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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