THE STRENGTH OF BONDS FOR TEMPORARY SERVICE
The second general fact is that certain bonds are of service for only a limited time and so need to be formed only to a limited and slight degree of strength. The data of problems set to illustrate a principle or improve some habit of computation are, of course, the clearest cases. The pupil needs to remember that John bought 3 loaves of bread and that they were 5-cent loaves and that he gave 25 cents to the baker only long enough to use the data to decide what change John should receive. The connections between the total described situation and the answer obtained, supposing some considerable computation to intervene, is a bond that we let expire almost as soon as it is born.
It is sometimes assumed that the bond between a certain group of features which make a problem a 'Buy a things at b per thing, find total cost' problem or a 'Buy a things at b per thing, what change from c' problem or a 'What gain on buying for a and selling for b' problem or a 'How many things at a each can I buy for b cents' problem—it is assumed that the bond between these essential defining features and the operation or operations required for solution is as temporary as the bonds with the name of the buyer or the price of the thing. It is assumed that all problems are and should be solved by some pure act of reasoning without help or hindrance from bonds with the particular verbal structure and vocabulary of the problems. Whether or not they should be, they are not. Every time that a pupil solves a 'bought-sold' problem by subtraction he strengthens the tendency to respond to any problem whatsoever that contains the words 'bought for' and 'sold for' by subtraction; and he will by no means surely stop and survey every such problem in all its elements to make sure that no other feature makes inapplicable the tendency to subtract which the 'bought sold' evokes.
To prevent pupils from responding to the form of statement rather than the essential facts, we should then not teach them to forget the form of statement, but rather give them all the common forms of statement to which the response in question is an appropriate response, and only such. If a certain form of statement does in life always signify a certain arithmetical procedure, the bond between it and that procedure may properly be made very strong.
Another case of the formation of bonds to only a slight degree of strength concerns the use of so-called 'crutches' such as writing +, −, and × in copying problems like those below:—
| Add | Subtract | Multiply |
| 23 61 — | 79 24 — | 32 3 — |
or altering the figures when 'borrowing' in subtraction, and the like. Since it is undesirable that the pupil should regard the 'crutch' response as essential to the total procedure, or become so used to having it that he will be disturbed by its absence later, it is supposed that the bond between the situation and the crutch should not be fully formed. There is a better way out of the difficulty, in case crutches are used at all. This is to associate the crutch with a special 'set,' and its non-use with the general set which is to be the permanent one. For example, children may be taught from the start never to write the crutch sign or crutch figure unless the work is accompanied by "Write ... to help you to...."
| Write - to help you to remember that you must subtract in this row. | Find the differences:— | ||||
| 39 23 | 67 44 | 78 36 | 56 26 | 45 24 | |
| Remember that you must subtract in this row. | Find the differences:— | ||||
| 85 63 | 27 14 | 96 51 | 38 45 | 78 32 | |
The bond evoking the use of the crutch may then be formed thoroughly enough so that there is no hesitation, insecurity, or error, without interfering to any harmful extent with the more general bond from the situation to work without the crutch.