Point-driven Mathematics Teaching. Studying and Intervening in Danish Classrooms

Do Danish mathematics teachers have a "point"? In this dissertation the concept of a mathematical point is clarified and defined as a statement presenting a clearly delineated and significant mathematical content or climax. It is examined to what extent Danish mathematics teachers in lower secondary schools emphasize such points in their teaching. Thus, 50 randomly selected mathematics teachers are filmed in one grade 8 math lesson and the dialogue investigated. The study identifies large variations and many influential components. There seems to be room for improvement.
In order to examine possibilities to strengthen the presence and role of mathematical points in teaching two intervention studies are conducted.
First a focus group of 5 of the original 50 teachers from each school are offered peer coaching by the researcher. This study indicates that different teachers appreciate peer coaching to individual desire and need, and the effect can be significant to the teachers' communication in the classroom.
Also, a lesson study is conducted with all 18 mathematics teachers at one school. It is shown that the group of all mathematics teachers at one school with a limited use of resources can be supported in significant changes to a point-oriented mathematics teaching. The teachers emphasized joint planning
of study lessons, and they regarded the peer coaching after each of these lessons as valuable.
The studies with the two teacher groups indicate different opportunities and challenges, and it is recommended that all schools appoint and support a mathematics tutor with responsibility for such to offer or arrange for peer coaching and guidance, including that mathematic teachers in teams arrange
systematically peer coaching as a lesson study. In mathematics teacher education is also recommended that the practice preparation, practice teaching and assessment are organized as a lesson study with focus on mathematical points.