Abstract
For Japan to be a leading country in the global society, it is indispensable that Japanese citizens each should have competencies of high quality on mathematical-scientific problem solving. In this report, we took up the Bowland Maths project of England and the COMPASS project of the EU as cases to be considered and compared them with the current conditions of mathematics education in Japan, and pointed out some of the main problems which we should address in conducting such teaching practice so as to foster competencies on mathematical-scientific problem solving. Those are the development of case study type- and inquiry-based teaching materials, teaching methods to promote discussions between students, the creation of frameworks for cross-curriculum learning, development of the tasks and the rubrics concerning formative assessment. And we pointed out that teachers' training (pre-service and in-service training for teachers) is the key to the solution of the problems and that the cooperation between industrial and educational circles is very important in that field.
