SUGGESTIONS TO TEACHERS. 1. MATERIAL objects should be used as illustrations far enough to make sure that the pupils clearly understand the value of numbers, how numbers are composed in addition, how they are separated in subtraction, how multiplication and division are performed, and how the elementary tables are constructed. When these things are comprehended, material objects should be dispensed with, and a thorough knowledge of the tables should be relied upon for the requisite results. 2. The tables should be made so familiar that when any two numbers are named, the result of a desired operation upon them shall, by the power of repeated association, instantly flash upon the mind. 3. Care should be taken that the definitions are clearly understood before they are learned. 4. The attention of pupils should be directed to the successive steps taken in the solution of the problems first given under any subject, and each pupil should be required to state the first step, the second step, and so on until all the steps are named and recorded on slates or blackboard. These steps should be combined, and thus the mode of building up a rule be made clear. The rule should be regarded, not as a guide to the solution of problems, but as a concise statement of what the pupils have already learned to do. 5. In addition, pupils should usually avoid naming the numbers to be added, but should give only the successive results. They should have much practice in adding and subtracting by 2's, 3's, 4's, etc. In multiplication, they may profitably use either form of expression2 times 2, 3 times 2, 4 times 2, etc.; or, two 2's, three 2's, four 2's, etc. Sometimes one of these expressions is preferable, sometimes the other. 6. The explanations given are not to be committed to memory. The definitions and principles, having been fully comprehended, ought to be fixed in the memory. The rules may or may not be learned, as teachers shall prefer. 7. Fractions should be amply illustrated by material objects, attention being specially called to the number and the size of the parts into which a thing is divided. 8. Care should be taken that the explanations given by pupils are logical in order and accurate in expression. 4 RTICLE 1.-1. Arthur has one white rabbit and one gray rabbit. rabbit. How 2. Arthur has two rabbits, and his sister has one. How many rabbits have both of them? 3. Jane had two books, and her father gave her two more. How many books had she then? 4. If you have three cents in one pocket, and two cents in another, how many have you in both? 5. James gave four cents for an orange, and two cents for an apple. How many cents did he give for both? 7 6. If you count the fingers and thumb on your right hand, how many will you find them to be? 7. How many are six books and two books? 8. Arthur has five lead pencils and four slate pencils. How many pencils has he? 9. Six trees and three trees are how many trees? 10. How many are one and one? Two and one? Three and one? Four and one? 11. How many are five and one? Six and one? Seven and one? Eight and one? Nine and one? 12. How many are two and two? Three and two? Four and two? Five and two? Six and two? 13. How many are seven and two? Eight and two? Three and two? Three and three? Four and three? 14. How many are five and three? Six and three? Seven and three? Four and four? 15. How many are five and four? Six and four? Five and five? 16. Count from one to ten. Count the fingers and thumbs which you have on both hands. 17. If you had five books, and should have three more given you, how many books would you then have? 18. How many are five and three? 19. How many are six and two? Four and three? Seven and three? Three and five? Eight and two? 20. If you have six books, and have four more given you, how many books will you then have? |
