The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
Successful responses to novel data, associations by similarity and
purposive behavior are in only apparent opposition to the fundamental
laws of associative learning. Really they are beautiful examples of it.
Man's successful responses to novel data--as when he argues that the
diagonal on a right triangle of 796.278 mm. base and 137.294 mm.
altitude will be 808.022 mm., or that Mary Jones, born this morning,
will sometime die--are due to habits, notably the habits of response to
certain elements or features, under the laws of piecemeal activity and
assimilation.
Nothing is less like the mysterious operations of a faculty of reasoning
transcending the laws of connection-forming, than the behavior of men in
response to novel situations. Let children who have hitherto confronted
only such arithmetical tasks, in addition and subtraction with one- and
two-place numbers and multiplication with one-place numbers, as those
exemplified in the first line below, be told to do the examples shown in
the second line.
ADD ADD ADD SUBT. SUBT. MULTIPLY MULTIPLY MULTIPLY
8 37 35 8 37 8 9 6
5 24 68 5 24 5 7 3
-- -- 23 -- -- -- -- --
19
--
MULTIPLY MULTIPLY MULTIPLY
32 43 34
23 22 26
-- -- --
They will add the numbers, or subtract the lower from the upper number,
or multiply 3 × 2 and 2 × 3, etc., getting 66, 86, and 624, or respond
to the element of 'Multiply' attached to the two-place numbers by "I
can't" or "I don't know what to do," or the like; or, if one is a child
of great ability, he may consider the 'Multiply' element and the bigness
of the numbers, be reminded by these two aspects of the situation of the
fact that
'9
9 multiply'
--
gave only 81, and that
'10
10 multiply'
--
Public-domain text, read in full here on John Shaqi.
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