Quanto \`e importante risolvere e far risolvere problemi?

TL;DR

This paper discusses the importance of problem-solving in mathematics education, emphasizing how engaging students with problems fosters exploration, heuristics, and deeper understanding of mathematical concepts.

Contribution

It highlights the role of didactic problem-solving situations as drivers of learning and connects mathematical manipulation levels to teaching strategies.

Findings

Problems serve as effective tools for mathematical learning

Engaging students with problems develops heuristics and exploration skills

Didactic situations can simulate real mathematical research

Abstract

Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small part of mathematics through these manipulations. In doing so, the pupils work on both the heuristics enabling them to confront themselves with a real mathematical research and knowledge in construction. Through examples of didactic situations of problem solving, this article aims to show how problems can be drivers of mathematics learning.