A didactic unit on mathematics and science education: the principle of mathematical induction

Among the mathematical methods which are taught in the last years of almost every high school, the mathematical induction deserves particular attention. It can be used both to define mathematical entities and to prove theorems. The second use is more common at high school level and is easier. Thus, I will basically focus on it, though analysing in depth two definitions by induction. The aim of this contribution is to offer the basic elements for a didact unit which could be developed in six/seven hours of lesson. In this editorial a didactic unit has been proposed. Here only the basic elements have been given. The unit might be enriched by tracing the history of the inductive principle, which is interesting and formative from an educational standpoint (see, e.g., Palladino-Bussotti 2002). From an epistemological-methodological perspective, it should be pointed out that mathematical induction is a method of proof, but not a method of discovery. It is not a heuristic procedure. The presentation of an organised set of lessons on the principle of mathematical induction is significant and appropriate in the last years of high school because: 1) it introduces the learners within a method typical of whole numbers; 2) it connects mathematical issues with logical ones; 3) it is useful in order to clarify the difference between the way of reasoning connoting mathematic and that typical of empirical sciences. Hence, it is also useful in a science education context; 4) it can be related to the history of mathematics, so as to show that mathematics is also a humanistic discipline, born from conceptual problems, and not only a technical one; 5) it has also connection with epistemological themes linked to the heuristic of mathematics.