The aim of our two consecutive papers is to advance understanding on the nature of proving activities required in the inquiry-based learning called Study and Research Paths (SRP), which is based on the paradigm of questioning the world proposed by Chevallard in the framework of Anthropological Theory of the Didactic (ATD). In this paper, we first introduce the paradigm of questioning the world and the notion of SRP as well as the Herbartian formula, the media-milieu dialectic, the five phases of SRP, and the seven dialectics, and then explore the nature of proving activities in SRP through a theoretical consideration on the process of elaborating an answer to a given question. In the situations of SRP, the learners need to ask why-questions in order to understand the answer obtained from the media and use it to elaborate their own answer. We as a result reached at the claim that the situations of SRP trigger the proving activities to understand the mathematical structure which are difficult to be realized in the ordinary mathematics class based on the ‘old’ paradigm of monumentalism, due to the didactic contract spontaneously created in such situations. This claim is to be empirically verified in the second paper and in our future study.
