Learning opportunities from group discussions: warrants become the objects of debate

In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In analyzing a videotaped episode of eight middle school students discussing a statistical problem, we observed that these students frequently challenged the arguments that their colleagues presented. These challenges invited students to be explicit about what mathematical principles, or warrants, they were implicitly using as a basis for their mathematical claims, in some cases recognize the modes of reasoning they were using were invalid and reject these modes of reasoning, and in other cases, attempt to provide deductive support to justify why their modes of reasoning were appropriate. We then describe what social and environmental conditions allowed the discussion analyzed in this paper to occur.

Kreativität im Alltag: Über Grundsätze kreativitätsorientierten Lehrens und Lernens

Zusammenfassung Schülern fällt es häufig schwer, sich phantasievoll und einfallsreich mit den ihnen im Klassenzimmer gestellten Aufgaben auseinanderzusetzen und sich — im Sinne des vorliegenden Artikels —kreativ zu verhalten. Obwohl angewandte Kreativität neue Perspektiven für ein menschenwürdiges Bildungswesen beitet, steht ein wissenschaftlich fundierter, praktisch orientierter Begriff der Kreativität, der auch kreative Facetten des alltäglichen Lebens umfaßt, noch aus. Eine eindeutige Berücksichtigung sowohl der kognitiven als auch der motivationalen und sozialen Elemente der Kreativität erlaubt dasDreikomponentenmodell der praktischen Kreativität, woraus sich eineKreativitätsdiagnostik mit Kriterien für eine Förderung der Kreativität im Klassenzimmer ergibt. Die Dimensionen dieses diagnostischen Schemas umfassenfachmännischen Gewandtheit, kreativitätsrelevante Fertigkeiten und Fähigkeiten undkreativitätsfördernde persönliche Merkmale. Diese drei Elemente der Schülerpersönlichkeit können nicht nur durch die didaktische Unterrichtsgestaltung und- durchführung, sondern auch durch kreativitätsfördernde Impulse von seiten des Lehrers sowie durch entsprechende Auswertungsverfahren zur Entfaltung gebracht werden. Zum Problembereich von Förderungsmöglichkeiten der Kreativität gibt es bereits eine Reihe von Darstellungen einzelner Aspekte der hier herauskristallisierten Komponenten der Kreativität, die allerdings in dieser Arbeit nur erwähnt werden können.Résumé Le élèves éprouvent souvent des fifficultés à faire preuve d'imagination et d'originalité dans la réalisation des tâches qui leur sont assignées à l'école, et à avoir un comportementcréatif, au sens pris dans cet article. Bien qu'une créativité appliquée offre de nouvelles perspectives à l'éducation humanitaire, un concept de créativité pratique et fondé sur la science, pouvant englober également les aspects créatifs de la vie courante, fait toujours défaut. Si l'on reconnaît franchement les éléments cognitifs, motivationnels et sociaux de la créativité, il apparaît alors possible de construire unmodèle de créativité pratique à trois dimensions. Lediagnostic de la créativité qui émane de ce modèle fournit les critères de promotion de la créativité en classe. Les dimensions de ce schéma diagnostique sontle savoir, les compétences et les aptitudes relatives à la créativités, etles qualités personnelles favorisant celle-ci. Le développement de ces trois éléments de la personnalité de l'élève peut être rehaussé non seulement par une planification et une application adéquates de l'enseignement didactique, mais aussi grâce à l'utilisation par l'enseignant de stimuli créatifs et de procédures d'évaluation appropriées. On a déjà recensé, dans le domaine de la promotion de la créativité, un certain nombre de rapports sur les différents aspects des composantes de la créativité exposées ici, qui ne peuvent faire l'object d'un examen exhaustif dans le présent article.

---

School pupils frequently find it difficult to be imaginative and original in tackling the tasks they are set in the classroom, and to behave — in the sense of the present article —creatively. Although applied creativity offers new propects for humanitarian education, there is still a lack of a practical and scientifically based concept of creativity which can also embrace the creative aspects of daily life. If cognitive, motivational and social elements of creativity are clearly recognized, it is possible to construct aThree Component Model of Practical Creativity. TheCreativity Diagnosis derived from this provides criteria for the promotion of creativity in the classroom. The dimensions of this diagnostic schema areexpert ability, aptitudes and skills relevant to creativity, andpersonal attributes conducive to creativity. The development of these three elements of pupils' personality can be encouraged not only by the proper planning and conduct of didactic teaching, but also by the teacher's use of creative stimuli and appropriate evaluation procedures. In the field of creativity promotion there are already a number of reports discussing individual aspects of the components of creativity drawn out here, which can only receive a brief mention in this paper.

     

Factors associated with successful and unsuccessful intervention with child abusive families

The authors conducted a treatment outcome study on 79 patients engaged in a program for maltreating parents. Treatment modalities included individual psychotherapy and counseling, group therapy, home visiting, and telephone advocacy with the duration of treatment ranging from 6 sessions to 36 months. On the basis of ratings by the primary therapist consensually validated by other staff, $\text{2}\text{3}$ of the sample demonstrated at least symptomatic improvement, whereas 28% improved significantly. Overall improvement was highly correlated with more subtle indices of childrearing, perception of the child, object relations, insight, and capacity for self-observation. The profiles of those maltreating parents who improved and those who did not emerged with respect to the impact of critical demographic, psychological, and therapeutic variables. Favorable outcomes were unlikely among parents who themselves had a history of maltreatment, who inflicted the more severe injuries, who entered the program involuntarily or who terminated against advice; while positive results were more prevalent in those parents with a less abusive childhood experience and who perceived a need for involvement in the program. Home visiting and advocacy appeared to enhance the potential for improvement.     

Situating graphs as workplace knowledge

We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of “transparency”, a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the notion of transparency to characterise instances of graph use by highly educated scientists in cases where the context was familiar: the scientists were able to read the situation “through” the graph. This paper explores the limits of the validity of the transparency metaphor. We present two vignettes of actual graph use by a factory worker, and contrast his actions and knowledge with that of a highly qualified process engineer working on the same production line. We note that in neither case the graphs were transparent. We argue that a fuller account that describes a spectrum of transparency is needed, and we seek to achieve this by adopting some elements of a semiotic approach that enhance a strictly activity-theoretical view.