are," perhaps sume one in the class will now be able to give the compound word; then go on, 66 seven and ten, eight and ten, nine and ten, ten and ten." When they can give the compound words readily from the simple ones, then give them the compound word, and let the class separate it into its two component words; thus: Teacher: "SevClass: "Seven and ten," &c. Thus far let the teacher be careful to present the name of the smaller of the two numbers first, for that is the order in which the compound word presents them; let the teacher say four and ten, and not ten and four. enteen." |