Lessons in dialogue form
If you want to build a ship,
don't drum up people together to collect wood
and don't assign them tasks and work,
but rather teach them to long
for the endless immensity of the sea.
Antoine de Saint-Exupéry
The concept of maths taught in dialogue form ( "Dialogischer Mathematikunterricht") first developed from the long-term cooperation of the mathematician Peter Gallin and the germanist Urs Ruf. This concept focusses on the priority of language, the idea of “putting into words” or verbalizing thoughts, results of discussions and newly acquired knowledge, but also by verbalizing ideas that have been rejected.
Learning from core ideas
The first core idea is always proposed by the teacher. Formulated intentionally subjective, it is meant to provoke general interest (“I really want to work on this”) and it should also give enough confidence in one’s own abilities (I am convinced I can do this”).
The teachers should present the complete problem right from the beginning, but in a way that the students are not shocked. Instead they should be inspired to work on the problem themselves independently. Give them a core idea concerning the subject.
In their diaries the students do not only write down their own ideas and approaches, but they also make entries in the form of personal comments on the subject and their work.
The following items may help to structure a typical travel diary:
|date||When did I make this entry?|
|subject||What are we working on at the moment?|
|task||What do I personally have to do?|
|aim||Why do we do that?|
|traces||How How can I approach the problem successfully?|
|looking back||What is my momentary position?|
|echo||Who can help me if I am lost?|
Travel or learning diaries are useful instruments to improve the student’s ability to express his ideas and for the exchange of ideas.
On the website of “Arbeitsgruppe dialogischer Mathematikunterricht” you will find a lot of background information and practical examples concerning math lessons in dialogue form (in German language).