# Mathematics teaching and teacher education: two studies

24 month seminar with Louise Meier Carlsen, followed by start-up seminar with Yukiko Asami-Johansson. As colleague expert, we are happy to announce the presence of Dr. Marianna Achiam, IND.

**Outline of Louise Meier Carlsens presentation:**

The seminar will start with a short presentation of a study on “What algebraic knowledge may not be learned with CAS -a praxeological analysis of the Faroese exam exercises?” I consider the types of tasks and the techniques required to solve the types of tasks both by paper and pencil and by CAS. Concluding that when CAS is used to solve traditional exercises the mathematical praxeology is reduced and basic algebraic knowledge may not be learned.

Furthermore I will present a research design for a course in algebra, arithmetic and numbers for mathematics student teachers with the integration of CAS with the research goal of developing the student teachers knowledge of teaching with CAS. The structure of the course is inspired by Japanese lesson study and thus the elements: pre-didactical system (the planning face), observational-didactical system (the research lesson) and post-didactical system (reflection meeting) are implemented. The structure of the pre-didactical system will be presented, the template for the lesson plan and the protocol for the post-didactical system. Furthermore I will also present the adaptation of notions of praxeology in which to analyse the development of student teachers knowledge on teaching with CAS, and finally an outline of the possible research questions and articles based on the research design.

**Outline of Yukiko Asami-Johansson's presentation:**

I will present an outline of my PhD-project entitled "Ecology of Japanese School Mathematics -with focus on the use of a structured problem solving approach". It consists of three parts:

- A case study of mathematics classroom with a structured problem solving approach in Japan
- Designing lessons using Japanese structured problem solving in Sweden
- A comparative study of teacher education in Japan, Finland and Sweden

My project aims

- to analyse the ecology of the mathematical praxeologies obtained in lessons designed according to the structured problem solving approach.
- to analyse if a sequence of the Japanese mathematics lessons and the approach give any significant effects with regard to students’ active participation in the learning of mathematics when it is implemented in a Swedish mathematics class.
- to provide a comparative analysis on the conditions and constraints that decide how mathematics courses for elementary school teacher education are carried out at universities in Sweden, Finland and Japan.

based on the following research questions:

- What are the distinct features of the praxeologies obtained when the structured problem solving approach is applied in a Japanese classroom?
- When applying the Japanese teaching approach in Swedish mathematics classrooms, what can be said about the mathematical and the didactical organisations? How does the approach promote students’ mathematical contributions in the classroom?
- Which institutional conditions and constraints have most impact on the teacher educators’ way of describing the transposition from “subject matter knowledge” to “taught knowledge” in Japan, Finland and Sweden?

I will present also the methodology, expected results and timeline of my project.