Teaching for the objectification of the Pythagorean Theorem

This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first level of objectification’ (through numbers) of the Pythagorean Theorem, showing also evidence of appropriate ‘fore-conceptions’ of the ‘second level of objectification’ (through proof) of the theorem. The triangle the sides of which are associated with the Basic Triple (3,4,5) served as a primary instrument for the students’ objectification, mainly, by facilitating their ‘generic abstraction’ of the Pythagorean Triples