Vanda Santos

Joana Teles, Vanda Santos, Pedro Quaresma

The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers and the normal practice of conjecturing and proving in schools is a major barrier to a wider use of such tools in an educational environment. Since the early implementations of geometry automated theorem provers, applications of artificial intelligence methods, synthetic provers based on inference rules and using forward chaining reasoning are considered to be more suited for education proposes. Choosing an appropriate set of rules and an automated method that can use those rules is a major challenge. We discuss one such rule set and its implementation using the geometry deductive databases method (GDDM). The approach is tested using some chosen geometric conjectures that could be the goal of a 7th year class (approx. 12-year-old students). A lesson plan is presented, its goal is the introduction of formal demonstration of proving geometric theorems, trying to motivate students to that goal

Pedro Quaresma, Vanda Santos

The introduction of automated deduction systems in secondary schools face several bottlenecks, the absence of the subject of rigorous mathematical demonstrations in the curricula, the lack of knowledge by the teachers about the subject and the difficulty of tackling the task by automatic means. Despite those difficulties we claim that the subject of automated deduction in geometry can be introduced, by addressing it in particular cases: simple to manipulate by students and teachers and reasonably easy to be dealt by automatic deduction tools. The subject is discussed by addressing four secondary schools geometry problems: their rigorous proofs, visual proofs, numeric proofs, algebraic formal proofs, synthetic formal proofs, or the lack of them. For these problems we discuss a lesson plan to address them with the help of Information and Communications Technology, more specifically, automated deduction tools.

Pedro Quaresma, Vanda Santos, Nuno Baeta

The Web Geometry Laboratory (WGL) is a collaborative and adaptive e-learning Web platform integrating a well known dynamic geometry system. Thousands of Geometric problems for Geometric Theorem Provers (TGTP) is a Web-based repository of geometric problems to support the testing and evaluation of geometric automated theorem proving systems. The users of these systems should be able to profit from each other. The TGTP corpus must be made available to the WGL user, allowing, in this way, the exploration of TGTP problems and their proofs. On the other direction TGTP could gain by the possibility of a wider users base submitting new problems. Such information exchange between clients (e.g. WGL) and servers (e.g. TGTP) raises many issues: geometric search - someone, working in a geometric problem, must be able to ask for more information regarding that construction; levels of geometric knowledge and interest - the problems in the servers must be classified in such a way that, in response to a client query, only the problems in the user's level and/or interest are returned; different aims of each tool - e.g. WGL is about secondary school geometry, TGTP is about formal proofs in semi-analytic and algebraic proof methods, not a perfect match indeed; localisation issues, e.g. a Portuguese user obliged to make the query and process the answer in English; technical issues-many technical issues need to be addressed to make this exchange of geometric information possible and useful. Instead of a giant (difficult to maintain) tool, trying to cover all, the interconnection of specialised tools seems much more promising. The challenges to make that connection work are many and difficult, but, it is the authors impression, not insurmountable.