Dreyfus T., Hadas N. (1996)
Proof as answer to the question why.

Zentralblatt für Didaktik der Mathematik 28 (1) 1-5.

Abstract
Students' concept of proof, their appreciation for its need as well as for its roles, depends on the curriculum, on the activities students are asked to carry out, on the questions they are asked and on how they are asked these questions. It is shown how the empirical approach to geometry (which is often associated with computer based dynamic geometry software) can be used as a basis for creating didactic situations in which students require proofs. Classroom experiences are reported, which show how situations arose in which students felt the need for proof in order to either explain phenomena they couldn't explain otherwise, or in order to convince themselves of counter-intuitive results.

© Zentralblatt für Didaktik der Mathematik

Article table of content

1. The need for proof

2. The need for proof in classroom situations

2.1. How many elements suffice to uniquely determine a triangle?
2.2. Does it have to be a parallelogram?

3. Other didactic situations

3.1. Altitudes of a triangle
3.2. The inscribed angle of a circle
3.3. The diagonals of a quadrilateral
3.4 The angle bisectors of a quadrilateral

4. Situations that elicit the need for proof