Speaking of Geometry A study of geometry textbooks and literature on geometry instruction for elementary and lower secondary levels in Sweden, 1905-1962, with a special focus on professional debates

Abstract: This dissertation deals with geometry instruction in Sweden in the period 1905-1962. The purpose is to investigate textbooks and other literature used by teachers in elementary schools (ES) and lower secondary schools (LSS) – Folkskolan and Realskolan – connection to geometry instruction. Special attention is given to debates about why a course should be taught and how the content should be communicated.In the period 1905-1962, the Swedish school system changed greatly. Moreover, in this period mathematics instruction was reformed in several countries and geometry was a major issue; especially, classical geometry based on the axiomatic method. However, we do not really know how mathematics instruction changed in Sweden. Moreover, in the very few works where the history of mathematics instruction in Sweden is mentioned, the time before 1950 is often described in terms of “traditional”, “static” and “isolation”.In this dissertation, I show that geometry instruction in Sweden did change in the period 1905-1962: geometry instruction in LSS was debated; the axiomatic method and spatial intuition were major issues. Textbooks for LSS not following Euclid were produced also, but the axiomatic method was kept. By 1930, these alternative textbooks were the most popular.Also the textbooks in ES changed. In the debate about geometry instruction in ES, visualizability was a central concept.Nonetheless, some features did not change. Throughout the period, the rationale for keeping axiomatic geometry in LSS was to provide training in reasoning. An important aspect of the debate on geometry instruction in LSS is that the axiomatic method was the dominating issue; other issues, e.g. heuristics, were not discussed. I argue that a discussion on heuristics would have been relevant considering the final exams in the LSS; in order to succeed, it was more important to be a skilled problem solver than a master of proof.