Abstracts - Earli

C 929 August 2007 08:30 - 10:30Room: -1.62SymposiumNetworking a variety of theories within a scientific domain - the caseof mathematics educationChair: Tommy Dreyfus, Tel Aviv University, IsraelOrganiser: Ferdinando Arzarello, Universita di Torino, ItalyOrganiser: Angelika Bikner-Ahsbahs, Universität Bremen, GermanyOrganiser: Stefan Halverscheid, Universität Bremen, GermanyOrganiser: Ivy Kidron, Jerusalem College of Technology, IsraelDiscussant: Baruch Schwarz, Hebrew University of Jerusalem, IsraelWe analyze a number of deep and connected issues of theory formation, which have becomerelevant for the mathematics education research community recently, and which we believe to beequally relevant for other educational research communities. The crucial importance of theory forresearch has become apparent to our research community in the 1970s and 1980s, mainly inEurope. The awareness of the need for theory has led to institutional requirements for theoreticalframeworks and hence to a plethora of theories with a large variety of purpose, breadth, tradition,elaboration, and mesh size. Some were used locally in the geographic sense, for example inFrance, others locally in the sense of the research focus, for example teacher beliefs. On the otherhand, the phenomena to be explained by our research are not local. As a research community, weaim to understand, in an integrated manner, the complex processes of learning and teachingmathematics: Motivation, cognition, communication, tool-use, and beliefs, within varying social,physical and historical contexts. Having many disconnected theories is detrimental to a scientificdiscipline since it hinders communication across borders between research teams, countries andcultures. Combining, networking or integrating several theories has considerable potential foradapting our theoretical understanding to the complexity of the practice of learning and teachingmathematics. However, the process of combining theories presents substantial difficulties, fromdifferent traditions using the same words from different issues to the identification of hiddenunderlying assumptions. In the symposium, we will discuss various aspects of the potential anddifficulties of combining theories. These are issues of concern to the mathematics educationresearch community. We propose to discuss them at EARLI because we believe that similar issuesare relevant to other research communities in education. We aim to identify these, and hope tolearn from their experienceEpistemic actions in modelling processes: Potentials and perspectivesStefan Halverscheid, Bremen University, GermanyThe nested epistemic actions model of abstraction in context and the modelling framework areconsidered simultaneously to analyse students’ work in a modelling situation with different toolsbut the same mathematical setting. The mathematical situation is given by the task to understandrectangular and circular billiard games. For this, two different tools are given to the students:Either they have the opportunity to carry out experiments on billiard tables or they are providedwith dynamic geometry software to simulate those. The empirical data of student groups workingin these contexts is used to relate theories on the modelling framework with the nested epistemic– 141 –