From Pestalozzi’s intuition principle to classrooms: the counting frame and innovations in the teaching of mathematics (Spain, nineteenth century)

Abstract: The mechanisms of dissemination of the counting frames in the teaching of mathematics in Spain during the nineteenth century are studied. José Mariano Vallejo and Pablo Montesino proposed them in order to facilitate an arithmetic initiation based on intuition, following Pestalozzi’s proposals. The diffusion channels considered were pedagogical texts, professional journals, and school material catalogues. Moreover, these proposals are compared with the existence of references to the counting frames in primary school textbooks in the nineteenth century.