UNJUSTIFIED ASSUMPTIONS BASED ON DIAGRAMS IN GEOMETRY

We investigated unjustified assumptions made by students when proving geometric statements. Geometric statements can be presented with a diagram or without. Diagrams can be accurate or sketchy. Unjustified assumptions may originate in an accompanying diagram. We thus asked whether the way in which a statement is presented has an effect on unjustified assumptions. We also attempted to find out what motivates students to make unjustified assumptions. Data were collected by means of written questionnaires and individual interviews. The main findings were that among all incorrect answers, 72 % were based on unjustified assumptions, and that students make unjustified assumptions with good reasons such as in order to remove obstacles. THEORETICAL BACKGROUND Fischbein (1993) introduced the term "figural concepts " to stress the double nature of geometric figures: conceptual and figural. The conceptual nature includes characteristics such as completeness, abstraction and generalization while the figural nature includes characteristics such as color, size and shape. The conceptual an