A gentle introduction to algorithm complexity for CS1 with nine variations on a theme by Fibonacci

In this paper, we propose our ideas about didactic methods and a few examples appropriate to motivate in students the comprehension of the basic principles related to algorithm complexity. Emphasis is put on avoiding formalisms and presenting gradually every new concepts. This paper as well provides for both: an organisation of these ideas and a collection of, we hope, useful examples and experiences that show these concepts in a natural way.