The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
Elliott ['14] has made a beginning by noting size of class during the
year of test in connection with his own measures of the achievements of
seventeen hundred pupils, supplemented by records from over four hundred
other classes. As might be expected from the facts just stated, he finds
no appreciable difference between classes of different sizes within the
same school system, the effect of the few months in a small class being
swamped by the antecedents or concomitants thereof.
The effect of the amount of time devoted to arithmetic in the school
program has been studied extensively by Rice ['02 and '03] and Stone
['08].
Dr. Rice ['02] measured the arithmetical ability of some 6000 children
in 18 different schools in 7 different cities. The results of these
measurements are summarized in Table 10. This table "gives two averages
for each grade as well as for each school as a whole. Thus, the school
at the top shows averages of 80.0 and 83.1, and the one at the bottom,
25.3 and 31.5. The first represents the percentage of answers which were
absolutely correct; the second shows what per cent of the problems were
correct in principle, _i.e._ the average that would have been received
if no mechanical errors had been made."
The facts of Dr. Rice's table show that there is a positive relation
between the general standing of a school system in the tests and the
amount of time devoted to arithmetic by its program. The relation is
not close, however, being that expressed by a correlation coefficient
of .36-1/2. Within any one school system there is no relation between
the standing of a particular school and the amount of time devoted to
arithmetic in that school's program. It must be kept in mind that the
amount of time given in the school program may be counterbalanced by
emphasizing work at home and during study periods, or, on the other
hand, may be a symptom of correspondingly small or great emphasis on
arithmetic in work set for the study periods at home.
A still more elaborate investigation of this same topic was made by
Stone ['08]. I quote somewhat fully from it, since it is an instructive
sample of the sort of studies that will doubtless soon be made in the
case of every elementary school subject. He found that school systems
differed notably in the achievements made by their sixth-grade pupils in
his tests of computation (the so-called 'fundamentals') and of the
solution of verbally described problems (the so-called 'reasoning'). The
facts were as shown in Table 11.
TABLE 10
AVERAGES FOR INDIVIDUAL SCHOOLS IN ARITHMETIC
KEY A: CITY
B: SCHOOL
C: Result
D: Principle
E: Percent of Mechanical Errors
F: Minutes Daily
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