Theoretical-technological questioning of mathematical activity: The case of the multiplication algorithm

This papers briefly presents a dimension of mathematical activity, the technologicaltheoretical questioning of mathematical techniques, which plays an important role in the construction of mathematical knowledge, even if it is relatively absent from school mathematics. This dimension includes the mathematical questions that appear when techniques are taken as an object of study. We use it to evaluate the economy, reliability and validity domain of some mathematical techniques, especially two multiplication algorithms, in order to compare their efficiency and to make its use more flexible. We propose the study of this dimension of mathematical activity both in school mathematics and teachers' training.