Some Examples of The Phenomenon of Metadidactic Slippage in School Practice

Background: In didactics of mathematics, the problem of metadidactic slippage (glissement metadidactique) evidenced by Guy Brousseau has been shown for decades. But the school didactic practice proposes behavioural models (mathematics teaching-learning) from which it is manifest that the subject is completely unknown. Objectives: This article intends to present and discuss the metadidactic slippage problem and give some negative examples of its influence, in particular, about the naive interpretation of the so-called Pólya heuristic regarding problem solving in mathematics. Design: Theoretical research in didactics of mathematics. Setting and participants: focuses on the school didactic practice of problem solving in mathematics. Data collection and analysis: Negative examples chosen from among those most diffused in the school world are analysed in the light of modern didactics of mathematics to identify metadidactic slippage in them. Results: Thanks to the slippage, the student learns a scheme, or an algorithm, not the desired mathematical topic T, which remains a mystery to the student (and sometimes also to the teacher). Conclusions: Before trying to “improve” the teaching-learning of mathematics with temporary and drastic measures, it is better, at least, to study it modestly.