TABLE II
PRELIMINARY TESTS
Reasoning—Unlimited Time
100 Different Pupils Tested Each Time
| Number of Problems | % Reasoned Correctly as Printed | % Reasoned Correctly as Reversed | Average % Reasoned Correctly | Weight According to Average % Correct | Weight Used as Probably the Best |
| 1 | 95 | 92.6 | 93.8 | 1 | 1 |
| 2 | 86 | 82.2 | 84.1 | 1.1 | 1 |
| 3 | 94 | 89 | 91.5 | 1 | 1 |
| 4 | 80 | 83 | 81.5 | 1.5 | 1 |
| 5 | 88 | 86 | 87 | 1.1 | 1 |
| 6 | 69 | 57.4 | 63.2 | 1.5 | 1.4 |
| 7 | 70 | 80 | 75 | 1.25 | 1.2 |
| 8 | 29 | 44 | 36.5 | 2.6 | 1.6 |
| 9 | 19 | 15.5 | 17.2 | 5.45 | 2 |
| 10 | 24 | 27.4 | 25.7 | 3.6 | 2 |
| 11 | 17 | 7.5 | 12.3 | 7.6 | 2 |
| 12 | 7 | 16.4 | 11.7 | 8 | 2 |
Precautions observed to make the Scoring Accurate
The simplicity of the tests made the scoring comparatively easy; and with the observance of the following precautions it is believed that a high degree of accuracy was attained. (1) In so far as practicable, all the papers were scored by a single judge—only two persons being employed on any phase of the work for the entire twenty-six systems; (2) each problem was scored through one hundred or more papers, then the next followed through, etc.; (3) the score for each part of each problem, the errors, etc., were entered on a blank provided with a separate column for each item; (4) where there was doubt as to how the score should be made, the scorer made a written memorandum of how the case was finally decided and this memorandum served as the guide for all future similar cases.
What the Scores Measure
As used in this study the words achievements, products, abilities, except where otherwise qualified, must necessarily refer to the results of the particular tests employed in this investigation. That some systems may achieve other and possibly quite as worth-while results from their arithmetic work is not denied; but what is denied is that any system can safely fail to attain good results in the work covered by these particular tests. Whatever else the arithmetic work may produce, it seems safe to say that by the end of the sixth school year, it should result in at least good ability in the four fundamental operations and the simple, everyday kind of reasoning called for in these problems. It does not then seem unreasonable, in view of the precautions previously enumerated, to claim that the scores made by the respective systems afford a reliable measure of the products of their respective procedures in arithmetic.