A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools

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

Four Geometry Problems to Introduce Automated Deduction in Secondary Schools

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.