If you want to educate others, you yourself need to be educated. If you want to have any kind of influence on young people, you yourself need to stay young and continuously work on yourself.


Simon Gfeller, Swiss teacher and author (1868 - 1943)

Teaching Practice > Mathematics
mathematic,dialogic learning
By: Prof. Dr. Peter Gallin, November 2014, published in: SINUS international: Towards New Teaching in Mathematics, Part III, University of Bayreuth, 2011

The Quadratic Equation – this is a topic to be taught in an inquiry based way after all

Some teachers of mathematics claim that the formula for the quadratic equation is incompatible with modern teaching methods and therefore has to be provided and proven by the teacher. The author Prof. Dr. Peter Gallin tries to demonstrate the opposite: It should be possible for learners to investigate the riddle of the quadratic equation in a self-organised way over a period of about four lessons.

First, the students are given a worksheet with a series of tasks on which they work independently. They are asked to note all of the steps and ideas along the way in a so-called “learning journal”. These journals are handed in and the teacher chooses the most notable contributions to be discussed in class. (“Collection of autographs”)

“This is the idea of “dialogic learning”: it arises whenever students' texts are used as the point of departure for further progress in the following lessons.”

The author illustrates his method with an example by a girl from his class who was able to generate a core-idea for the technique of completing the tasks on the worksheet. Based on this idea she developed the general formula to solve any quadratic equation.

The article, which can be downloaded here, will be of interest to all teachers who want to try out new methods on the path of dialogic learning. We are convinced that the method of working with learning journals and collections of autographs can be adapted to other topics in a range of teaching subjects!


Full article


Forum group "Mathematics" see here

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