The Emergence of the Idea of the Mathematics Laboratory in the Early Twentieth Century

The idea of offering students spaces where they could carry out activities spontaneously and constructively, develop their own individuality, and socialise, frequently appears in the studies of pedagogists, psychologists and educators at the turn of the twentieth century. Examples of this are found in the works of the American John Dewey, whose vision on education is related to the pragmatism of Charles S. Peirce and William James; the German Georg Kerschensteiner, an advocate of the Arbeitsschule, or ‘work-school’; the Belgian Ovide Decroly; the Swiss Edouard Claparède and Adolphe Ferrière; the French Alfred Binet, one of the principal promoters of the ‘active school’; and the Italian physician and pedagogist Maria Montessori, among others. All these scholars were especially interested in the formation of children during the first years of their lives, and mathematics is not always mentioned in their reflections, but the idea of a school-laboratory spread also among mathematicians, who extended it to secondary schools. In my paper, after briefly mentioning the points of view of some of the pedagogists who were active at the turn of the twentieth century and either had an interest in mathematics or were in contact with scientific circles (Dewey, Kerschensteiner, Wells), I will discuss the contributions of the mathematicians John Perry, Eliakim Hastings Moore, Émile Borel and, Felix Klein, and then focus on Giovanni Vailati’s ‘school as laboratory’. By comparing the various models of mathematics laboratories proposed, I will try to make clear the most significant differences between them, and their innovative aspects. The paper is supplemented by a transcription of an unpublished letter by David Eugene Smith.