Variations autour d’une situation de comparaison de quantités pour l’apprentissage des unités de numération

Although research has shown that numeration units are essential for learning whole numbers, students in France still face challenges in understanding units, since learning is often limited to designating the position of digits in the writing of numbers. This article investigates a study conducted among 4th and 5th graders, comprised of a baseline scenario and variations, which examines a quantity comparison problem that aims to strengthen the understanding of numeration units as a system of units organized according to the decimal principle. Using teaching design methodology, we describe the design choices (a priori analysis) and examine in-class implementation as well as discussions with students (a posteriori analysis). The results illustrate a variety of teaching methods, some of the difficulties that students face, and opportunities to further an understanding of numeration units.