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.
Students from 11 to 12 years old were invited to derive the meaning of five unknown words, each embedded in three contexts. We focused on the students' proficiency in three activities: decontextualization of the target word meanings from the contexts (decontextualization), testing initial ideas about the word meanings with subsequent contexts (cumulative testing), and formulating dictionarylike definitions (defining). We compared eight students of high and eight students of low verbal ability. The students were led individually through the process of deriving the meaning of the target words, while thinking aloud. The study showed that even young students of low verbal ability are capable of performing meaning-derivation activities that are in general ascribed to mature students of high verbal ability.
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