Digital artifacts in Mathematics Education: How can we study the learning processes they promote?

This contribution is an elaboration of what was presented by the first author at her invited conference "Digital Artifacts in Mathematics Education" held in September 2023 at the XXII Congress of the Italian Mathematical Union. The aim of the paper is to present to those who are less familiar with qualitative research in Mathematics Education fundamental aspects to consider when studying mathematics learning mediated by digital artifacts. Three examples are presented that show glimpses of mathematical learning mediated by digital artifacts; we discuss how such student learning processes can be captured through adaptations of the Theory of Semiotic Mediation. In the discussion of the three examples, we also highlight the fundamental role played by task design and by the educator in promoting the students’ mathematics learning.