PRACTICE IN THE CASE OF ADDITION.
By Edward L. Thorndike, Teachers College, Columbia University.
The experiment reported here was designed to secure information concerning only the amount and rate of improvement and the value of the practice experiment as a method for school work. The practice was not continued long enough nor taken under uniform enough conditions to justify inferences concerning changes in the rate of improvement; and I shall make no attempt to analyze out the factors producing the improvement.
The experiment consisted in adding daily for seven days fortyeight columns each of ten numbers (no I's or o's being included). Seven printed blanks had been arranged of equal difficulty.[1] The forty-eight sums were written. The time required was recorded in seconds. The subjects were nineteen university students eight men and eleven women.
The time taken and the number of examples wrong for each set for each of the nineteen subjects are recorded in Table I. Table II repeats Table I with an addition of one per cent, of the time for fortyeight examples for each example wrong. That is, I estimate that half the time for one example is a just allowance to balance its inaccuracy. This system of allowance is, of course, arbitrary, but it will not prejudice any of the conclusions which I shall draw. They would be the same by any reasonable allowance. Table III summarizes conviently the facts as to the amount and rate of improvement, and its relation to initial ability.
Taking the whole group together, improvement in speed and in accuracy are about equal, the median reduction in time regardless of errors being 31 per cent, and the median reduction in errors regardless of time being 29 per cent. By the scores with allowance for errors the median improvement in general efficiency in addition is 33 per cent. The average improvement is 29 per cent. This is for less than one hour of practice (about fifty-three-minutes).
The individuals vary from cases making no improvement (F and G) to a case of nearly fifty percent, improvement (K).
That the practice represented by only 2,592 additions made by an educated adult whose addition associations have been long established and often used should produce an improvement of threetenths, bears witness to the continued plasticity or educability of the synapses involved. It also supports the contention that the degree of efficiency shown by persons in any intellectual function is a result chiefly of specific training in it or the elements of it and only slightly of the transfer to it of the effects of training other functions. If the general training of from -fifteen to twenty-five years of a scholarly life were responsible for a large fraction of one's efficiency in "quickness of association" or "accuracy in response," one would not by so little specific training be able to improve so much.
The amount of improvement in this experiment may also add to our confidence that the method of the practice experiment wherein
- ↑ The improvement is measured from the average of series 1 to the average of series 7, that is, over 6 X 48 examples, each involving nine additions.
