Hypotheses production tool – a means for learning deductive proving
Presented by Dr. Zlatan MAGAJNA
Type: Oral presentation
Track: Proving in Mathematics Education at University and at School
Verification of a claim is just one of the aims of proving in school geometry and, in general, in school mathematics. Often other aspects of proofs and proving are more important, e.g. explanation, systematisation, communication. These aims mutually interact with the used technology and also with the proving related content. Introducing new technologies into school geometry thus requires a re-evaluation of the aims of proving and also a reconsideration of the curricular content. This is the case of dynamic geometry and, to a bigger extent, in the case of computer theorem provers. As a complement to dynamic geometry systems and a possible alternative to computer theorem provers a different kind of tool is proposed: a hypotheses production tool. Contrary to dynamic geometry systems, which emphasise changes in dynamic geometric constructions, the hypothesis production tool looks for (less visible) invariants in geometric constructions. These invariants are considered as hypotheses and are used as steps in proving claims about a considered construction. It is up to students to find connections between the hypotheses, to provide deductive arguments between them and to organise the arguments into a proof. Such approach gives rise to certain obstacles, but supports the currently recognised aims of proving in school geometry and is rather coherent.