Get in (Multi)touch with the Tangent

Calculus marked an epochal change in the evolution of scientific thought. However, this subject poses several difficulties, and researchers in mathematics education highlighted obstacles and proposed different approaches in this field of mathematics. We think that a fruitful perspective can be rooted in the history of mathematics and scientific instruments. Indeed, we retrace the first approach, due to Leibniz, to the “inverse tangent problems” (nowadays lost, after the 19th-century arithmetization of calculus). One of the authors recently invented and patented an educational artifact called T-integraph, starting from these historical ideas. To overcome its material limitations, we propose an interactive and multitouch app for the tangent, one of the mathematical contents “touched” using the T-integraph. After a brief description of the software system, we sketch a hands-on workshop activity involving pre-service Mathematics teachers.