10. The names and signs or abbreviations of the mcasures in common use should also be taught, and be as familiar to the pupil as the signs of operation, and used from the first in all oral and written work. 11. At the same time the pupil should be made familiar with the equal parts of numbers or things, from one half to one tenth inclusive. 12. The practical use of arithmetic is not oral, but mental; therefore, the eye and the hand, rather than the ear and the tongue, are the instruments of work. 13. The eye should be trained to act promptly. The pupil should see results, using the lips and tongue in naming them. As much depends upon this eye-training in all figure work, as in reading, in order to secure rapidity in reaching results. 14. Monotony should be guarded against, and the exercises varied, by plenty of easy slate work. 15. Pupils should be encouraged also to bring their slates from home, filled with neatly arranged work. 16. Every pupil should be provided with a foot-rule divided into inches, and taught to use it until measurements with it are familiar. 17. The same usage should be observed, whenever practicable, in the use of other standard measures, as the yard measure, the liquid pint, quart, and gallon measures, the dry quart and peck measures, the different weights, etc. 18. In estimating. the value of the pupil's work, the time taken to do the work, and also the neatness should be noted. 19. Finally, to secure the best results in the least time, and in a manner most in accordance with the laws of mental growth, should be the constant aim of the teacher. LESSON II. SIGNS OF NUMBERS. The signs or symbols of numbers are words, figures, and letters. Each of the first nine numbers is expressed by a single figure in the Arabic notation, and by letters in the Roman notation, as shown on the preceding page. The figure 0 is called naught, zero, or cipher. These ten figures, when combined according to certain principles, can be made to express any number. The following symbols of numbers should also be learned: LESSON III. Since these signs of numbers must be known perfectly, before any slate work can be performed, pupils should be exercised daily, a few minutes, upon combinations similar to the following, until they are thoroughly familiar with them. The above to be read rapidly by line, then by column. When the number symbols as far as ten, 10, X, have been learned, then pupils may write upon the slate, paper, or board, and repeat orally, the symbols of numbers from ten to twenty, applying them to familiar objects, thus: Then from twenty to thirty, and from thirty to forty, and so on to one hundred. LESSON IV. SIGNS OF OPERATIONS. = 1. At the same time that number signs are taught, the meaning and use of the following word signs, +, -, -, X, ÷, and $, should also be taught. 2. This sign, +, named plus, which means more, is used in the place of the word and. Thus, instead of writing, 2 and 3 are 5, we may write, 2+3 are 5, and read, 2 plus 3 are 5. 3. This sign, =, named equality, is used in place of the word are. Thus, instead of writing, 3 and 2 are 5, we may write, 3+25, and read, 3 plus 2 equals 5. Read the following: 6 + 2 = = 8 8 + 2 = 10 3+2+27 4 + 3 + 2 = 9 |