Abstracts - Earli

actions model of abstraction in context. The guiding question is what epistemic actions inmodelling situations actually are. It is also investigated whether epistemic actions differ accordingto whether a modelling approach with experimental tools or a simulation approach with computertools is taken.Potential and problems with networking theories in view of the role of cognition in differenttheoriesTommy Dreyfus, Tel Aviv University, IsraelMathematics education as a research domain deals with the learning and teaching of mathematics.One of the central concerns of mathematics educators is therefore how learners conceivemathematical contents – fundamentally a cognitive issue. This contribution focuses on how threetheories of learning mathematics, the Theory of Didactic Situations, the Three Worlds ofMathematics, and the Nested Epistemic Actions Model of Abstraction in Context deal with thiscognitive issue. We found that they have different cognitive priorities, they describe different partsof the process of coming to know, they are relevant at different time scales, and they have differentgrain sizes of analysis. Given these differences, we analyze whether and how they can complementand enrich each other. The theoretical work involved in connecting or networking them is highlynon-trivial, because it entails a detailed examination of the constructs used in each theory, and theexistence and relevance of related constructs in the other theories. Moreover, hidden assumptionsunderlying the different theoretical frameworks may imply possible contradictions. The work ofestablishing links between theories is important for the progress of mathematics education. We askwhether it is equally important in other educational research areas.Potential and problems with networking theories in view of the role of context in different theoriesIvy Kidron, Jerusalem College of Technology, IsraelWe investigate the role of context in mathematics leaning processes. The complexity of learningprocesses might be related to the different contextual influences on the learner’s construction ofknowledge. Among the contextual influences, we include the epistemological nature of the givenmathematical domain, the learner’s previous knowledge, the social interactions and/or the"instruments" which are used in the learning process. Some parts of the context are given inadvance, for example, the nature of the mathematical content domain. Other parts of the contexthave a "dynamic" nature in the sense that the learner interacts with the context. This might be thecase for social interactions or the interaction of a solitary learner with a computer. In all thesecases, context has a crucial influence on the learning process. Each theoretical framework has itsown way to consider the role of context on the learning process. In this presentation, we analyzethe insights offered by three different theoretical approaches, the process-object approach, theinstrumental approach and the nested epistemic actions model of abstraction in context on thecontextual influences of the learner’s construction of knowledge. Moreover, we analyze how thenetworking between the three approaches permits a deeper analysis of the role of context and as aconsequence a deeper understanding of the learning processes.Potential and problems with networking theories in view of the role of verbal and nonverbalcommunication in different theoriesFerdinando Arzarello, Universita di Torino, ItalyConsidering the phenomenology of learning processes in mathematics classes, a variety ofsemiotic resources are observable, namely those used by students and teachers in their actions and– 142 –