The present research approached a problem which has a twofold aspect: the concept of angle and the techniques needed to represent how pupils construct that concept in their cognitive structure during their years in school. In order to access the knowledge of the concept of angle, we used the pathfinder associative networks. This technique provided us with the data of the 458 networks of the participating students, using 11 concepts related to the general concept of angle. We used quantitative indicators on the network characteristics: coherence, complexity, and similarity with others. Results showed how the pupil's cognitive structure evolutioned during instruction and what were the most relevant concepts for them. On the basis of the results, we have proposed what we call the "Theory of Nuclear Concepts" which offers a new focus to understanding how the processes of teaching and learning occur.