Abstract:

The teaching and learning strategy through the spiral model is aligned with studies that establish that mathematics is best learned little by little and over long periods of time. In this way, students' retention of concepts and skills increases significantly. The same thing happens in Mathematics competitions, learning occurs in stages, reviewing concepts and going deeper as new knowledge is integrated. In this work we talk about spiral learning and present examples of this methodology in mathematics Olympiads.

The American psychologist Jerome Bruner during the sixties observed that very good results could be obtained in highly complex classes such as mathematics, applying a methodology that consisted of presenting the student in the first instance with a series of concepts and skills at a level basic, so much so that they could be learned in a very intuitive and practical way, once these skills were mastered, concepts of greater complexity and difficulty were subsequently introduced progressively, these supported by the knowledge previously acquired, not only in the first stage, but also those that came from other topics of the subject and even from other branches of study and daily life. From this he develops what we know today as the spiral teaching methodology.

In this work we present the fundamental ideas of this methodology, we also show, through concrete examples, how this methodology can be applied particularly in mathematics competitions. We use examples of competitions with more participation, which are used internationally as a tool for popularizing mathematics, such as the mathematics kangaroo, to higher mathematical level Olympiads such as the Ibero-American mathematics Olympiad or the international mathematics Olympiad.

Keywords:

Mathematics competitions, Spiral methodology.