Relevance to the theory of intelligence testing of the stugy of errors in thinking

Abstract

In such a study as this it is impossible strictly to separate the statement of results and the discussion of them, and much that belongs under the heading of discussion is already contained in the preceding pages. The function of the final section must therefore be to draw together these earlier scattered discussions and summarise the conclusions and questions that emerge from the work as a whole. This purpose can perhaps best be served by a consideration of the errors that were found to recur most frequently in a variety of problems; and by an attempt to relate findings to the opinion expressed in Chapter III that the study of errors may be of direct service in the development of intelligence testing in three main ways.The main recurrent errors were:(1) Rigid separation of the "components" of a problem in such a way that no allowance is made for the possibility of overlap or inclusion of one within the other.(2) Failure to handle asymmetrical relationships successfully and with understanding of the equivalence of different statements.(3) Abandonment of reasoning at a point in a problem where there are two possibilities,1 one of which must be rejected. This might be (a) more or less conscious; or (b) apparently unaccompanied by any awareness of an inadequacy of reasoning.(4) Failure to reconsider a conclusion once reached, even if it led to evident contradiction.The second contribution to intelligence testing that we might look to the study of errors to make was said in Chapter III to be the augmenting of our ability to make direct inferences from final solutions to "underlying events ", the advantage to be derived being, of course, that we might then assess a child's mental powers on the evidence of his written answers with more precision and confidence than are possible to us in the present state of our knowledge. This is a more ambitious suggestion than the first one; and the opinion that we can never make such inferences with perfect confidence has already been expressed. (See page 37 ) We may study five hundred children and find that in every case where a certain wrong solution is offered it seems to be due to the same defect in understanding. But we must recognise that it is never impossible for another child to come along and arrive at this same solution in a different way.This reservation made, however, the work so far done would seem to give some indication of what it might be possible to achieve.There are in fact two possibilities: to be content with classifying wrong solutions according to the errors which are found commonly to underlie them; or deliberately to construct questions so as to invite certain errors and render less probable the occurrence of others. Now obviously if follow -up shows the occurrence of some kinds of error to be more significant than that of others, control of errors by deliberate question construction will be very desirable; for if the purpose of a question is to assess the child's freedom from or liability to a certain sort of error and he solves the question wrongly because of a different incompetence that purpose will not have been served. Ways of exercising this control are therefore important to consider; and the most obvious is by informed choice of exact wording and manner of presentation; though again there is a reservation to make, because it is of great importance to remember that children are active in the interpretation of problems, and however skilfully they are constructed we can never be sure that each child will be affected by variations in the same way. This, however, does not make it unimportant to have knowledge of the most common effects of certain sorts of change. To investigate these fully, numerous comparative studied would have to be undertaken; but the results of the present study provide some suggestions of the kind of difference which it might be important to consider. For instance, the premisses of Problems L and M were stated in hypothetical or conditional form, while those of Problem N were stated categorically, and it has already been suggested (page 119) that this may have had the effect of making the common -sense distractors in the latter problem particularly attractive. Again, in Problem A the possible importance of using names which readily form a set was mentioned (page 69); and the significance of the wording of the negative statement "Tom has never been inside Central School" was considered on pages 72 and 73 The footnote to page 93 has suggested that in Problem D the statement "Niay is older than Jean" may have, in its context, an effect different from that of the statement "Jean is younger than May "; just as, in Problem J, the substitution of "Tom is smaller than Harry" for "Harry is taller than Tom" might make errors of asymmetry less likely to occur by firmly associating Tom with the smaller end of the scale. Further, in both D and J, the effect of syntactical changes might be considerable. In each case the relationships on which the problem mainly depends are stated in a rather long and involved sentence. If two or even three sentences had been used to give the same information, so that there was less risk of losing sight of the grammatical subject, some of the overlap errors might not have occurred. This possibility was mentioned on page 100.The conclusion to which this argument leads, then, is that the differences between the failures of reasoning and the failures to reason are such that attempts should be made to assess their occurrence separately, for purposes both of prediction and of finding ways of helping children to overcome them. Whether we choose to call them both failures of intelligence or to reserve this name for the failures of reasoning alone is unimportant. What is important is that the existence of a distinction between them should be recognised, that the existence of similar distinctions involving other categories of error should be explored, and that further study should be directed to their nature and significance.