The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
This attaches no blame to Dr. Stone or to Mr. Courtis. Until very
recently we were all so used to the artificial problems of the
traditional sort that we did not expect anything better; and so blind to
the language demands of described problems that we did not see their
very great influence. Courtis himself has been active in reform and has
pointed out ('13, p. 4 f.) the defects in his Tests 6 and 8.
"Tests Nos. 6 and 8, the so-called reasoning tests, have proved the
least satisfactory of the series. The judgments of various teachers and
superintendents as to the inequalities of the units in any one test, and
of the differences between the different editions of the same test, have
proved the need of investigating these questions. Tests of adults in
many lines of commercial work have yielded in many cases lower scores
than those of the average eighth grade children. At the same time the
scores of certain individuals of marked ability have been high, and
there appears to be a general relation between ability in these tests
and accuracy in the abstract work. The most significant facts, however,
have been the difficulties experienced by teachers in attempting to
remedy the defects in reasoning. It is certain that the tests measure
abilities of value but the abilities are probably not what they seem to
be. In an attempt to measure the value of different units, for instance,
as many problems as possible were constructed based upon a single
situation. Twenty-one varieties were secured by varying the relative
form of the question and the relative position of the different phrases.
One of these proved nineteen times as hard as another as measured by the
number of mistakes made by the children; yet the cause of the difference
was merely the changes in the phrasing. This and other facts of the same
kind seem to show that Tests 6 and 8 measure mainly the ability to
read."
The scientific measurement of the abilities and achievements concerned
with applied arithmetic or problem-solving is thus a matter for the
future. In the case of described problems a beginning has been made in
the series which form a part of the National Intelligence Tests ['20],
one of which is shown on page 49 f. In the case of problems with real
situations, nothing in systematic form is yet available.
Public-domain text, read in full here on John Shaqi.
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