“Precision”, “Approximation”, and Experimental Mathematics at School in the Age of Digital Educational Technology

This paper explores the interrelations between “precision”, “approximation”, and experimental mathematics supported by digital educational technology in the classroom. It examines the epistemic and pedagogical challenges and opportunities these links create in school mathematics and what is required of teachers to address them. Instances of “approximation” mathematics, emerging from experiments performed with digital tools, are analyzed and evaluated from the standpoint of “precise,” deductive mathematics. The study presents examples where “approximate” computations—or inferences based upon them—are incorrect from the standpoint of “precision” mathematics. It also shows how to correct or further investigate such discrepancies and how school mathematical practices would profit from such approaches. In addition, it discusses instances where experimental mathematics reveals issues typically outside the school curriculum but still conceptually accessible, yielding unexpected or unfamiliar results. The paper also considers recurrent sequences and their hands-on exploration in the context of the interrelation between the three realms of mathematics. The analysis of the examples through the prism of three realms of mathematics linked by digital technologies outlines the ensuing epistemic shift in the mathematics classroom. The teachers’ expectations in view of this shift are analyzed and presented.