The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
Such is in some measure true of man's intellectual life. In recalling a
forgotten name, in solving certain puzzles, or in simplifying an
algebraic complex, there is an annoying lack of the name, solution, or
factor, a trial of one after another response, until the annoyance is
relieved by success or made less potent by fatigue or distraction. Even
here the _difficulty_ does not do anything--but only the annoying
interference with our intellectual peace by the problem. Further,
although for the particular problem, the annoying lack stimulates, and
the successful attainment stops thinking, the later and more important
general effect on thinking is the reverse. Successful attainment stops
our thinking _on that problem_ but makes us more predisposed later to
thinking _in general_.
Overt negative reaction, however, plays a relatively small part in man's
intellectual life. Filling intellectual voids or relieving intellectual
strains in this way is much less frequent than being stimulated
positively by things seen, words read, and past connections acting under
modified circumstances. The notion of thinking as coming to a lack,
filling it, meeting an obstacle, dodging it, being held up by a
difficulty and overcoming it, is so one-sided as to verge on phantasy.
The overt lacks, strains, and difficulties come perhaps once in five
hours of smooth straightforward use and adaptation of existing
connections, and they might as truly be called hindrances to
thought--barriers which past successes help the thinker to surmount.
Problems themselves come more often as cherished issues which new facts
reveal, and whose contemplation the thinker enjoys, than as strains or
lacks or 'problems which I need to solve.' It is just as true that the
thinker gets many of his problems as results from, or bonuses along
with, his information, as that he gets much of his information as
results of his efforts to solve problems.
As between difficulty and success, success is in the long run more
productive of thinking. Necessity is not the mother of invention.
Knowledge of previous inventions is the mother; original ability is the
father. The solutions of previous problems are more potent in producing
both new problems and their solutions than is the mere awareness of
problems and desire to have them solved.
Public-domain text, read in full here on John Shaqi.
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