Effects of Training in the Use of Social and Cognitive Strategies: An Intervention Study in Secondary Mathematics in Co‐Operative Groups

ABSTRACT

This article reports on an intervention study into the effects of a training in the use of social and cognitive strategies on the learning outcomes of students in secondary mathematics education. Special attention is given to differential effects for high‐ and low‐achieving students. The focus on differential effects is derived from studies into learning in small co‐operative groups, and from the results of meta‐analyses into the effects of training in learning strategies. From these studies it can be concluded that in general such programs contribute to learning. However, it seems that low‐achieving students are unable to benefit from interventions of the kind investigated (i.e., co‐operative learning and training in learning strategies). The main question is whether it is possible to design an instructional program from which all students benefit, and from which the low‐achieving students profit more than their counterparts in the control‐program. In the present study three instructional programs for co‐operative learning were compared: (i) an experimental program with special instruction in the use of social strategies; (ii) an experimental program with special instruction in the use of cognitive strategies; and (iii) a control program without training in either cognitive or social strategies. The programs were identical with respect to mathematical content and general instructional settings (a combination of whole‐class instruction, working in co‐operative groups and individual work). The experiment addressed the following research question: what are the general and differential effects of a training in the use of social and cognitive strategies on the results of learning in secondary mathematics? The research was conducted in two schools for secondary education in a total of 21 classes, involving a total of 511 students. The design was a pretest‐posttest control group design, using two experimental groups and one control group. The data were analysed from a multi‐level perspective. The outcomes of the investigation clearly show the effects of the intervention. Teaching cognitive and social strategies has the expected, positive effects. In addition to this main effect, a compensatory effect for the low‐achieving students was found. The low‐achieving students in the experimental conditions outperformed their counterparts in the control group.

     

The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning

Previous research has shown that – due to the extensive attention spent to proportional reasoning in mathematics education – many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the ‘illusion of linearity’. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. In this article, the empirical evidence for this phenomenon is expanded to the domain of probabilistic reasoning. First, we elaborate on the notion of chance and provide some reasons for expecting the over generalization of linear models in the domain of probability too. Afterwards, a number of well-known and less-known probabilistic misconceptions are described and analysed, showing that they have one remarkable characteristic in common: they can be interpreted in terms oft he improper application of linear relations. Finally, we report on an empirical investigation aimed at identifying the ability of 10^th and12^th grade students to compare the probabilities of two binomial chance situations. It appears that before instruction in probability, students have a good capability of comparing two events qualitatively, but at the same time they incorrectly quantify this qualitative insight as if the variables in the problem were linked by a linear relationship. Remarkably, these errors persist after instruction in probability. The potential of this study for improving the teaching and learning of probability, as well as suggestions for further research, are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kieferchirurgische Operationsplanung mit Hilfe von Techniken der virtuellen Realit?t

Zusammenfassung.   Für ein vollst?ndig computergestütztes Planungssystem zum Zwecke der kieferchirurgischen Operationsplanung ist die Bereitstellung von virtuellen Werkzeugen für den Chirurgen eine grundlegende Voraussetzung. Ausgehend von den Volumendaten mit Sch?del- und Kieferknochen des Patienten erm?glicht ein einfaches Interface unter Verwendung einer geeigneten Visualisierung und haptischer Eingabeger?te die interaktive Definition und Manipulation einzelner virtueller Knochensegmente. Wir haben moderne kraftrückgekoppelte Ger?te aus dem Niedrigpreisbereich eingebunden und auf ihre F?higkeit untersucht, das dreidimensionale Verst?ndnis im Planungsproze?durch Anlehnung an die Vorg?nge bei der chirurgischen Prozedur zu erh?hen. Durch diese Eingabeger?te ist es m?glich, die Knochensegmentierung für eine Osteotomie des Unterkiefers intuitiver und schneller durchzuführen. Die definierten Teilvolumina ergeben zusammen mit ihrer r?umlichen Neuanordnung auf Grundlage einer kephalometrischen Analyse einen Operationsplan. Nach erfolgter Planung werden die Planungsergebnisse in den Operationssaal übertragen. Die intraoperativen Techniken beinhalten die Visualisierung der Planungsergebnisse, die Steuerung der Anwendung über Sprache und die Bestimmung der Patientenposition mittels eines elektromagnetischen 3D-Trackingsystems. Eingegangen am 27. April 2000 / Angenommen am 21. Februar 2001     

Das MeDoc-System – ein elektronischer Publikations- und Nachweisdienst für die Informatik

Zusammenfassung.   Ziele des MeDoc-Projektes waren die Konzeption, prototypische Entwicklung und Erprobung volltextbasierter Informations- und Publikationsdienste für die Informatik, um den Informationsaustausch und die Literaturversorgung in der Wissenschaft effektiver gestalten zu k?nnen. Dazu wurde im Rahmen des Projektes ein internet-basiertes System entwickelt, in dem Informatik & Fachinformation im Volltext gespeichert, recherchiert, abgerufen und gelesen werden kann und das die Suche nach Informatik-Literatur in heterogenen, verteilten Informationsquellen im Internet unterstützt. Das Informationsangebot ist dabei teilweise kostenpflichtig. In diesem Artikel werden Ziele, Funktionalit?t und Architektur des MeDoc-Systems beschrieben. Eingegangen am 19. Januar 1998 / Angenommen am 27. April 1998     

Validation study of a method for assessing complex ill-structured problem solving by using causal representations

The important but little understood problem that motivated this study was the lack of research on valid assessment methods to determine progress in higher-order learning in situations involving complex and ill-structured problems. Without a valid assessment method, little progress can occur in instructional design research with regard to designing effective learning environments to facilitate acquisition of expertise in complex, ill-structured knowledge domains. In this paper, we first present a method based on causal representations for assessing progress of learning in complex, ill-structured problem solving and discuss its theoretical framework. Then, we present an experimental study investigating its validity against adapted protocol analysis. This study explored the impact of a massively multiplayer online educational game, which was designed to support an interdisciplinary STEM education on ninth-grade students’ complex, ill-structured problem solving skill acquisition. We identify conceptual similarities and differences between the two methods, present our comparative study and its results, and then discuss implications for diagnostics and applications. We conclude by determining how the two approaches could be used in conjunction for further research on complex and ill-structured problem solving.