It is obvious that the elements selected must not only be right but also be in the right relations to one another. For example, in the problems below, the 6 must be thought of in relation to a dozen and as being half of a dozen, and also as being 6 times 1. 1 must be mentally tied to "each." The 6 as half of a dozen must be related to the $1.00, $1.60, etc. The 6 as 6 times 1 must be related to the $.09, $.14, etc.
These are a grocer's prices for certain things by the dozen and for a single one. He sells a half dozen at half the price of a dozen. Find out how much you save by buying 6 all at one time instead of buying them one at a time.
Doz. Each 1. Evaporated Milk $1.00 $.09 2. Puffed Rice 1.60 .14 3. Puffed Wheat 1.10 .10 4. Canned Soup 1.90 .17 5. Sardines 1.80 .16 6. Beans (No. 2 cans) 1.50 .13 7. Pork and Beans 1.70 .15 8. Peas (No. 2 cans) 1.40 .12 9. Tomatoes (extra cans) 3.20 .28 10. Ripe olives (qt. cans) 7.20 .65
It is obvious also that in such arithmetical work as we have been describing, the pupil, to be successful, must 'think things together.' Many bonds must coöperate to determine his final response.
As a preface to reasoning about a problem we often have the discovery of the problem and the classification of just what it is, and as a postscript we have the critical inspection of the answer obtained to make sure that it is verified by experiment or is consistent with known facts. During the process of searching for, selecting, and weighting facts, there may be similar inspection and validation, item by item.
REASONING AS THE COÖPERATION OF ORGANIZED HABITS
The pedagogy of the past made two notable errors in practice based on two errors about the psychology of reasoning. It considered reasoning as a somewhat magical power or essence which acted to counteract and overrule the ordinary laws of habit in man; and it separated too sharply the 'understanding of principles' by reasoning from the 'mechanical' work of computation, reading problems, remembering facts and the like, done by 'mere' habit and memory.
Reasoning or selective, inferential thinking is not at all opposed to, or independent of, the laws of habit, but really is their necessary result under the conditions imposed by man's nature and training. A closer examination of selective thinking will show that no principles beyond the laws of readiness, exercise, and effect are needed to explain it; that it is only an extreme case of what goes on in associative learning as described under the 'piecemeal' activity of situations; and that attributing certain features of learning to mysterious faculties of abstraction or reasoning gives no real help toward understanding or controlling them.