Arithmetical Reasoning

PROCEDURE. The following problems, printed in clear type, are shown one
at a time to the subject, who reads each problem aloud and (with the
printed problem still before him) finds the answer without the use of
pencil or paper.

(a) _If a man's salary is $20 a week and he spends $14 a week,
how long will it take him to save $300?_
(b) _If 2 pencils cost 5 cents, how many pencils can you buy for
50 cents?_
(c) _At 15 cents a yard, how much will 7 feet of cloth cost?_

Only one minute is allowed for each problem, but nothing is said about
hurrying. While one problem is being solved, the others should be hidden
from view. It is not permissible, if the subject gives an incorrect
answer, to ask him to solve the problem again. The following exception,
however, is made to this rule: If the answer given to the third problem
indicates that the word _yard_ has been read as _feet_, the subject is
asked to read the problem through again carefully (aloud) and to tell
how he solved it. No further help of any kind may be given.

SCORING. _Two of the three_ problems must be solved correctly within the
minute allotted to each. No credit is allowed for correct method if the
answer is wrong.

REMARKS. We have selected these problems from the list used by Bonser in
his _Study of the Reasoning Ability of Children in the Fourth, Fifth,
and Sixth School Grades_.

Our tests of 279 "at age" children between 12 and 15 years reveal the
surprising fact that the test as here used and scored is not passed by
much over half of the children of any age in the grades below the
high-school age. Of the high-school pupils 19 per cent failed to pass,
21 per cent of ordinarily successful business men (!), and 27 per cent
of Knollin's unemployed men testing up to the "average adult" level. To
find average intelligence cutting such a sorry figure raises the
question whether the ancient definition of man as "the rational animal"
is justified by the facts. The truth is, _average_ intelligence does not
do a great deal of abstract, logical reasoning, and the little it does
is done usually under the whip of necessity.

At first thought these problems will doubtless appear to the reader to
be mere tests of schooling. It is true, of course, that in solving them
the subject makes use of knowledge which is ordinarily obtained in
school; but this knowledge (that is, knowledge of reading and of
addition, subtraction, multiplication, and division) is possessed by
practically all adults who are not feeble-minded, and by many who are.
Success, therefore, depends upon the ability to apply this knowledge
readily and accurately to the problems given--precisely the kind of
ability in which a deficiency cannot be made good by school training. We
can teach even morons how to read problems and how to add, subtract,
multiply, and divide with a fair degree of accuracy; the trouble comes
when they try to decide which of these processes the problem calls for.
This may require intelligence of high or low order, according to the
difficulty of the problem. As for the present test, we have shown that
almost totally unschooled men of "average adult" intelligence pass this
test as frequently as high-school seniors of the same mental level.

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Arithmetical Reasoning