Characteristics of the shifts from configural reasoning to deductive reasoning in geometry

The study aimed at characterising the shift from configural reasoning to proof construction in geometry. One hundred eighty-two preservice primary teachers solved two geometry problems in which they had to generate a proof from the information provided by a geometrical configuration. Results indicated that proof construction was linked to the way pre-service teachers coordinated the different apprehensions, as identified by Duval (1995), mediated by the existence of strategic knowledge. Strategic knowledge is undertood as the ability to see some specific geometrical statements as premises of a geometrical proposition that can be used to deduce intermediate statements or the conclusion. We argue that pre-service teachers need to be aware of the connections between specific geometrical facts when they construct a proof by linking visualisation to formal reasoning. We conclude with implications for teacher education programmes.The research reported here was financed in part by Spanish Ministry of Economy, Industry and Competitiveness MINECO—Spain, under Grant no. EDU2014-54526-R and EDU2017-87411-R