Abstract
Four potential modes of interaction with diagrams in geometry are introduced. These are used to discuss how interaction with diagrams has supported the customary work of ‘doing proofs’ in American geometry classes and what interaction with diagrams might support the work of building reasoned conjectures. The extent to which the latter kind of interaction may induce tensions on the work of a teacher as she manages students’ mathematical work is illustrated.
Kurzreferat
Vier mögliche Formen der Interaktion mit geometrischen Darstellungen werden aufgezeigt. Diese Formen werden thematisiert um deutlich zu machen, wie visuelle Darbietungen im am erikanischen Geometrieunterricht das alltägliche Geschäft des Beweisens, unterstützen. Dadurch soll auch gezeigt werden, welche Art der Interaktion mit geometrischen Darstellungen es erlaubt, das Herstellen begründeter Vermutungen zu unterstützen. Zugleich wird das Ausmaß illustriert, mit welchem die letztere Art von Interaktion Spannungen innerhalb der unterrichtlichen Arbeit, der Lehrerin hervorruft, die sich darum bemüht, die mathematischen Beiträge, d.h. die mathematische Arbeit, der Schülerinnen und Schüler zu organisieren.
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