The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
We now know that the training depends largely on the particular data
used, so that efficient discipline in reasoning requires that the pupil
reason about matters of real importance. There is no magic essence or
faculty of reasoning that works in general and irrespective of the
particular facts and relations reasoned about. So we should try to find
problems which not only stimulate the pupil to reason, but also direct
his reasoning in useful channels and reward it by results that are of
real significance. We should replace the purely disciplinary problems by
problems that are also valuable as special training for important
particular situations of life. Reasoning sought for reasoning's sake
alone is too wasteful an expenditure of time and is also likely to be
inferior as reasoning.
The second matter concerns the relative merits of 'catch' problems,
where the pupil has to go against some customary habit of thinking, and
what we may call 'routine' problems, where the regular ways of thinking
that have served him in the past will, except for some blunder, guide
him rightly.
Consider, for example, these four problems:
1. "A man bought ten dozen eggs for $2.50 and sold them for 30 cents
a dozen. How many cents did he lose?"
2. "I went into Smith's store at 9 A.M. and remained until 10 A.M.
I bought six yards of gingham at 40 cents a yard and three yards
of muslin at 20 cents a yard and gave a $5.00 bill. How long was
I in the store?"
3. "What must you divide 48 by to get half of twice 6?"
4. "What must you add to 19 to get 30?"
Public-domain text, read in full here on John Shaqi.
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