The Relationship of Problem-Solving Styles to the Factor Composition of Tests

This study was undertaken to learn more about the way in which the characteristics being measured by a test vary with the kind of examinee taking the test or with the problem-solving style he uses in approaching test problems. Briefly, the procedure for this study included the following steps: (1) The subjects took 15 tests which would later be examined by factor analysis. (2) In order to find out what problem-solving styles the subjects used, they were required to fill out a questionnaire about their background and their approach to test problems, and were interviewed while they solved items similar to ones they had faced on the tests. In all, more than 100 items of information about each subject were gathered. (3) As an aid in recognizing the important problem-solving styles in these data, the intercorrelations of the interview, questionnaire, and test variables were factor analyzed. (4) These variables, after being grouped and selected by the factor analysis, were used to divide the subjects into 17 different pairs of subsamples representing different problem-solving styles or different background characteristics that might be expected to affect the way in which a person solves problems. (5) All subsamples in the 17 pairs and also the whole group were then used in performing separate factor analyses of the same 15 tests, in all of which five factors were extracted and rotated. (6) Factor loadings and factor intercorrelations were compared for the two subsamples in each pair. The problem-solving approaches used for dividing many of the pairs of subsamples distinguished some kind of systematizing approach from a scanning approach. This is a distinction emphasized by Bloom and Broden and probably related to Gardner's Focusing vs. Scanning and Witkin's Analytic Attitude or Field-Independence. While some of the divisions into pairs of subsamples revealed no substantial differences either in the loadings of the 15 tests on the five factors or in the intercorrelations of the factors, many interesting differences occurred. In particular the development of a systematic approach to solving the items of a test frequently reduced the loadings of that test on the factor which usually characterized it best. Also, for subjects using a systematic rather than an intuitive or scanning approach to test items, the space factor was usually found to be relatively less correlated with the verbal and mathematical factors and the verbal and mathematical factors were found to be more highly correlated with each other. An attempt is made to account for these findings psychologically by supposing that systematic persons develop specialized techniques for solving the visible, concrete spatial problems that are quite different from the symbolic techniques that they can use for solving problems in either of the symbolic areas, verbal and mathematics.