In this work we analyze the specialized knowledge about periodic numbers of a group of prospective mathematics teachers by means of a task for teacher development. The results revealed that a KoT and the KPM knowledges were displayed in the transformation of a periodic number to a fraction. In the discussion there appeared a resistance to accept the equality 0, 9 ̅ =1. The prospective teachers (PTs) based their initial discussion on their beliefs rather than on mathematical arguments.

No abstract

In collaborative learning, students not only have to acquire knowledge, they also have to learn to regulate the process of acquiring knowledge. In the traditional classroom, the function of regulation rests with the teacher. In the collaborative classroom, however, the responsibility for learning has in part been handed over to the students. We examine how students, who work as members of a community of learners, construct shared understanding. In particular, we want to explore what interactive and discursive tools students use in their collaboration. We present observations made during a series of innovative mathematics lessons in an 8th grade classroom at a Dutch primary school in which children (between I I and I3 years of age) worked as "researchers" who were encouraged to formulate questions for exploration and to collaborate in answering them. Both in small group discussions and in discussions involving the whole class, students worked on the construction of arguments and the creation of shared knowledge. The construction and diffusion of knowledge occurred in "cycles of argumentation" to which many children contributed and in which ideas were repeated and elaborated upon. Because, in students' collaboration, learning is made dependent on proposing and critically discussing arguments, the character of knowledge, acquired under these circumstances, is different from knowledge acquired in a more traditional classroom setting,

No abstract

No abstract