Page:State manual and course of study.djvu/29

 1. A “ four-bundle ” — represent it by figure 4.

2. Discoveries in four, given in order of teaching: Four ones. Two twos. Three and one. Two and one and one. Four minus (or less) one. Four minus two. Four minus three. Four minus four. One-half of four. One-fourth of four,

(Remember this is oral work with objects.) Develop all numbers up to ten as explained above with the number four, being careful to use no combination that will introduce a number larger than ten. This work will take the greater part of the first year. No haste should be made. The same questions should be repeated in different forms until the pupils know at once how to proceed to find results.

Symbols: — When the above work is accomplished begin to use the plus and minus signs, but teach no signs until pupil can perform the following with objects:

1. Count to 20. 2. Find the sum, not above 12, of any two numbers. 3. Find the difference of any two numbers not above 10. 4. Find result of two 3’s, three 4’s, two 5’s, etc. 5. Find i of 2, of 4, of 6, of 8, of 10, of 12. 6. Find i of 6, of 9, of 12. 7. Find i of 8, of 12. 8. Divide among 2, 3, or 4 pupils, 6, 8, 10, or 12 things.

(Bear in mind that these are not to be taught as facts, but the pupil is shown how to find results with objects.)

It is very important that pupils understand the sign language, and the following plan is helpful:

Send pupils to the black-board. Tell them a story, instructing them to place the sign + or — when you pause in the story; e. g., “I had ten dollars and found five dollars” (pause, and pupils write 10 + 5), “then I earned four dollars” (pause, and pupils write + 4), “ then I lost six dollars ” (pause, and pupils write — G). Repeat the exercise daily until there is no hesitation in placing the proper sign.

Principles of Grube:—