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.
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.
A field study with 16-year-old students in senior general secondary education was undertaken with the following research question: ''Do students working in pairs on investigation tasks with the computer attain more conceptual level raising in mathematics when they are supported by a teacher who stimulates their interaction (process help) than when they are supported by a teacher who gives mathematical help (product help)?'' Students in both conditions improved, but the two types of help showed no significant difference in level raising. Also, students in both conditions had serious problems with the learning materials, and wanted the teacher to explain and correct more. For students at this level of education, learning with investigation tasks in small groups appears to be very difficult.
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