Mathematical Activities in Multidisciplinary Study and Research Paths: through a Teaching Experiment in Japanese Junior High School

Abstract

　　The aim of this paper is to advance understanding on the characteristics of mathematical activities that take place in the multidisciplinary Study and Research Paths (SRP) based on the paradigm of questioning the world.  SRP formulated within the Anthropological Theory of the Didactic is the inquiry activity aiming at nurturing researcher’s attitude and allowing students to use any media (internet, book, etc.) and to learn mathematics according to its necessity during inquiry.  We carry out a teaching experiment for the students of grade 8 in Japanese junior high school, using the question related to the population explosion on earth.  A sequence of four lessons are designed and implemented in five classes.  The data collected in this teaching experiment are analyzed by means of different concepts related to SRP: the questions-answers dialectic is identified to clarify the multidisciplinarity of students’ inquiry, the media-milieu dialectic to see the dynamism of students’ autonomous activities, and mathematical praxeologies to characterize the mathematical activity in the multidisciplinary SRP.  The result of analysis implies first of all a great potential of implementing SRP in Japanese junior high school, in particular as a multidisciplinary activity which is strongly emphasized today by the Japanese Ministry of Education.  The analysis also shows that there are two different kinds of mathematical activities in the inquiry process.  On the one hand, it is the mathematical activity as a tool to construct an answer to the question of other discipline (in our case, social studies).  Mathematical praxeologies in such a case appear explicitly in distinction from the praxeologies of other discipline.  On the other hand, it is the mathematical activity which is in a mixture with the activity of social studies, wherein the type of tasks identified is not purely mathematical but interdisciplinary one including the elements of mathematics and social studies.