A teacher at the local secondary school (teacher A) who was particularly interested in the new technique volunteered to try it out on a class of 12-year-olds who were just beginning an O-level course in Mathematics. As a first step, therefore, teacher A was given an intensive course in the new educational technique to acquaint him with the instructional materials, audio-visual aids, and so on that were to be used. Throughout the next school-year he taught his pupils according to the new principles that he had learned. At the end of this year the psychologist visited the school and tested the mathematical abilities of the children by means of a newly devised objective test. This test was designed to assess not only efficiency in basic arithmetical skills (addition, multiplication, and so on) but also the child's understanding of fundamental mathematical concepts. The test was scored out of 100. The mean score for the 30 children in the class was 75, with a range of scores from 31 to 100.

In order to compare this performance with that shown by children taught by more orthodox procedures the psychologist then got in touch with the headmaster of a school in a town some distance away who gave permission for a class of children to be tested. The psychologist deliberately avoided testing other children in teacher A's school; he was worried that such children might have heard something from their friends about the special procedures used by teacher A and that this might influence their test performance. The test carried out on the children from the distant school yielded a mean score of 50 with individual scores ranging from 40 to 60. A t-test comparing these scores with those produced by teacher A's class revealed a significant diffference, t= 4.7, df = 58, p < .05.

In a follow-up study carried out some years later, the psychologist gained access to the O-level grades of the two groups of children. For the purpose of numerical analysis the grades (A to E) were turned into numbers by giving an A grade a score of 10, a B grade a score of 9, and so on down to 6 for E. Unclassified O-level papers received a score of 5. Expressed in this way the children from teacher A's class had an average of 7.3 at O-level; those from the other class an average score of 6.8. A t-test comparing these scores revealed no significant difference between the two classes. The psychologist also used the O-level scores in an attempt to validate his own objective test of mathematical ability. Comparing each child's score on the objective test with the score obtained at O-level showed there to be a significant positive correlation between the two, r = .20, p < .05.

On the basis of these results, the psychologist reached the following conclusions:

- that his own objective test is an adequate measure of mathematical ability;
- that the new teaching technique is in general superior to orthodox techniques;
- that the advantage bestowed by the new technique dissipates when this form of teaching is discontinued and that, therefore, it should be used throughout the O-level course.

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