Making the network concept visible
Here is a problem as it is found in many textbooks.
Draw a circle as big as possible into an equilateral triangle. How much of the area of the triangle (percentage) is covered by that of the circle?
Different ways of solution are not mentioned here. Try yourself to find a solution with the help of the following diagram.
The following instruction can add to a reflexion about different ways of solving the problem:
What mathematical terms and content items have been used in dealing with the problem? Present them clearly in a diagram.
A general brainstorming with the whole class is recommended in order to collect as many different ideas as possible.
The diagram below may give you an idea of the possible network process. To make it as little confusing as possible it does not contain all possible links.
A mouseclick will give you the enlargement of the diagram.
This example is taken from: "Mathematikunterricht für individuelle Lernwege öffnen", V. Ulm, Kallmeyer 2004.