Imaginary dialogues in secondary class mathematics lessons – understanding students’ mathematical thinking processes
Résumé
The aim of this article is to discuss the use of imaginary dialogues in mathematics education in order to stimulate students’ inner mathematical discourse of the scalar product and to make their thinking understandable for teachers. Imaginary dialogues are a form of mathematical writing that encourages students to continue a written and unfinished dialogue between two imaginary individuals discussing a mathematical problem. Analysing students’ texts, teachers might be able to trace students’ mathematical thinking processes. Results can be used by teachers to modify teaching instructions. In a research project, 10th grade students of Lower Austria are writing about their thoughts on the scalar product. A qualitative case study determines whether the concept of mental models is sufficient to represent students’ thinking or whether there are other teaching- relevant aspects worth considering. First evaluation results are presented.
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