Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Ethnomethodologie als handlungstheoretische Grundlage einer Didaktik der Kommunikation

Our focus is the question as to how communication in school and instruction can be organized in an open-ended yet methodical fashion. Accordingly we proceed from the thesis that teaching methodology must be in accordance with the methodology od everyday activities so that school instruction can build on the structure of reflexive communication. We therefore adopt ethnomethodology as a theory of everyday activities in order to establish a repertoire of teaching methodologies. Taking an ethnomethodological perspective we analyze two examples of pupil aggression from the aspect of the reflexivity of accounts and develop suggestions for openended teaching methodologies.