Proving Activities on Study and Research Paths


Dr. Koji Otaki, Hokkaido University of Education, Japan


In this presentation, I introduce some results from an ongoing research project with my colleagues, on the nature of proving activities in the inquiry-based learning, within the research programme of the anthropological theory of the didactic (ATD). The teaching and learning of mathematical proof is an important issue in research on mathematics education. In particular, it is well known that many students do not feel the necessity and functionality of proof and proving. Our conjecture on this student difficulty is that it is mainly a traditional didactic paradigm, monumentalism, in mathematics education practice that conditions such a phenomenon (difficulty). In other terms, teaching and learning situations based on other paradigms may not give rise to such a phenomenon. We thus investigate the proving activities in the study and research path (SRP) based on the paradigm of questioning the world. SRP is an inquiry-based teaching and learning characterised by ATD, which refers to the real researcher’s activities. We analysed the relationship between SRP and proving activities, designed and implemented a SRP to gather the data on proving activities in SRP. The SRP is related to a cube root calculation with a simple pocket calculator. A main finding is that proving activities for understanding mathematical works have naturally emerged in the SRP.