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

• Published in: Mathematics education research journal Vol. 31; no. 3; pp. 259 - 277
• Main Authors: Llinares, Salvador, Clemente, Francisco
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2019; Springer; Springer Nature B.V
• Subjects: Education; Elementary School Teachers; Geometry; Logical Thinking; Mathematical Logic; Mathematics Education; Mathematics teachers; Original Article; Preservice Teachers; Reasoning; Teacher education; Validity; Visualization; Discursive and operative apprehension; Proof; Visualisation; Deductive reasoning; Configural reasoning; Geometrical thinking
• ISSN: 1033-2170; 2211-050X
• DOI: 10.1007/s13394-018-0253-7

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.