Mathematics teaching development as a human practice: identifying and drawing the threads

This article was published in the journal, ZDM Mathematics Education [© FIZ Karlsruhe] and the definitive version is available at: http://dx.doi.org/10.1007/s11858-012-0437-7The didactic triangle links mathematics, teachers and students in a consideration of teaching– learning interactions in mathematics classrooms. This paper focuses on teachers and teaching in the development of fruitful learning experiences for students with mathematics. It recognises primarily that teachers are humans with personal characteristics, subject to a range of influences through the communities of which they are a part, and considers aspects of teachers’ personhood, identity and agency in designing teaching for the benefit of their students. Teaching is seen as a developmental process in which inquiry plays a central role, both in doing mathematics in the classroom and in exploring teaching practice. The teacher-as-inquirer in collaboration with outsider researchers leads to growth of knowledge in teaching through development of identity and agency for both groups. The inclusion of the outsider researcher brings an additional node into the didactic triangle

The mediating role of a teacher’s use of semiotic resources in pupils’ early algebraic reasoning

The final publication is available at Springer via http://dx.doi.org/10.1007/s11858-012-0421-2.This paper focuses on the semiotic resources used by an experienced sixth-grade teacher when her pupils are working on a mathematical task involving written text and the two inscriptions of figure and diagram. Socio-cultural analytical constructs such as semiotic bundle, space of joint action and togethering are applied in order to enable and frame the collective activity of the teacher and pupils. Four extracts from different situations in the classroom illustrate the important role of both teacher gestures and pupil gestures, interacting with other modalities such as speech and inscription, in the process of making sense of pupils’ appropriation of coordinating two dimensions in a diagram. It is argued that the nature of the mathematical task is an important entry point into early algebraic reasoning. The study emphasises the mediating role of the dynamics of semiotic bundles produced in teacher–pupil dialogues as a promising way to address the fundamental relationships between mathematics, pupil and teacher in a classroom context in order to provoke pupil involvement and engagement when experiencing mathematics