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Article ID: CBB935801822

On the history of units in French elementary school arithmetic: The case of proportionality (2022)

Chambris, Christine (Author)
Visnovska, Jana (Author)

Historia Mathematica
Volume: 59
Pages: 99-118
Publication date: 2022
Language: English

DOI: 10.1016/j.hm.2021.04.003

URI: https://www.sciencedirect.com/science/article/pii/S0315086021000240

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Public schools Philosophy of mathematics Teaching; pedagogy Number theory; number concept Ratio and proportion 20th century 21st century 19th century France

The measurement of magnitudes was at the foundation of numbers and calculation in academic mathematics until the 19th century. It provided units and the concrete and abstract numbers that formed the basis of school arithmetic up to the mid-20th century in France. Our analysis of changes in teaching resources for proportionality (late 19th to the early 21st century) documents how the disappearance of magnitudes in academic knowledge was followed by the loss of the differentiation of the conceptual complexity of mathematical ideas related to proportionality. These changes made teaching and learning about proportionality considerably more difficult, and we later witness their gradual, but not yet systematic, reversal. Résumé La mesure des grandeurs a été aux fondements des nombres et du calcul dans les mathématiques académiques jusqu'au XIXe siècle. Elle a fourni les unités et les nombres concrets et abstraits qui ont constitué la base de l'arithmétique scolaire jusqu'au milieu du XXe siècle en France. Notre analyse de l'évolution des ressources pour l'enseignement de la proportionnalité (de la fin du XIXe siècle au début du XXIe siècle) documente la façon dont la disparition des grandeurs dans les mathématiques académiques a été suivie par une perte de différenciation de la complexité conceptuelle des notions mathématiques liées à la proportionnalité dans les ressources pour l'enseignement. Ces évolutions ont rendu l'enseignement de la proportionnalité considérablement plus difficile, nous assistons par la suite à un retour progressif mais non systématique.

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