Teachers’ involvement in designing MERLO items: boundary crossing

Meaning Equivalence Reusable Learning Objects (MERLO) items are a new kind of didactical tool that can be designed by teachers and used in classes, in activities aimed at engaging students in deep reasoning, exploring, arguing on mathematical concepts. The interactions across communities of mathematics teachers and educators in online professional development are studied with attention to the phenomenon of boundary crossing of MERLO item, which is considered as a boundary object in this paper. The study is directed to the analysis of a first (international) crossing of the object MERLO that passes institutional boundaries (Australian and Italian school system), and of a second crossing of the same object - inside the Australian institution - that passes boundaries (from static to dynamic representations) that we interpret in terms of method both for teachers and researchers. This passage is possible thanks to the use of a dynamic geometry software (GeoGebra) that supports a modification in the design of the item. The analysis shows boundary crossing as a process of transformation that can influence a modification (more or less stable) in the practices of the teachers and provides a deep research insight according to existing theoretical frameworks.