This paper addresses the development of mathematics teaching to improve mathematics learning for students of mathematics at all levels. It focuses on the design of activity for classroom intervention in which teachers are centrally involved along with didacticians. Research and development are closely inter-related with both teachers (insiders) and didacticians (outsiders) taking research roles. Three models or paradigms are described and compared: design research; learning study; and co-learning inquiry. A theoretically-based, innovative, iterative design process is indicated for reliable developmental outcomes. It is suggested that teachers need to be partners in design and study. The nature of partnership is raised as a question for further exploration in connection with the dissemination and sustainability of approaches to development.
This paper reports on a project designed to develop inquiry communities between teachers and didacticians, aimed at improving the learning of mathematics in classrooms, and at studying the processes, practices, issues and outcomes in and of the project. Theoretical notions of inquiry and community underpin the project. The focus here is largely methodological, tracing the origination and development of the project and decisions taken through its first phases. The project is seen to be situated within a 'developmental' research paradigm in which research both studies the developmental process and contributes centrally to it. Issues in the interpretation of inquiry practices in mathematics learning and teaching and the building of communities at various levels are seen as important outcomes. The roles and relationships of teachers and didacticians emerge as key concepts in the developmental process.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.