ABSTRACT. This article addresses the issue of helping students who work collaboratively on mathematical problems with the aim of raising the level of their mathematical understanding and competence. We investigated two kinds of teacher interventions aimed at helping students. The rationale of these interventions was based on a process model for interaction and mathematical level raising. One kind of interventions focused on the interaction between the students, the other -on the mathematical content of the tasks. The effects of the two kinds of interventions were investigated using a pre-test -posttest comparison of students' learning outcomes and analyzing the transcripts of students' verbal utterances and worksheets. Our analyses point to interventions focused on students' interactions as more effective in terms of students' learning outcomes. Theoretical and practical implications of the research are discussed.

The study focused on the interaction between two secondary school students while they were working on computerized mathematical investigation tasks related to probability theory. The aim was to establish how such interaction helped the students to learn from one another, and how it may have hindered their learning process. The assumption was that interaction is beneficial for students if they can perform certain key activities, namely showing, explaining, justifying, and reconstructing their work. Both students attained mathematical level raising. However, the student who explained frequently and criticized himself attained more mathematical level raising than the student who did not explain her work frequently or criticize herself.

How children regulate their own collaborative learningDekker, R.; Elshout-Mohr, M.; Wood, T. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. In this article we analyze the dialogic learning of one pair of students in order to investigate how these students cope with a collaborative learning situation in the classroom. Our aim is to substantiate the claims that not only are young students (8 year olds) capable of solving mathematical problems collaboratively, but that they also take an active role in regulating their collaborative learning activities. More specifically, our claim is that children appear to apply constructs of 'mathematical level raising', 'social interaction' and 'division of time' to steer their own collaborative learning and that they are rather successful in balancing these three aspects. The analysis is exploratory, but this new perspective on collaborative learning is relevant theoretically and consequential for classroom practice.

This article adds to current research on enhancing student discourse in mathematics teaching specifically in secondary schools but with equal relevance to elementary schools. Three mathematics teachers in secondary education were confronted with the question of how to encourage students to discuss their work with each other in the daily practice of their mathematical lessons. In response to this question the teachers devised three different approaches to encourage student discourse. One of the teachers chose to experiment with another setting to perform mathematical tasks that involved students working together on a group test. The second teacher experimented with a new kind of help when students were working on their maths tasks and asked for assistance. The third created a new setting in which the teacher (temporarily) did not provide mathematical hints and the students had to solve their own problems. The three teachers were very motivated, but they all had difficulties in not giving explanations themselves when supporting their students in their collaborative mathematical learning. They found that temporarily diminishing their product help stimulated discussion between students. It also became clear that the process of teacher reflection and follow-up discussions with the researcher/observers promoted changes of practice.

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