CHAPTER II
THE MEASUREMENT OF ARITHMETICAL ABILITIES
One of the best ways to clear up notions of what the functions are which schools should develop and improve is to get measures of them. If any given knowledge or skill or power or ideal exists, it exists in some amount. A series of amounts of it, varying from less to more, defines the ability itself in a way that no general verbal description can do. Thus, a series of weights, 1 lb., 2 lb., 3 lb., 4 lb., etc., helps to tell us what we mean by weight. By finding a series of words like only, smoke, another, pretty, answer, tailor, circus, telephone, saucy, and beginning, which are spelled correctly by known and decreasing percentages of children of the same age, or of the same school grade, we know better what we mean by 'spelling-difficulty.' Indeed, until we can measure the efficiency and improvement of a function, we are likely to be vague and loose in our ideas of what the function is.
A SAMPLE MEASUREMENT OF AN ARITHMETICAL ABILITY: THE ABILITY TO ADD INTEGERS
Consider first, as a sample, the measurement of ability to add integers.
The following were the examples used in the measurements made by Stone ['08]:
| 596 | 4695 | |
| 428 | 872 | |
| 2375 | 94 | 7948 |
| 4052 | 75 | 6786 |
| 6354 | 304 | 567 |
| 260 | 645 | 858 |
| 5041 | 984 | 9447 |
| 1543 | 897 | 7499 |
| ——— | ——— | ——— |
The scoring was as follows: Credit of 1 for each column added correctly. Stone combined measures of other abilities with this in a total score for amount done correctly in 12 minutes. Stone also scored the correctness of the additions in certain work in multiplication.
Courtis uses a sheet of twenty-four tasks or 'examples,' each consisting of the addition of nine three-place numbers as shown below. Eight minutes is allowed. He scores the amount done by the number of examples, and also scores the number of examples done correctly, but does not suggest any combination of these two into a general-efficiency score.
927
379
756
837
924
110
854
965
344
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