TO THE TEACHER. In order that the teacher may use this book in the most successful way, it is necessary that she should give careful heed to the following suggestions: The book is designed for young children; it is supposed that they have no knowledge of numbers except such as they may have picked up unconsciously in their plays, and in their home life. They will often be found able to count — that is, to say the names of the numbers in order-as far as to twenty or farther. THE CHILD'S CONDITION.-It is the teacher's first business to ascertain with respect to every child in the class, just how far his present knowledge extends, so that she may waste no time in attempting to teach him what he knows already; nor, on the other hand, attempt to teach him what is so far in advance of his present knowledge that he will be incapable of understanding it. The first lessons in this book are constructed on the supposition that the child can read with some fluency; that he can write and draw to some extent. If the teacher attempts to use the book with children who are not up to this standard, she will need to aid them accordingly. HOW TO USE THE BOOK.-With children in the primary grades, most of the successful teaching must be oral. To help the teacher in this work, the oral exercises preceding each lesson are specially prepared.* These exercises and questions are intended to be suggestive merely; the good teacher will devise exercises for her own use, either additional to those given, or in place of some of them. Enough exercises of this kind should be used to accomplish their purpose, but no more. When the child knows instantly and without effort that five and two are seven, with the facts implied in that knowledge, it is a very great mistake to drill him any longer on exercises which aim to teach those facts. The child's lessons are intended chiefly to furnish him seat work; the oral exercises are intended to help the teacher in preparing the child to do his seat work intelligently. When the *The child needs to read only the portions marked "For Study." 7 pupil's seat work is completed, the teacher should not fail to examine it carefully, noting both its accuracy and its neatness. SOME FUNDAMENTAL PRINCIPLES.- Use objects. In Arithmetic, as in everything else, the child gets his first conceptions through the use of his senses. Hence, all his first operations with numbers should be performed with objects. To insure variety and to promote interest, the teacher should be supplied with an abundance of objects, such as buttons, spools, kernels of corn, beans, nails, etc. For a good reason, which will appear in the course of our work, splints of wood, something like jackstraws or toothpicks, are recommended for most frequent use. Splints especially prepared for this purpose are for sale by all the principal dealers in supplies for primary schools; but the teacher can readily prepare them for herself, or get some older pupil to do so. In every case the child should use splints, or counters of some kind, till he has mastered the general truth to be learned, but no longer. It is as great an error to continue the use of objects too long as it is to attempt to teach numbers without using objects at all, which was formerly the custom. If at any time, however, it is found that a pupil has failed to learn what he was supposed to have learned from the use of his counters, turn him back to their use temporarily, and thus correct his deficiency. Do not confound figures with numbers. It is believed that failing to distinguish between numbers and the figures that represent them is the source of a vast deal of confusion in pupils' minds. We do not "add figures," "multiply one figure by another," find "how many times one figure is contained in another," etc. To keep the matter clear from the start, many questions are suggested in these lessons similar to the following: Where is the number? Where is the figure that "stands for it"? Where is the number that this figure "stands for"? etc. How many? What? Essentially, number is ratio. The number seven, used abstractly, signifies merely the ratio of a quantity of units of any kind to one unit of the same kind by which the quantity is measured. But no one can have a clear thought of the measured quantity till he knows clearly what the measuring unit is. Now this is so important that we deem it essential that it should be brought to the pupil's consciousness even from the start. Hence the frequency of the questions, How many? What? or What kind? in the suggested exercises. PRIMARY ARITHMETIC. PART I. LESSON 1. NOTE. The following oral exercises prepare pupils for written work during the study hour. Be sure that many of the exercises call for action on the part of the child. (The exercises with the class should precede the pupil's seatwork.) ORAL EXERCISE. Show me one book; one table; one stick of crayon. Point toward one boy; one window; one door; one tree. Bring me one pencil, Lucy. Take one step, Fred. Nod your head one time, Charley. Can you spell one? the figure that means one? Can you make This is it-1. (Teacher makes the figure and the word on the board.) See this boy. How many boys are there? Make the figure 1, and write the word one, carefully on paper at your seat. 9 LESSON 2. ORAL EXERCISE. How many hands have you? Show me as many fingers as you have hands; as many splints. Show me two shells; two spools; two table-legs. (Let the teacher substitute the names of pupils for the names in the book.) Harry, bring me two books. Two pencils, Mary. Two sticks of crayon, Ethel. Two buttons, Albert. Each of you may take one block in your right hand. Take one block in your left hand. Now put these blocks together. How many blocks in all? One block and one block taken together are how many blocks? Hattie may bring me one pencil. Elmer may bring me one pencil. I will put these pencils together. How many pencils together have I? Elmer may bring me two other pencils. One pencil and one pencil are how many pencils? Mabel had one doll, and her aunt gave her one more. How many dolls had Mabel then? Fred may tell the story of Mabel and her dolls. FRED: Mabel had one doll. Her aunt gave her one more. She then had two dolls." George wanted a top that would cost him two cents. He had one cent. How many more cents must he get? Each of you may hold up two splints. Now you may lay one of them on the table. How many splints have you left? George may tell the story. GEORGE: "I had two splints and laid one splint on the table. I then had one splint left." Two blocks less one block are how many blocks? Maggie may make two marks on the board. Willie may erase two of them. How many marks are left? Two marks less two marks leave how many marks? Irene may tell the story. IRENE: "Maggie made," etc. (Incidentally call the pupil's attention to the changes in words, when more than one is meant; that is, to the formation of plurals.) Answer as quickly as you can, using only one word: One and one are how many? Two less one are how many? Two less two are how many? One less one are how many? How many ones are there in two? Who can write the word two? The figure that means two is at the left of the picture of the little girl. The word two is at the right of the picture. NOTE.-These exercises will suggest to the teacher the variety that can be introduced. They may be extended as much as is necessary, or any may be omitted if not needed. Suit the work to the child's condition. All the work should proceed as promptly as it is possible for the pupils to follow it. FOR STUDY. See this girl. are there? How many eyes has she? How many feet? How many hands has the doll? How many arms? has the doll? How many feet have you? Make one short line on your slate. Now make one more beside it. How many lines taken together have you made? |