数学教育における学習作業空間論に関する総合的研究 ―有意味世界の生起・維持・変容としての数学学習を捉える中核理論の提案―

抄録

　　The overall objectives of this multidisciplinary research are to make mathematics curriculum principles involving designing a learning environment and propose a multifunctional, practical framework for a formative assessment by the participants and observers.  The program of this research consists of three parts: the core theory, designing methodology, and curriculum assessment.  This article deals with the core theory including generation and construction of objects, as well as bringing forth, maintaining and changing a world of mathematical significance.  The theory finally proposes the nested model to describe macro / mezzo / micro structure of worlds of significance in a mathematics classroom.  

　　This research especially focuses on the mathematical working spaces theory developed by Kuzniak et al. to describe the way to generate (mathematical) objects and intention theory to explain the participants’ attitudes and emotions during mathematics lessons.  Behaviors and local interactions between individual students at a micro level will evolve toward actions by a pair or small group of them at a mezzo level.  The participants’ activities ultimately lead to systemic ones at a macro level by harmonizing some mezzo level actions with each other, which seem to have a certain holistic system from a view point of the observers.  This research suggests these findings through theoretical and practical discussions and summarizes them as the nested model.