Teachers' practices and resources in the Hungarian "Guided Discovery" approach to teaching mathematics: presenting and representing "series of problems"

In the Hungarian "Guided Discovery" approach to teaching mathematics, teachers' planning work plays a crucial role. Teachers following the approach develop teaching trajectories based on "series of problems". This work includes the choice, creation, transformation, organization and networking of problems with regard to various teaching objectives. However, most of this planning work remains implicit; the structure and rationale of the teaching trajectories are often inaccessible for an external observer (including, for example, student teachers). An ongoing project based on teacher-researcher collaboration aims to reveal the hidden characteristics and principles of teachers' work with series of problems through the creation of innovative resources for teachers. In this paper, we present the design of this collaborative work, a process we designate "reverse engineering", and analyse the development process of resources, focusing particularly on the emergence of new vocabulary and representation tools serving as mediators in the communication between teachers and researchers.