Write the missing numerators:—
| 1 2 | = | 12 | 8 | 10 | 4 | 16 | 6 | 14 | ||||||
| 1 3 | = | 12 | 9 | 18 | 6 | 15 | 24 | 21 | ||||||
| 1 4 | = | 12 | 16 | 8 | 24 | 20 | 28 | 32 | ||||||
| 1 5 | = | 10 | 20 | 15 | 25 | 40 | 35 | 30 | ||||||
| 2 3 | = | 12 | 18 | 21 | 6 | 15 | 24 | 9 | ||||||
| 3 4 | = | 8 | 16 | 12 | 20 | 24 | 32 | 28 |
Find the products. Cancel when you can:—
| 5 16 | × 4 = | 11 12 | × 3 = | 2 3 | × 5 = | ||
| 7 12 | × 8 = | 8 5 | × 15 = | 1 6 | × 8 = |
SIGNIFICANCE FOR RELATED ACTIVITIES
The use of bodily action, social games, and the like was discussed in the section on original tendencies. "Significance as a means of securing other desired ends than arithmetical learning itself" is therefore our next topic. Such significance can be given to arithmetical work by using that work as a means to present and future success in problems of sports, housekeeping, shopwork, dressmaking, self-management, other school studies than arithmetic, and general school life and affairs. Significance as a means to future ends alone can also be more clearly and extensively attached to it than it now is.
Whatever is done to supply greater strength of motive in studying arithmetic must be carefully devised so as not to get a strong but wrong motive, so as not to get abundant interest but in something other than arithmetic, and so as not to kill the goose that after all lays the golden eggs—the interest in intellectual activity and achievement itself. It is easy to secure an interest in laying out a baseball diamond, measuring ingredients for a cake, making a balloon of a certain capacity, or deciding the added cost of an extra trimming of ribbon for one's dress. The problem is to attach that interest to arithmetical learning. Nor should a teacher be satisfied with attaching the interest as a mere tail that steers the kite, so long as it stays on, or as a sugar-coating that deceives the pupil into swallowing the pill, or as an anodyne whose dose must be increased and increased if it is to retain its power. Until the interest permeates the arithmetical activity itself our task is only partly done, and perhaps is made harder for the next time.
One important means of really interfusing the arithmetical learning itself with these derived interests is to lead the pupil to seek the help of arithmetic himself—to lead him, in Dewey's phrase, to 'feel the need'—to take the 'problem' attitude—and thus appreciate the technique which he actively hunts for to satisfy the need. In so far as arithmetical learning is organized to satisfy the practical demands of the pupil's life at the time, he should, so to speak, come part way to get its help.
Even if we do not make the most skillful use possible of these interests derived from the quantitative problems of sports, housekeeping, shopwork, dressmaking, self-management, other school studies, and school life and affairs, the gain will still be considerable. To have them in mind will certainly preserve us from giving to children of grades 3 and 4 problems so devoid of relation to their interests as those shown below, all found (in 1910) in thirty successive pages of a book of excellent repute:—