The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
The process of learning to respond to the difference of pitch in tones
from whatever instrument, to the 'square-root-ness' of whatever number,
to triangularity in whatever size or combination of lines, to equality
of whatever pairs, or to honesty in whatever person or instance, is thus
a consequence of associative learning, requiring no other forces than
those of use, disuse, satisfaction, and discomfort. "What happens in
such cases is that the response, by being connected with many situations
alike in the presence of the element in question and different in other
respects, is bound firmly to that element and loosely to each of its
concomitants. Conversely any element is bound firmly to any one response
that is made to all situations containing it and very, very loosely to
each of those responses that are made to only a few of the situations
containing it. The element of triangularity, for example, is bound
firmly to the response of saying or thinking 'triangle' but only very
loosely to the response of saying or thinking white, red, blue, large,
small, iron, steel, wood, paper, and the like. A situation thus acquires
bonds not only with some response to it as a gross total, but also with
responses to any of its elements that have appeared in any other gross
totals. Appropriate response to an element regardless of its
concomitants is a necessary consequence of the laws of exercise and
effect if an animal learns to make that response to the gross total
situations that contain the element and not to make it to those that do
not. Such prepotent determination of the response by one or another
element of the situation is no transcendental mystery, but, given the
circumstances, a general rule of all learning." Such are at bottom only
extreme cases of the same learning as a cat exhibits that depresses a
platform in a certain box whether it faces north or south, whether the
temperature is 50 or 80 degrees, whether one or two persons are in
sight, whether she is exceedingly or moderately hungry, whether fish or
milk is outside the box. All learning is analytic, representing the
activity of elements within a total situation. In man, by virtue of
certain instincts and the course of his training, very subtle elements
of situations can so operate.
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Public-domain text, read in full here on John Shaqi.
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