The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
gave only 100, or the like; and so may report an intelligent and
justified "I can't," or reject the plan of 3 × 2 and 2 × 3, with 66, 86,
and 624 for answers, as unsatisfactory. What the children will do will,
in every case, be a product of the elements in the situation that are
potent with them, the responses which these evoke, and the further
associates which these responses in turn evoke. If the child were one of
sufficient genius, he might infer the procedure to be followed as a
result of his knowledge of the principles of decimal notation and the
meaning of 'Multiply,' responding correctly to the 'place-value' element
of each digit and adding his 6 tens and 9 tens, 20 twos and 3 thirties;
but if he did thus invent the shorthand addition of a collection of
twenty-three collections, each of 32 units, he would still do it by the
operation of bonds, subtle but real.
Association by similarity is, as James showed long ago, simply the
tendency of an element to provoke the responses which have been bound to
it. _abcde_ leads to _vwxyz_ because _a_ has been bound to _vwxyz_ by
original nature, exercise, or effect.
Purposive behavior is the most important case of the influence of the
attitude or set or adjustment of an organism in determining (1) which
bonds shall act, and (2) which results shall satisfy. James early
described the former fact, showing that the mechanism of habit can give
the directedness or purposefulness in thought's products, provided that
mechanism includes something paralleling the problem, the aim, or need,
in question.
The second fact, that the set or attitude of the man helps to determine
which bonds shall satisfy, and which shall annoy, has commonly been
somewhat obscured by vague assertions that the selection and retention
is of what is "in point," or is "the right one," or is "appropriate," or
the like. It is thus asserted, or at least hinted, that "the will," "the
voluntary attention," "the consciousness of the problem," and other such
entities are endowed with magic power to decide what is the "right" or
"useful" bond and to kill off the others. The facts are that in
purposive thinking and action, as everywhere else, bonds are selected
and retained by the satisfyingness, and are killed off by the
discomfort, which they produce; and that the potency of the man's set or
attitude to make this satisfy and that annoy--to put certain
conduction-units in readiness to act and others in unreadiness--is in
every way as important as its potency to set certain conduction-units in
actual operation.
Public-domain text, read in full here on John Shaqi.
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