Proving Activities in SRP based on the Paradigm of Questioning the World (II): through a Teaching Experiment for Undergraduate Students

Abstract

　　 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 the preceding paper, we explored the nature of proving activities in SRP through a theoretical consideration and pointed out that the situations of SRP would trigger authentic proving activities to understand the mathematical structure.  In this paper, we report the results of a teaching experiment conducted for undergraduate students of a teacher training university in Japan, and verify our claim.  A series of mathematics classes based on SRP was designed around the question of finding a method of calculating the cube root of a given number by using a simple pocket calculator.  We analyzed the data collected in this experiment from the following viewpoints: what kind of didactic contract is there in the realized situations, what kind of proving activities arise due to the didactic contract, and how the didactic contract promote or prevent the proving activities?  As a result, we found that the students were engaged in many proving activities by asking by themselves why-questions in the process of inquiry, due to the didactic contract entirely different from the one identified in the ordinary mathematics classroom.  We also identified that these proving activities play various functions of proof in the media-milieu dialectic.