Vital need: Discuss with the class the various occupations of life and secure expressions of preference. Some may plan to be real estate agents, others contractors or book keepers, etc. “George, you plan to be a book keeper.” “Let us suppose that I have given you the job of book keeper in my factory.” “Show that you are worth your wages by adding these numbers: 1243⁄4, 6472⁄3.” “What! can’t do it?” “Then I don’t want you!” etc.
II. Preparation:
(2) Bring to the foreground the necessary foundational knowledge. Suggestions:
| 4 bushels | 8 parts |
| + 3 bushels | + 2 parts |
| 7 bushels | 10 parts |
III. Presentation:
(3) Make evident the crucial fact. Suggestions:
| Add | 2 fifths | 3 eighths | 3/8 |
| + 1 fifth | + 1 eighth | + 1/8 | |
| 3 fifths | 4 eighths |
(4) Without further suggestion, give the young discoverer suitable opportunity for finding the sum of 3/8 and 1/8. In the act of discovering, an implicit hypothesis takes form in the mind through analogous reasoning. This point marks the climax of the lesson—the supreme moment, when the skill and tact of the teacher is assessed to the limit. Just here the child must have a comfortable environment where perfect concentration is possible. Nothing must be forced; and there should be nothing suggestive of disgrace or shame, if the youthful Columbus is unsuccessful. The first attempt should be without books. If more help is needed, access to books may be given. If the investigation is still without definite result, then as a last resort the teacher may, in the presence of the child, add fractions, solving with deliberation example after example, until the child believes he has discovered the process.
(5) Stimulate a desire to verify the facts discovered.
Suggestions leading to verification: Afford opportunity for mathematical demonstration. Illustrations: The fractions 1/4 and 3/8 have been added in this way—