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.     

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.     

Social perspective-taking and adjustment in emotionally disturbed,learning-disabled,and normal children

Preadolescent emotionally disturbed, learning-disabled, and normal boys were compared on social perspective-taking and behavioral measures to examine possible contributions of social cognitive deficits to children's adjustment problems. Antisocial-prosocial and withdrawn-gregarious behavior dimensions were studied through subscales derived from teacher ratings. Results indicated that across all groups, high perspective-taking was associated with significantly less withdrawal than was low perspective-taking; within groups, this finding was significant only for the emotionally disturbed boys. Contrary to theoretical assumptions, antisocial behavior was not significantly related to perspective-taking across the sample. Among emotionally disturbed boys, relatively higher affective perspectivetaking was significantly correlated with higher antisocial behavior. This positive correlation for the emotionally disturbed group was significantly different from the nonsignificant negative correlation between antisocial behavior and perspective-taking among normals. Findings for learning-disabled boys were intermediate. between results for emotionally disturbed and normal boys on both perspectivetaking and behavioral measures, and the learning-disabled group generally did not differ significantly from either other group. Theoretical and clinical implications of the findings are discussed The authors acknowledge the invaluable assistance and cooperation of many teachers and principals in Jefferson County School District in Colorado, especially Ms. Norma Sobesky, coordinator of the program for Significantly Impaired Emotionally and Behaviorally Disturbed Children, and Ms. Beth Young, coordinator of the program for Perceptual and Communicative Disorders.     

Black Students' Reactions to Feedback Conveyed by White and Black Teachers1

The present investigation examined some processes mediating self-fulfilling prophecies among black students. Specifically, we hypothesized that feedback conveyed by black and white teachers would differentially influence black students' perceptions of how the teacher viewed their success/failure, effort, ability, luck and task difficulty. In addition, we hypothesized that negative feedback would affect perceptions of evaluations differently than positive feedback. Ninety black undergraduates participated in an experiment in which a black or white teacher (confederate) expressed one of five evaluative feedback responses to a student's score on an analogies test. The results provided partial support for the first hypothesis: black female students perceived white teachers as assessing their performance less positively: that is, they perceived them to underestimate their ability and the difficulty of the task. Negative feedback also led students to believe the teacher held an unfavorable but inaccurate impression of their ability and effort, and that the teacher underestimated the difficulty of the task. These findings suggest that black students—black females in particular—may assume that white teachers hold less favorable assessments of them than black teachers and all students may be sensitive to negative evaluations.     

A device for teaching the theory of technique.

The usefulness of comparing dream psychology and neurosis psychology is demonstrated in the teaching of a course on the theory of technique at the Pittsburgh Psychoanalytic Institute. Candidates are assigned the task of writing a five-minute segment of free associations using assigned background material, resistances to be demonstrated, and assigned current and past conflicts. The candidates then present their free associations to the class for analysis. Explication of educational and developmental issues is given.     

Processing strategies in sentence comprehension

Response latencies in sentence-picture verification tasks were compared as a function of whether a mismatch was located in the logical subject (LS), verb (V), or logical object (LO) of the sentence. Sentences were presented auditorily and varied in voice and reversibility. The comparison process for nonreversibles was clearly serial self-terminating: latencies for both actives and passives were ordered LS < V < LO, or, after practice with a small number of mismatch types, LS < LO < V. Latencies for reversibles were ordered V < LS = LO, suggesting either a verb-first comparison process or an LS-V-LO comparison process which did not terminate with a subject-mismatch because of the confusability of the subject and object. The results attest to the importance of considering the "naturalness" of stimuli in sentence processing tasks, and the flexibility of subjects' encoding and comparison strategies both within and across task contexts.