: It is believed that this will, under the guidance of a judicious teacher, give him valuable training, not only in reasoning, but also in the use of language. He is required also, in many cases, to derive his own rules from the preceding solutions and principles. In order that he may understand the practical application of Arithmetic, and at the same time acquire a knowledge of the business use of the science as he proceeds, the problems given are largely, almost wholly, drawn from the actual business operations of life. The fact that a large number of pupils never study Arithmetic for any great length of time, and the necessity of their studying that only which will be of practical utility to them in after life, has been kept constantly in view in adapting the book to their wants. Extended exercises are given in the application of the fundamental rules, because these are the basis of all the operations of Arithmetic. The definitions given are brief and accurate, and it is thought they are all clothed in such language as the pupils can readily comprehend. Every effort has been put forth to make the book a desirable one, not only for the pupil in learning the elements of Arithmetic, but also for the teacher in presenting the principles to the mind of the learner. It is believed, and confidently hoped, that progressive teachers everywhere will find it well adapted to their wants. CENTRAL STATE NORMAL SCHOOL, LOCK HAVEN, PA., July 19, 1877. A. N. R. SUGGESTIONS TO TEACHERS. THE author neither desires nor aims to give here a detailed method of teaching the whole subject of Arithmetic, but rather to suggest a few hints which he hopes may be of practical service to those who use the book. OBJECTS. Since children acquire knowledge most readily through their perceptive faculties, the teacher should illustrate largely by the use of objects. This means of illustration should be used from the beginning, for the reason that the child thinks concretely-that is, in connection with objects. The idea of ten ones, or a ten, can be best taught by putting together ten objects and calling the collection a ten; in a similar manner ten tens, forming a hundred, and so on. So also the idea of a fraction and of fractional parts can be taught best in connection with objects. Objects themselves are much superior in this respect to pictures. In the selection of objects care should be taken, especially in teaching the idea of a fraction, that such objects be used as cannot be divided without destroying their unity. Thus, an apple is much better for illustration than a stick or a line; for if an apple be divided into any number of equal parts, none of these parts are units; but a stick may be divided into other sticks, or a line into other lines, each of which is still a unit. NUMERAL FRAME.-Teachers will find the numeral frame a great aid in teaching all the fundamental rules. It has the advantage of being compact and convenient, and is always at hand. It is among the most serviceable articles of school furniture. COUNTING. Give much attention to the exercises in counting following each of the tables. It is believed that if these exercises are judiciously used, pupils will perform the operations of the fundamental rules with much greater rapidity and exactness. Don't continue these exercises, however, till they become tedious or monotonous. TESTS.-Whenever possible give your pupils experience in the actual application of measurements. Thus, let them in the absence of a foot-rule or a yardstick mark a lath into feet and inches, and by the use of this determine the height and length of their desks, the blackboard, the recitation seats, the doors, etc., and of the schoolroom itself. If no set of weights can be secured, let paper or muslin bags filled with sand or corn, representing the ounce, the pound, the quarter-pound, etc., be used. The pupil is thus more readily taught, because he gains his knowledge largely by observation, and the judgment is trained and cultivated while the knowledge is being acquired. SOLUTIONS. The solutions given in this book are simple and concise. Teachers are not expected, however, to confine themselves strictly to those given by the author. Many problems will admit of several solutions. It will be well, therefore, for the teacher to encourage the pupils to give solutions of their own. He should be careful to see, however, that no unnecessary words are used, and that the solutions are given in good language. This will train the pupils to think and reason for themselves. In the written work everything should be done neatly, whether on the slate or on the blackboard. Pupils should be taught how to make figures. They frequently do not make neat figures, because they have never been taught. THOROUGHNESS.-Do not hurry. Let your pupils mas ter everything thoroughly as they pass over it. It is believed that the exercises in this book are sufficiently extended and well graded to enable the learner to master the elements of the different subjects presented. But should the teacher deem it necessary to have more extended exercises, both teacher and pupils will find it advantageous often to originate problems for themselves. The teacher should be sure that the pupil understands the principles as he proceeds. It is too often the case that he is hurried along from one subject to another without having a clear comprehension of each, and therefore spends years in doing the work of as many months. HELP. Let the teacher give no help where the pupil can overcome any difficulty by his own efforts. Every obstacle the learner surmounts unaided, and every difficulty he overcomes, makes him stronger and better prepared to contend successfully with the next. If help is needed, let it come indirectly in the shape of hints or suggestions. A single suggestion will often put a pupil on the right track or start a train of thought which will lead to success, and the knowledge thus gained without actual aid will be doubly valuable to him. ORAL ARITHMETIC.-The exercises in Oral Arithmetic are not designed to be comprehensive. In many cases the teacher will find it advantageous to have his pupils solve some of the written problems orally. A portion of the class may be solving their problems on the blackboard while another part of the class may be solving by the oral process. Thus much valuable time may be economized, and the solutions and principles, being discussed by both methods in the same recitation, will be more fully comprehended and more definitely understood. |