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In the context of a community of practice (CoP), eleven secondary mathematics teachers collaborated in exploring various resources that aim to support teaching statistics that fosters learners in developing statistical thinking and reasoning (DSTR). The tracking of a certain material resource, namely the dynamic software tools for statistics instruction (STSI), revealed three phases in the process of the resource’s integration in the community’s shared repertoire. A qualitative analysis illuminates the characteristics and particularities of each phase in terms of the negotiation of meaning with respect to the practice of the community. We also consider and discuss aspects that seem to frame the transition among the various phases of this process and implications for the re-sourcing process of the DSTR practice.

This study investigates teachers’ argumentation aiming to convince students about the invalidity of their mathematical claims in the context of calculus. 18 secondary school mathematics teachers were given three hypothetical scenarios of a student's proof that included an invalid algebraic claim. The teachers were asked to identify possible mistakes and explain how they would refute the student's invalid claims. Two of them were also interviewed. The data were analysed in terms of the content and structure of argumentation and the types of counterexamples the teachers generated. The findings show that teachers used two main approaches to refute students’ invalid claims, the use of theory and the use of counterexamples. The role of these approaches in the argumentation process was analysed by Toulmin's model and three types of reasoning emerged that indicate the structure of argumentation in the case of refutation. Concerning the counterexamples, the study shows that few teachers use them in their argumentation and in general they underestimate their value as a proof method.

In this paper, we present the design and implementation of a microworld as a possible learning environment for the concept of conservation of area and its measurement. This microworld is the result of the synthesis of three models. The first is the model of the subject matter. The second is a model of children's sensory-motor actions while they face specific measurement tasks. The third is a model of learning viewed as an active, subjective and constructive process. All these models are enriched by the features of the electronic media which have an impact on the children's cognitive development. The modelling is the result of the study of past research in the above areas but also reflects the designers' beliefs about the nature of mathematics, its teaching and learning, and about the ways that computers can be used in the teaching and learning of mathematics. The requirements for the design of the software emerged from the educational requirements defined as a result of the modelling. The aim of this microworld is to provide the students with a set of tools to create their own objects (shapes) and transform or compare them using measurement or conservation concepts. The rationale of the design of this computer environment and an analysis of its main features are presented. Finally, the design of the pilot study of evaluation of the microworld is presented and the results of this study are discussed.

This study focuses on 12 years old children's approaches to area measurement in a project environment. These approaches are not explored through a specific set of mathematical tasks. The tasks, here, are defined through researchers' and children's interactions in a classroom. The children by working in small groups are asked to make a proposal about the location and the form of an area which would be given to them for their leisure activities. This environment defines different contexts where the children act and consider different aspects of the area measurement. These aspects are identified and compared among the three groups of children. The study has shown that the concept of area measurement carries different cultural dimensions for the children. Moreover, the children use those elements of the concept which fit in with their personal experience and the tasks they have to face.