Graphical representation and generalization in sequences problems

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it

Generalized composition law from 2x2 matrices

Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded values. We show how this generalization directly provides phase factors such as the Wigner angle in special relativity and how this generalization is connected in the simplest case with the composition of 2x2 S matrices.Comment: Accepted for publication in Am. J. Phy