Many other definitions and principles you may readily explain by some simple drawing or illustration. Aim to give a practical turn to every Evercise.— This you will best do by asking such incidental questions as shall have a bearing upon common business operations. So far as possible, require your pupils, not only to state the “how” of performing an example, but also to show that they fully comprehend the same, by solving problems given at the time, but not taken from the text-book. Let me suppose you have a class in mensuration. You ask a pupil how he will obtain the superficial feet in the floor of the school-room. His answer will be, “multiply the length by the width,” and he may give these words without being able to perform the operation. That you may know whether he comprehends the definition, or not, give him a rule or measuring-tape, and ask him to get the contents of the room. If he can do that properly and accurately, you may feel sure that the words of the rule An Example. are understood. So let it be at every step; let the rule be elucidated and confirmed by the performance of some pertinent question. As another example on this point, let us take the subject of interest. The members of the class are able to repeat the rules and explanations with promptness. If you wish to ascertain if the words they have repeated convey the intended information, step to the blackboard, and write a note, as follows: — Now call upon your class to tell how much it will require to pay the above note at the present time, on some previous day, or on some future day, that you may designate. If the subject of indorsements is under consideration, prepare some notes in due form, note the payments upon the back in the usual and proper manner, and, passing them to members of the class, require them to ascertain the amount due on each at the present time. If results are correct, you may feel satisfied that the subject is clearly comprehended. In fine, let it be a part of your daily practice to propose to your pupils practical questions, prepared by yourself for the purpose of illustrating and confirming the passing recitation. A lad may be able to give the rule for ascertaining the contents of a load or pile of wood, and not be able, by actual measurement and figures, to “carry the rule into practice”; and yet this is the more important part. In all your teaching, aim judiciously to combine theory and practice. Encourage your pupils to bring into the school-room such practical business operations as may come within their observation out of the school-room. In this way you will obtain a valuable variety, embracing such operations as the farmer, the merchant, the mechanic, etc. will have occasion to perform. By pursuing this course, your pupils will be so trained that they will not be confused and entirely thrown from the arithmetical track, if called upon to perform some simple business question outside of the school. How many there are among those who have professedly been through the Arithmetic, - even the “hardest Arithmetic you can name,” — who would be completely nonplussed, if some farmer should ask them to cast the interest on a certain note, or ascertain the contents and worth of a load of wood at a specified amount per cord, or if some carpenter should ask them to estimate the cost of a pile of boards at a given sum per thousand feet ! Make Fractions intelligible. Be sure that Fractions are well understood. — Most teachers and pupils fail in not giving sufficient attention to fractions. If the various operations in fractions are clearly explained by the teacher, and followed by frequent practice by the pupils, the results will be favorable. Let it be your aim to give thorough instruction and frequent drill in exercises involving the various principles of fractions. Facility and accuracy here will be of great service in all other arithmetical exercises. I once knew an entire school in which most of the pupils had been nearly through (that is, had been taken nearly through) written arithmetic, and yet not one could answer the following simple question proposed by a visitor: “If an apple and a half cost. a cent and a half, what will one apple cost 7” Who cannot see that in such a school the subject of fractions had not received merited attention ? . But I have already sufficiently enlarged upon the subject under consideration. I hope the hints I have given may not prove entirely useless. In closing, I will say, if you would be a successful teacher of arithmetic, study to have fresh examples and new modes of illustration as often as possible, always endeavoring to teach the subject, and not the mere words of the book. t’, Your sincere friend, LETTE R. X W III. BOOK-KEEPING. – PHYSIOLOGY. — DRAWING. — HISTORY. — SINGING. MY DEAR FRIEND: — I HAVE already considered the several branches usually taught in our Common Schools. Pupils should be thoroughly instructed in these, and not be allowed to substitute other branches in their stead, nor to allow other studies to engross any part of the time and attention which should be devoted to the elementary branches already alluded to. If pupils are properly trained in these, they will have a firm and desirable foundation, on which a superstructure may be reared as circumstances may favor and require. But if these elementary branches are neglected, or but imperfectly taught, any superstructure will be in a toppling and unpleasant condition. Let me again urge you to be thorough in all your teaching, — but in no cases more so than in relation to those subjects which form the very basis of the educational structure. How many men may be found in each of the learned professions, who have suffered, and will suffer, their lives long, from a |