The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
As a matter of fact, only a small part of drill work in arithmetic
should be the formation of isolated bonds. Even the very young
pupil learning 5 and 3 are 8 should learn it with '5 and 5 = 10,'
'5 and 2 = 7,' at the back of his mind, so to speak. Even so early,
5 + 3 = 8 should be part of an organized, coöperating system of bonds.
Later 50 + 30 = 80 should become allied to it. Each bond should be
considered, not simply as a separate tool to be put in a compartment
until needed, but also as an improvement of one total tool or machine,
arithmetical ability.
There are differences of course. Knowledge of square root can be
regarded somewhat as a separate tool to be sharpened, polished, and used
by itself, whereas knowledge of the multiplication tables cannot. Yet
even square root is probably best made more closely a part of the total
ability, being taught as a special case of dividing where divisor is to
be the same as quotient, the process being one of estimating and
correcting.
In general we do not wish the pupil to be a repository of separated
abilities, each of which may operate only if you ask him the sort of
questions which the teacher used to ask him, or otherwise indicate to
him which particular arithmetical tool he is to use. Rather he is to be
an effective organization of abilities, coöperating in useful ways to
meet the quantitative problems life offers. He should not as a rule
have to think in such fashion as: "Is this interest or discount? Is it
simple interest or compound interest? What did I do in compound
interest? How do I multiply by 2 percent?" The situation that calls up
interest should also call up the kind of interest that is appropriate,
and the technique of operating with percents should be so welded
together with interest in his mind that the right coöperation will occur
almost without supervision by him.
As each new ability is acquired, then, we seek to have it take its place
as an improvement of a thinking being, as a coöperative member of a
total organization, as a soldier fighting together with others, as an
element in an educated personality. Such an organization of bonds will
not form itself any more than any one bond will create itself. If the
elements of arithmetical ability are to act together as a total
organized unified force they must be made to act together in the course
of learning. What we wish to have work together we must put together and
give practice in teamwork.
Public-domain text, read in full here on John Shaqi.
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