Analysis of fraction errors by a model of cognitive science

In clinical interviews, grade 7 students of average abilities worked out some problems on the topic of fractions; the problems were given to the children in different forms of representation. From the examples it is illustrated that, even if children are dealing with similiar exercises and even if they had been taught in the same way, their mathematical thinking might be quite different. The differences in the children’s behavior seem to come from differences in the internal representation of their knowledge of the concepts and procedures. To explain why the children handled as they did, a theoretical framework is needed. In this paper, Davis and McKnight’s «hypothetical mechanisms» are used to explain children’s understanding of fractions. A revised version of Minsky’s and Davis’ frame-model seems to be especially useful to explain the relationship between the teacher’s notions, the children’s «concept images» and the real-world aspects of mathematics.     

The Relationship of Socio‐cognitive Oversimplification and the Social Behaviour of Adolescents

When processing information about their world, people systematically reduce objective complexity. This is true not only of cognitive problem‐solving, but also other everyday situations, for example where decisions are required in situations relevant to morality. The developmental psychological perspective suggests that the adequate handling of situations like these requires, on the one hand, an age‐related, increasing differentiation in social cognition and, on the other hand, an ever more effective structuring and integration of information. However, the operation of the latter developmental process might carry the risk that complexity reduction (in the sense of oversimplification) substitutes for adequate psychosocial development. Undue emphasis on complexity reduction may suggest situation‐specific action alternatives, which though inappropriate, are ‘easier to handle’. In an empirical study using 176 pupils from Polytechnic High Schools in (East) Berlin, we test the hypothesis that a tendency towards oversimplification in (fictitious) situations of moral relevance is systematically related to deviant behaviour at school. Results show that students exhibiting deviant behaviour do indeed have a stronger tendency to oversimplify social cognition. It can also be shown that the frequency of complex social cognitions generally increases with age. This trend, however, is found for non‐deviant students only. For deviant students a decrease in complex social cognitions with increasing age was found. Furthermore, it can be shown that these results are not confounded with the effects of gender or academic grade.     

Contents Volume 12 (2000)

Volume Contents

Contents Volume 12 (2000)     

Depression and suicidal ideation in sexually abused children

Sixty-five sexually abused children were administered the Children's Depression Inventory (CDI) following investigation of their abuse to determine the relationship of victims' depression and suicidal ideation with victims' age, post-investigation residence, nature of the abuse, and mothers' belief of victim and compliance with treatment recommendations. Results indicated that older victims were more likely to describe themselves as being depressed. In addition, older victims and those whose mothers were less compliant were more likely to have CDI scores that were above the 90th percentile reported by Smucker, Craighead, Craighead, and Green (1986). Suicidal ideation was more likely in victims who were older, whose mothers were less compliant, who were not removed from their homes, and who had been molested by a family member.     

Dilemmas in the quest for inclusion

In 1995, on the occasion of his 'retirement', Professor Klaus Wedell wrote a leading article for BJSE entitled 'Making inclusive education ordinary'. Last October, Professor Wedell, also known to BJSE's readers as the author of the regular 'Points from the SENCo-Forum' column, delivered the Gulliford Lecture at Birmingham University. Here he makes the text of his lecture accessible to a wider audience.
In this article, Professor Wedell places some of the ideas he discussed in 1995 in a contemporary context. He explores the systemic rigidities that create barriers to inclusion; he offers creative ideas for new ways to approach the challenges of inclusion; and he argues persuasively for much greater flexibility, at a range of levels, in order to facilitate change, development and innovation. Building on these themes, Professor Wedell summarises a series of implications for policy and practice. These concern teaching and learning; staffing and professional expertise; and grouping and locations for learning. In concluding his article, Professor Wedell calls on the Government to consider in more depth the issues that are raised by moves towards inclusion – particularly those issues that concern the individual learner in relation to the shared curriculum. This article will be of interest to anyone who recognises these and other tensions in the movement towards inclusion.     

Some observations and remembrances of Kenneth W. Spence

Kenneth W. Spence was among the most influential learning theorists of the 20th century. He was not only a pioneer in the genesis of computational models but an articulate systematist and scholar regarding the place of theory in psychology. The following observations and remembrances were offered at the University of Iowa as part of a tribute to his contributions on the 100th anniversary of his birth.     

The myth of literacy relapse: Literacy retention among Moroccan primary school leavers

The issue of literacy retention is central to the educational policy concerning of most developing countries. It has been variously suggested that 4–6 years of primary education may serve as an inoculation against ‘relapse’ into illiteracy in the Third World. This paper reports on one of the first longitudinal studies designed to address this question, by investigating the nature of literacy and cognitive retention in a sample of 72 adolescents two years following fifth grade departure from primary school in Morocco. The present study found that these school leavers, when reassessed two years later, showed a significant increase in performance in first literacy (Arabic), modest gains in second literacy (French), no change in cognitive skills, and a decrement in math skill. Furthermore, urban leavers gained more literacy than rural leavers, and girls more than boys. The present findings do not support the hypothesis of literacy ‘relapse’ or loss of academic/cognitive skills after five grades of primary schooling. It was also found that girls retained more academic skills than boys, but were much less likely to be employed, a finding which calls into question certain claims about the impact of schooled knowledge and literacy on employment in developing countries.     

Encouraging Example Generation: A Teaching Experiment in First-Semester Calculus

Abstract

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article presents three student case studies. These case studies are representative of our findings and serve to summarize the activities we found useful. They also serve as examples of various student experiences during the teaching experiment. One student expressed a continued negative view to using example generation. Two increased in skills and experience and expressed positive changes in views.     

Gender, Learning and Social Practice

The aim of this paper is to analyse the relationship between learning and gender at the workplace, by means of an empirical study. It is argued that gendered participation is learnt at the workplace and does not constitute a ‘natural’ division. The empirical part of the paper is based on a qualitative study of a bakery in which gender and learning in vocational training are the key focus. For centuries, bakeries have been masculine workplaces. However, in recent years, the percentage of female apprentices has increased. This paper takes a situated perspective on learning and gender, by focusing on how everyday work practices influence the discourses in workplace practice, and how this affects participant perceptions of themselves. Furthermore, Holzkamp’s distinction between expansive and restrictive perspective on learning is central to understanding the role of gendered discourses. In the first part of the paper, gender is situated in the bakeries, emphasizing the historical circumstances, physical environment and economic aspects that create a specific gendered discourse. In the second part of the paper, the focus is on how various ways of learning are situated in the bakeries.

Dissociation of the blocking of conditioned eyeblink and conditioned fear following a shift in US locus

Two experiments with rabbits investigated the concordance of two measures of conditioning, eyeblink and potentiated startle, during a blocking sequence with paraorbital shock reinforcement. In both, a shift in the locus of shock from one eye to the other between the conditioning of an element and a compound of that element and a new cue had differential effects on the two measures of conditioning to the new cue. When the shock was unchanged, diminished conditioning in relation to controls (i.e., blocking) was observed on both measures. When the shock was changed, little conditioning was observed in startle, but control-equivalent amounts were observed in eyeblink (i.e., blocking occurred on the former but not the latter). The results are interpreted as showing a dissociation of the associative learning involving the emotive features of Pavlovian reinforcers and that involving the remaining sensory-perceptual features, and more compatible with a diminished US-processing, than with a CSprocessing, view of blocking.