Department of Educational Studies, UWI, Mona, Jamaica
1987 (revised 1989)
The Topic
Suppose I solemnly promise you that if Mrs Thatcher wins the next election in England I shall abandon the study of critical thinking, and suppose Mrs Thatcher does win, then you might reasonably expect my research interests to shift. Suppose you know that most teachers are women and you believe that most women like children you might be inclined to conclude that most teachers like children.
These are deliberately everyday examples; the point is to suggest that we constantly move from beliefs or thoughts to other beliefs or thoughts which we think are supported by the first set. We reason or infer from the first set to the second. In some cases we know that what we are doing is risky (I used to see a lot of Datsun 180s whose licence plates began with ND; if I'd concluded that all such cars in Jamaica had that sort of licence plate I'd know I might turn out to be mistaken, though in a different context I might think a similar extrapolation an acceptable risk) but in other cases we think that our starting point gives us a kind of guarantee — at least if we start out OK we cannot end up wrong. This second sort of case is where we are hoping to have a deductive link from our premises to our conclusion. My two examples in the preceding paragraph are meant to exemplify such would-be deductive, would-be airtight arguments.
One of our many problems is that we often make mistakes in this sort of thinking. Whereas my first example is OK (though your expectations might not be confirmed unless my promise is reliable) my second isn't — all the female teachers might be selected from the minority of women who don't like children so we have a case where the premises could be true without the conclusion being true as well. It is usual to say that such arguments that don't really work, though they may appear to, are invalid.
The research that I am going to be using is concerned to investigate average levels of competence at various sorts of simple deductive reasoning, under various conditions. The sorts of connection between statements I have been talking about have been studied formally by logicians ever since Aristotle produced a theory that covered some simple but important types of inference. Logicians typically classify arguments by reference to the sorts of statement that figure essentially in them: our first example has as its premises a conditional statement and the antecedent of that conditional whereas the second argument involves two statements about most of a kind. But one can also investigate how different types of content (everyday content as in the earlier examples, or obviously fictitious content, or symbols, or specialized technical terminology, or content with logically superfluous items [some uses of negatives or compound statements, for instance]) affect people's ability. The work I am using is based on adaptations of tests that address both the formal and some of these content-related aspects and that were produced by Robert Ennis in the course of his extensive investigations in the U.S.; they consist of multiple choice questions of the following sort:
- Most teachers are women
- Most women love children
- Most teachers love children?
Respondents are offered a choice of Yes [= it must be true], No, Maybe, and are told that their decisions must be made simply on the basis of what they are told they know — no further information is to be employed. The tests examine formally different logical structures, with 6 such questions for each structure. Most of the content is everyday, but often one item involves clearly false claims and another uses some symbols. Ennis takes mastery of a principle to be displayed by getting at least 5 out of 6 such questions right; getting 4 right is considered to be on the borderline.
It should be emphasized that these tests tell us only about the average competence of groups by reference to the norms provided by standard logic. It need not be assumed that people employ the logical principles in their actual thinking. There is considerable evidence that they don't in fact (see Johnson-Laird, 1983, for some of it together with an attractive alternative account) but it is arguable that we should remain agnostic in the present state of psychological theory (Norris, 1985).
Research in Jamaica and the rest of Caribbean
Such tests were first used in Jamaica by Nolan in an investigation into competence on 12 principles of conditional reasoning among students in a comprehensive school in Hanover (results are most easily available in Nolan and Brandon, 1984). The same test was also administered to a number of other smaller groups in varied Jamaican schools. Since then a number of shorter tests (each involving 6 principles) have been devised and used on students in Jamaica, trainee teachers in St Lucia, and most extensively on practising teachers who have applied for Mona Faculty of Education courses. Such teachers are mostly in Jamaica, but there have been a fair number from other islands, particularly as applicants to the UWIDITE Certificate programme. These teachers are virtually all non-graduates, whose tertiary level education has been at a Teachers' College. They tend to be working in primary or non-High School secondary schools.
As is to be expected, most of the teachers, trainee or practising, are female but the samples tested were not obtained with a view to looking for gender differences. Nor were the students tested at school — these findings are in that sense peripheral — and in several cases groups that took a particular test were skewed in ways that make a comparison by sex of dubious validity.
The Findings
With that proviso, the most consistent result from all the investigations mentioned is that there are no or very few differences in deductive logical reasoning ability between the sexes. In Nolan's school the overall correlation between sex (coded 1 for male, 2 for female) and the total score on the 72 item test was r (203) = -.011, p = 0.4378. (Here this is a Pearson product-moment correlation produced by SPSS; it is numerically identical with the appropriate point-biserial coefficient.) Among the trainee teachers in St Lucia the T test result for male and female trainees was t (95) = 1.43, p = 0.157. In the 1987 Entrance Examination for the B.Ed. the analogous result was t (222) = .718, p = 0.473.
The above values indicate a slight, though statistically quite insignificant, male advantage. When Nolan examined different classes within the school, girls were slightly ahead in most of them though the boys caught up in the grade 11 Arts and Vocational classes. Though this might be the expected pattern, one should note that only one of the mean differences was significant taken in isolation (for grade 11 Vocational, t (23) = 2.12, p = 0.045). Of the 11 mixed classes tested with the 72 item reasoning test, there was only one other in which there was a significant difference, t (17) = -2.73, p = .014, and this was one of the untypical groups — a grade 7 in an expensive private secondary school.
