Principle of Induction in Initial Teacher Training

The Principle of Induction is a method that allows generalizations in the theory of natural numbers, and from it, it is possible to discuss the notion of infinity in Mathematics in Basic Education. Given the importance of this method, we developed this research with the aim of identifying specialized knowledge about the Principle of Induction presented by Mathematics undergraduate students. In light of theorizations on the Specialized Knowledge of Mathematics Teachers, the data were produced through a qualitative study that adopted group interviews and document analysis as methodological procedures. The results indicate that the undergraduate students demonstrate specialized knowledge about the Principle of Induction by being able to distinguish it from empirical induction. Regarding the Principle of Induction in Basic Education, the group argued in favor of the use of manipulative materials and empirical induction, emphasizing the importance of considering students' individual needs in the transition from Arithmetic to Algebra.