Authoritarian versus authoritative teaching
Polya and Lakatos
pp. 71-83
in: Gila Hanna, Hans N. Jahnke, Helmut Pulte (eds), Explanation and proof in mathematics, Berlin, Springer, 2010Abstract
Lakatos argued that a proof, when presented in the usual "Euclidian" style, may leave the choice of theorem, definitions and proof-idea mysterious. To remove these mysteries, he recommended a "heuristic" style of presentation. This distinction was already present in the work of Polya. Moreover, Polya was directly concerned with teaching and consequently paid attention to the emotional and existential experience of the student. However, Polya lacked Lakatos's account of proof analysis and was not a fallibilist. Therefore, the question of whether Lakatos advanced pedagogy from where Polya left it reduces to two questions: (1) does proof analysis have a place in the classroom? and (2) does fallibilism have a place in the classroom? In this paper, I argue that the answers are (1) Yes and (2) No.