THE DEVELOPMENT OF KNOWLEDGE CONCERNING WRITTEN ARITHMETIC: A CROSS-CULTURAL STUDY

This study is concerned with the manner in which Western mathematics is assimilated by children raised in traditional African cultures. It was predicted that after an initial period of difficulty in learning school arithmetic, African children (Baoulé and Dioula from the Ivory Coast) acquire basic concepts, develop invented strategies, and make errors similar to those of American children. Further, it was predicted that Dioula children, since they are members of a commercial culture, perform at a somewhat higher level than the Baoulé, members of a farming culture which does not seem to stress computational activity. To investigate these hypotheses, American, Baoulé, and Dioula children at two age levels were given a variety of arithmetic problems involving basic skills (e.g., reading numbers), number knowledge (e.g., place value), and calculational abilities (e.g., written computation). The results showed that, in general, older African and American children (fifth- and sixth-graders) were quite similar in all respects. The only large and significant differences occurred in the case of younger children (second- and third-graders). At this level American children generally performed at a higher level than Africans, as predicted, and Dioula occasionally at a higher level than Baoulé, also as predicted. At the same time, qualitative aspects of African and American children's performance were similar: for example, both groups made the same types and proportions of errors in written calculations. The results generally support the hypotheses and can be explained in terms of both educational and cognitive factors.     

Challenging the Myths of Industrial Arts

The majority of the thousands of industrial arts majors that graduate each year in the nation take jobs in business and industry—not as teachers in schools and colleges as in the past. Many counselors are unaware of this and many other important facts about the field of industrial arts. This article provides insights to prepare job counselors as they counsel potential and established industrial arts majors and graduates.     

Reality therapy: Icing on the cake of behavior modification

The paper presents a conceptual model for therapeutic intervention based on a behavioral orientation. Behavioral therapy is viewed on a continuum ranging from basic operant techniques to cognitive strategies applied to human interaction. It is hypothesized that the elements of reality therapy, with its emphasis on human interaction, are needed to provide closure to the therapeutic intervention and to help maintain new coping behaviors. Utilizing the context of an institutionalized client, suggestions for how this process might occur are discussed.     

Proportionality,linearity, and parameter constancy: Messick and Sentis reconsidered

Messick and Sentis found greater support for weak proportionality in subjects' outcome allocations (suggesting that subjects wish to maintain a constant ratio between outcomes across situations when inputs are held constant) than for constant differences between outcomes. They claimed that their data thus provided stronger support for Adams' ratio definition of equity than for Harris' linear formula. A dialogue between the two sets of authors establishes that (1) so far as their specification of fair outcomes is concerned, Adams' formula is a special case of the linear formula; (2) weak proportionality does not necessarily follow from Adams' formula and can be derived from the linear formula; (3) Adams' formula applied to subjective (rather than experimenter-defined) inputs nevertheless provides a more natural base from which to derive weak proportionality than does the linear formula in its general form; (4) excellent fits to several sets of data, including much better fit to Messick and Sentis' data than that provided by weak proportionality, are obtained if we assume that subjects use allocations which are a weighted average of those implied by Adams' formula, the Equality principle, and Komorita and Kravitz' Equal Excess Norm; and (5) a fit to Messick and Sentis' data that is almost as good as that provided by the weighted solutions model is obtained by assuming that subjects apply Adams' formula to subjective inputs and subjective outcomes that are different from the corresponding experimenter-defined values. It is agreed that the delineation of the relationships among observable properties of outcome distributions, alternative equity formulae, and different psychological processes is as important as it can be devious.     

The computer psychiatrist: How far have we come? Where are we heading? How far dare we go?

The use of computers in psychiatry and psychology is reviewed. It is noted that computers are already being used successfully for consultation, interviewing, and continuing education. Issues related to the usage of computers in mental health are discussed. Guidelines for future work in the area are suggested.     

The effect of thematic content on the ‘Wason selection task’

This paper concerns the differential effects of use of ‘thematic’, rather than abstract (symbolic), content on the ‘Wason selection task’. An effect of thematic content has been reported several times, originally by Wason & Shapiro (1971), but Manktelow & Evans (1979) report five experiments that failed to obtain an effect and argue against the validity of the content effect in general. However, it is pointed out that four of their experiments use a novel content and that there are previous reports of non-effective content in the literature. It is concluded that a particular type of thematic content cannot be treated as a ‘random sample’ of thematic content in general, and that their argument thus rests upon their failure to produce an effect of the specific (’towns and transport’) content used by Wason and Shapiro. This produces an essentially empirical controversy which is settled in two ways. First, Manktelow and Evans’s criticisms of two previous replications are shown to be misleading. Second, an experiment is reported that exactly copies the Wason and Shapiro design and produces a significant effect of content. It is concluded that the Manktelow and Evans result most probably was due to a Type 2 error. Finally, a hypothesis is developed to account for both the effect of certain types of content and the lack of effect of others, including that used in Manktelow and Evans’s first four experiments.     

Two subjective scales of number

The way in which the apparent magnitude of numbers grows with their absolute magnitude was measured with a modified version of the direct technique Marks and Slawson (1966) used to determine the psychophysical exponent for loudness. This modified technique required subjects to estimate how evenly and randomly a sequence of integers appeared to sample the numerical continuum. The results indicate that the apparent magnitude of numbers increases with a decelerated power function of their arithmetic magnitude when a series samples from an open-ended range. However, when an upper boundary of the range is specified, the subjective scale seems to be linear. Random productions of numbers parallel the results found with judgments of presented sequences. The two scales of number provide the basis for an interpretation of the difference between magnitude and category scales: that subjects use numbers differently when the response scale is open-ended Imagnitude estimation than when it has a fixed upper limit tcategory scale. Given the assumption that subjects use numbers in this way in the two tasks, the qualitative relation between magnitude and category scales is predicted.     

Integrality over different paradigms: Card sorting and two-stimulus matching

Orthogonal interference—indicating the cohesiveness between geometrical dimensions—was examined using two separate tasks: (1) card sorting and (2) two-stimulus matching requiring same/different responses. The card-sorting results of the present experiment were contrasted with the results of our previous research (1977, 1979) which used the two-stimulus matching task. Results were generally similar in that the orthogonal interference and, consequently, the degree of integrality/separability were the same for both tasks. Evidence was found for the emergence of a new nominal dimension. This and other results are only compatible with a weaker form of the global-to-local hypothesis of perceptual processing.