The paper describes a study of the contexts of six teams, expert in research and development of digital media for learning mathematics, who cross-experimented in classrooms with the use of each other’s artefacts. Contextual issues regarding the designed tasks and technologies, the socio-systemic milieu and the ways in which the researchers worked with the teachers were in focus. We analysed the ways in which a set of mutually constructed and negotiated questions aiming to illuminate otherwise tacit contextual issues operated as boundary objects amongst the teams. We discuss the need to develop special tools such as these boundary objects in order to elicit issues of context and the ways they may affect the production of theory.

Enlarging-shrinking geometrical figures by 13 year-olds is studied during the implementation of proportional geometric tasks in the classroom. Students worked in groups of two using ‘Turtleworlds’, a piece of geometrical construction software which combines symbolic notation, through a programming language, with dynamic manipulation of geometrical objects by dragging on sliders representing variable values. In this paper we study the students’ normalising activity, as they use this kind of dynamic manipulation to modify ‘buggy’ geometrical figures while developing meanings for ratio and proportion. We describe students’ normative actions in terms of four distinct Dynamic Manipulation Schemes (Reconnaissance, Correlation, Testing, Verification). We discuss the potential of dragging for mathematical insight in this particular computational environment, as well as the purposeful nature of the task which sets up possibilities for students to appreciate the utility of proportional relationships.

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially designed microworld which combines graphical and symbolic notation of fractions represented as points on the number line. We used the students’ interactions with the available representations as a window into their conceptual understanding and struggles in making sense of fraction asnumber-measure. We report on the features of the available representations from an epistemological point of view, on the design of activities aiming at creating meaningful problem contexts for fractions as well as on the meanings generated by the students by some illustrative examples of their work indicating the potential of the activities and tools for expressing and reflecting on the mathematical nature of fraction as number-measure.