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The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4th European Congress on Mathematics Education (CERME4). That is, this paper includes a discussion of trends seen within CERME4 reports1 on theory usage by European researchers in seven of the fourteen working groups and (a) Outlines similarities and differences in theory usage and (b) takes a futuristic stance on ways in which researchers from different traditions could understand each other. Such an enterprise would further Hans-Georg Steiner's vision of bridging theoretical traditions which are independently formulated in different regions of the world.

Theory usage and theoretical trends in Europe: a survey and preliminary analysis of CERME4 research reports