The research at hand concerns the joint call in the field of education research. The themes in the joint call that will be dealt with are, as follows; learning and skills development (especially mathematics and science skills), and priorities in teacher training and school development (including e.g. pedagogical knowledge and teaching practices, school management skills). In the project we will develop a model for improving the level of understanding, the skills and self-confidence of teacher and pupils, with the active participation of teachers, using certain open-ended problems, that has a wide spectrum of applications in two countries, Finland and Chile. The similarity and the differences of both countries will lead to solutions that are valid for a broad variety of countries and therefore of international interest. The purpose in the project is to develop a model for improving the level of understanding and performance of pupils and teachers when using open-ended problems in elementary school mathematics, with the active participation of teachers, and experimentation in real classrooms in Chile and Finland. Research in the project will be implemented as a three-year follow-up study in the elementary school (comprehensive school in Finland, Enseñanza Básica in Chile) using quasi-experimental design. One may separate research in two different levels: pupils’ development and teachers’ development. The researchers follow in the experiment from grade 3 to grade 5 of the elementary school the development of pupils’ learning of understanding and problem solving, as well as teachers’ preparations, implementation and reflection (self-evaluation) of their mathematics lessons.