Automated reasoning in elementary geometry: towards inquiry learning (original) (raw)

2018, Pädagogische Horizonte

We claim that the inquiry-based learning approach to geometry can be improved by considering a recently implemented algorithm for the automatic conjecturing and proving of elementary geometry statements. The new method we describe relies on some Automated Reasoning Tools commands, now available in the dynamic geometry software GeoGebra, that provide with mathematically rigorous answers to any query posed by a user about the truth or falsity of any geometric statement and that, if the conjectured statement is wrong, present further hypotheses that should be considered for the pro position to become true. We argue, by providing examples of mathematical investigations that may be better approached by the students by using our method during the exploration process, how these tools may be helpful for supporting inquiry-based learning at various education levels. Some of the potential implications of our proposal (such as providing to automated reasoning programs, for the first time, the possibility of a real impact in education, or the possibility of automatizing the development of automated mentors, etc.) are briefly stated. It is yet ongoing work to develop a systematic approach to confirm the benefits of the proposed method.