Mathematical objects are multiple connected one to each other, but also with nonmathematical objects and thus build up a network with manifold linkages, characterizing the structure of mathematics. During teaching and learning processes some parts of this network are carried over into pupils’ minds, changing their structure. This paper presents part of a study carried out in Germany, investigating the transformation of a network to the topic “sets of two equations in straight form” during teaching and learning processes. Especially there are compared the network, that teachers stated to have taught in middle grade classes, and the networks, their students really learned. Overmore, there are provided findings on students’ abilities in using their network knowledge for problem solving.