When one administers several tests to a fairly large number of groups, it is to be expected that odd groups will turn out statistically different by chance. Reviewing the data we have on students and teachers it is true that on occasions there are statistically significant differences between males and females, but there does not seem to be much in the way of a particular pattern here. In very recent analysis it appears that the 1986 B.Ed. entrants displayed a general male advantage, though it is interesting that while Certificate entrants reveal not unexpected slight differences between subjects (Maths and Integrated Science teachers scoring slightly higher than English or Religious Education, for example) within those subjects there is no sex difference whatever. Unfortunately it is not possible to disaggregate the B.Ed. entrants, where the skewness might be due to a male predominance in secondary subject teaching areas or administration.
One question out of 36 on one of the tests displayed a male advantage on two separate occasions (All the boys in John's class are cricketers; Fred is a cricketer. Is it true that Fred is not in John's class?) and this question exemplifies one of the invalid principles of inference (and a distractingly odd negative question line). It might be that female scores tend to be slightly lower on invalid principles — such was found in Nolan's data for the higher achieving students and for the 1987 B.Ed. entrants (significantly so on one small set of numeric items [t (222) = 2.527, p = 0.012] and on the set of invalid items taken together [t (222) = 2.803, p = 0.006]). But unfortunately scores on invalid principles can easily be inflated for those persons who are prepared to answer "Maybe" when they are uncertain — the instructions tell candidates to skip questions they do not feel sure about. So rather than a female tendency to be taken in by invalid argument, these slight suggestions might be more a matter of male incomprehension of the instructions. Some support for this interpretation can be given by noticing that student scores on invalid principles are often higher than their teachers', though there is no other reason to suppose them more insightful with respect to these problems.
(Subsequent analysis of five years' data from the Entrance Examinations confirms the suggestion that males score higher on invalid items: only in 1986 is the male score on valid items significantly different from the female mean score, whereas in four out of the five years the male average score on invalid items is significantly higher. Data can be found in tables 6 and 7 of Brandon (1989). Besides the suggestion in the paragraph above, one might also speculate that their slightly higher status positions in the school system give the male candidates sufficiently greater self-confidence to offer "Maybe" — it is notorious that teachers dislike admitting to not knowing the answer and this may seem to be implied by giving that response.)
Rather than dwell on what are in all cases very small differences, almost all of an accidental nature, the point I would prefer to stress is the unimportance of gender in comparison with age and social situation. Age is obviously important and needs no further stress, except to note that as with many other skills adulthood usually brings stasis.
[The original file is corrupt at this point so the first half of the next sentence is new.] While it is common to think that primary-school girls are intellectually ahead of the boys, these logic tests have only been given in grade 7 of secondary or All-Age schools and there they do not often reveal significant differences.
But in this, as also in most of the abilities consciously stressed by the school, social setting is crucial. Grade 7 girls at a private secondary school are performing at a higher level than most grade 11s in a comprehensive. Indeed they are performing better than the majority of teachers in the entrance examinations.
Within streamed schools one can also see the development or stagnation of deductive ability — in Nolan's comprehensive the "New Secondary" stream seems to keep time while the top stream moves ahead.
The important point here is that deductive ability is not something that is explicitly taught in school. Reasoning of this sort is virtually always "caught" rather than taught. I am more impressed by the possibility that the way schools are structured and the types of cognitive challenge they offer to different groups of students mould what the home has provided in the way of cognitive abilities rather than trying to account for the outcomes by some supposed variation in intelligence.
But the fact that reasoning is not taught also accounts for the fact that in general teachers are no better at it than students. If we compare teacher trainees in St Lucia with Jamaican High School students (Brandon, 1985), or Jamaican New Secondary students with the UWI entrants (Douglas-Smith, 1987) we do not find any remarkable differences in deductive competence — there is a slight advantage for the teachers on valid principles (perhaps because they are more watchful for the catch questions) but none whatsoever for the invalid principles. And the final point is that these generally shared levels of ability are pretty poor — in the case of invalid principles extremely poor.
The Significance of non-significance
I have argued that in general, and despite popular stereotypes, the males we have tested do not perform any differently from the females on tests of deductive logical competence. I have suggested that the much more significant differences are those produced by age and social situation. I have noted in passing that some factors seem to make small differences (the subject a teacher teaches, perhaps) but that reasoning ability is almost always left to be picked up informally.
If we find then that there are types of scholastic achievement that are strongly skewed sexually, it would appear that we cannot use any supposed innate differences in logical reasoning ability to explain it.
References
Brandon, E.P. (1985). On what isn't learned in school. Thinking, vol. 5, no. 4, 22-28.
Brandon, E.P. (1989). The deductive logical competence of non-graduate Caribbean teachers. Unpublished paper.
Douglas-Smith, J. (1987). An investigation into the relationship between everyday logical reasoning ability and reasoning in science in grade ten students of (urban) new secondary schools. Unpublished B.Ed. study, University of the West Indies, Mona.
Johnson-Laird, P. N. (1983). Mental Models. Cambridge.
Nolan, C. A. and Brandon, E. P. (1984). Conditional reasoning in Jamaica. Paper given to the Conference on Thinking, Harvard (ERIC Document Reproduction Service No. SO 016 755).
Norris, S. (1985). Review article — the choice of standard conditions in defining critical thinking competence. Educational Theory, vol. 35, 97-107.
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