In this Research Keynote presentation, I present the general scientific orientations of our research lab, leading to specific ones about my current research programme focused on mental mathematics. In so doing, examples will be given of tasks used and of students' ways of engaging with these. These various examples of tasks and students’ strategies are used throughout the presentation to explain the nature of the findings developed in this research programme, and make concrete underlying conceptualisations about students' strategy processes in mental mathematics environments. Bio: Jérôme Proulx is a professor of mathematics education (didactique des mathématiques : www.profmath.uqam.ca/~jproulx), and runs the Laboratoire Épistémologie et Activité Mathématique (www.leam.uqam.ca). His research focuses on epistemological issues related to cognition and/in mathematics. His current research programme is dedicated to mental mathematics and school mathematics content development.