These proposed measures of ability to apply arithmetic illustrate very nicely the differences of opinion concerning what applied arithmetic and arithmetical reasoning should be. The thinker who emphasizes the fact that in life out of school the situation demanding quantitative treatment is usually real rather than described, will condemn a test all of whose constituents are described problems. Unless we are excessively hopeful concerning the transfer of ideas of method and procedure from one mental function to another we shall protest against the artificiality of No. 3 of the Stone series, and of the entire Courtis Test 8 except No. 4. The Courtis speed-reasoning test (No. 6) is a striking example of the mixture of ability to understand quantitative relations with the ability to understand words. Consider these five, for example, in comparison with the revised versions attached.[3]
1. The children of a school gave a sleigh-ride party. There were 9 sleighs, and each sleigh held 30 children. How many children were there in the party?
Revision. If one sleigh holds 30 children, 9 sleighs hold .... children.
2. Two school-girls played a number-game. The score of the girl that lost was 57 points and she was beaten by 16 points. What was the score of the girl that won?
Revision. Mary and Nell played a game. Mary had a score of 57. Nell beat Mary by 16. Nell had a score of ....
3. A girl counted the automobiles that passed a school. The total was 60 in two hours. If the girl saw 27 pass the first hour how many did she see the second?
Revision. In two hours a girl saw 60 automobiles. She saw 27 the first hour. She saw .... the second hour.
4. On a playground there were five equal groups of children each playing a different game. If there were 75 children all together, how many were there in each group?
Revision. 75 pounds of salt just filled five boxes. The boxes were exactly alike. There were .... pounds in a box.