Plenary Lectures
The Speakers and the Topics of the Lectures
For this school we have excellent speakers who will give lectures on a level which will allow the participants to start with their own research, to get new ideas concerning their ongoing research, and to classify their own research in frame of the present research landscape in mathematics education.
Regina Bruder TU Darmstadt, Germany 

Longterm construction of modelling competence Intelligent knowledge about the mathematical modelling (as a reflecting knowledge) and action competence with regard to the relevant part actions of modelling can be built up horizontally (within one school year) and vertically (about the school years away, e.g., with the socalled competence trainings). For methodical realisations in the lessons suitable learner's models are required. The activity theory offers such a model. On this basis ways are indicated how to come to the competence development models for mathematical modelling which can illustrate a longterm competence construction at individual level. As a conclusion from these considerations central elements of a teaching concept are discussed for sustainable acquisition of modelling competence. Moreover results from the project LEMAMOP as well as technologysupported learning offers from the teacher training are reflected. Both show the rich potential of digital tools for mathematical competence construction. 

Gilbert Greefrath WWU Muenster, Germany 

Mathematical Modelling in Germany: Approaches and Developments This introduction to the German discussion of mathematical modelling presents definitions, pedagogical aims, typical modelling cycles and key examples of the German debate on mathematical modelling and gives an overview of central pragmatic and specific approaches. In addition this presentation addresses current development in research, educational standards, modelling competencies, comparative studies and final exams and discusses the role of technology in mathematical modelling. 

Stefan Krauss University of Regensburg, Germany 

Aspects of modeling in the COACTIVStudy In the COACTIV research program mathematics teachers of German PISAstudents were examined and tested in 2003/2004. In the talk several aspects concerning "modeling competencies" that were implemented in the framework of COACTIV will be introduced and respective results will be reported. By doing so, the PISAstudents' attitudes to and competencies in mathematical modelling will be addressed in the same way as corresponding teacher scales (e.g., on the role that modeling plays in their teaching or whether they consider modeling crucial for the discipline of mathematics at all). Both for student and teacher scales psychometric properties and descriptives, but also school type differences will be reported and correlations between student and the corresponding teacher scales will be analyzed. The talk will be based on an bookchapter by Bruckmaier, Krauss & Blum (that currently is in press). 

John Monaghan University of Agder, Norway and University of Leeds, Great Britain 

Artefacts in the real world and artefacts in mathematics education research My talk has two themes. The first is linked to a research project ‘Linking school mathematics to outofschool activities’. Teacherresearchers in this project chose activities that they considered relevant to their students. Artefacts (and digital artefacts in particular) abounded in these activities. The second theme is the use of digital technologies in data collection and analysis. In this part I shall report on the work of two PhD students (one of whom researched student modelling) who collected data that could not have been collected if they had not used digital technology (and, in one case, the technology allowed two distinct methodological approaches to be ‘networked’). 

Jana Trgalová University of Lyon, France 

Dynamic geometry and its manifold usages: implications of modelling Dynamic geometry (DG) software is perhaps the most widely used digital technology. Yet, its usages are often teachercentered and limited to illustrating geometric properties. Drawing on research highlighting various functions of dragging, I will present manifold usages allowed by DG affordances, question their pedagogical added value and discuss their possible exploitation for mathematics modelling. 

Pauline Vos University of Agder, Norway 

Mathematics as a tool (to solve reallife problems) and mathematics learning with tools In this presentation, I will discuss quantitative and qualitative research on concepttool dualities. For example, mathematical concepts (logarithms, integrals, etc) are not just pure ‘ideas’ but also tools that assist people to solve reallife problems (aka mathematical modelling). We can also look at digital tools, and ask how the learning of mathematics becomes more conceptual, more engaging … or more mechanistic and procedural? 