A quantitative study of French 19th century geometry textbooks

Background: School textbooks constitute a valuable material of investigation in the history of education, which has developed in many disciplines, in connection with their history. In history of mathematics education, some studies are based on a qualitative analysis of a small number of textbooks, whereas others use quantitative arguments in addition. In this framework, my approach is to analyse the use of areas in French geometry textbooks of the 19th century, by articulating qualitative and quantitative methods, from a corpus that I have built. Objectives: In my study paper, I analyse information from statistical data collected on this corpus, and I put these results in perspective with other studies conducted in the history of school publishing and mathematics education. Design: My methodology consists in starting from hypotheses accepted in related studies, confronting them with my quantitative data, and then putting results into a qualitative perspective. Setting and participants: This work was carried out in conjunction with training on quantitative tools in human and social sciences provided by PROGEDO Loire in Nantes. Data collection and analysis: I first built up a database of geometry textbooks using a general source and exploited it statistically. Then, I studied specifically a more restricted corpus, focused on the notion of area, using multivariate analysis tools. Results: My results confirm some of the assumptions assumed in other studies (evolution of school publishing, porosity of primary and secondary education orders), challenge others (opposition between theoretical and practical geometry) and sometimes deepen them with additional information. Conclusion: This work answered questions but raised new ones, notably on links between sustainability, target audience and content on areas of a textbook.