Bernd Blasius, Institute of Chemistry and Biology of the Marine Environment, University of Oldenburg

Even though I am familiar with computer-aided presentation technology as a modeller, I have deliberately decided to use the traditional medium of the blackboard in my lectures on modelling. I am not aware of any other medium that enables a comparable dynamic presentation of complex issues, provided there is enough board space, coloured chalk and sponge and the board is used in a carefully planned manner.

• Dynamics: The blackboard enables a dynamic structure of the material, in which complex relationships are successively constructed by the lecturer.

• Erroneous paths: the sponge makes it possible to go astray or to try out suggestions from students "on the spot" and thus increases the interaction between lecturer and students.

• Area: In mathematical modelling, longer logical relationships often have to be represented. This is favoured by the large board area available. The lecture theatres at the ICBM normally have two wide blackboards. I divide each board into three to four adjacent blocks, resulting in a "total viewing area" corresponding to the content of around 6-8 PowerPoint slides that are visible at the same time.

• Structure and board layout: This space becomes valuable if it is used sensibly in the board layout. It is not enough to simply "write down" the "material" from left to right, wipe it off when the board is full and then start again from the beginning. Instead, I endeavour to create a carefully structured blackboard in which content on entire halves of the board is not wiped away for the full duration of the lecture and thus remains visible for comparison.

• Colour: The blackboard becomes much clearer through the use of colour. I use coloured chalk only minimally but carefully, especially in sketches. For example, sketches with several state variables can quickly become confusing and can be separated by the colour.

• Interactive dialogue between lecturer and students: In order to actively involve the students, I repeatedly ask questions in which the students are encouraged to make independent suggestions for the further development of the models, which can normally be tried out directly on the blackboard. This successive development of an algorithm or model requires a medium that makes this possible interactively, and in my experience only works with the blackboard.

• The hand-drawn sketch At a time when students are constantly confronted with "perfect" computer-generated drawings and images, I would like to emphasise the value of the hand-drawn sketch in my lectures. This is particularly important in everyday modelling research, which consists to a large extent of qualitative sketching of dependencies that are typically not specified in practice by precise analytical formulae. The blackboard is ideal for teaching these skills.

• Geometric visualisation means translating abstract relationships into simple geometric shapes and lines (e.g. a flow in phase space). I use these systematically as an essential tool to reveal the principles behind the abstract equations and make them comprehensible. My experience shows that this inclusion of the visual imagination makes a decisive contribution to making the formal level of abstraction of mathematics "transparent".