Beyond the Horizon: a Non-Euclidean Riemannian Laboratory in the Lower Middle School

Banfi, Massimo (2015) Beyond the Horizon: a Non-Euclidean Riemannian Laboratory in the Lower Middle School. Master thesis, Scuola universitaria professionale della Svizzera italiana (SUPSI).

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Non Euclidean geometries are by act of birth abstract and axiomatic, though they have been made popular by their 2D models – surfaces of sphere and hyperboloid, by which they are commonly proposed at our school level. We questioned the effectiveness of these approaches for learning non Euclidean geometry in our lower middle school and designed and implemented a laboratory based on an radically different non Euclidean epistemology that we developed out of a focused analysis of the historical epistemological processes that led from Euclid’s geometry to Riemannian manifolds and to general relativity. In conjunction, we critically revised our psycho-educational frame of reference for geometry cognition and learning. In the resulting laboratory, the students started by building outdoor an embodied sensorimotorial model of going straight (straight line) - discerning curvature of the ground (manifold) and “curvature” of the movements. On their “flat land” discovered non Euclidean behaviors of their straight lines, circumferences and triangles – when extended beyond the horizon. Initially students were puzzled by the replacement of static geometry with kinematics and by the paradoxical non Euclidean behaviors of the figures. Faster than expected, many of them, considered “evident” the non Euclidean behaviors and were able to effectively use curvature as a means to explain them. Many students appeared having reorganized their conceptions of straight line, curvature as well as convictions about triangles or circumferences, whereas “the parallels “were epistemologically and didactically more difficult. Relatore: Alberto Piatti. Materia: matematica

Item Type: Thesis (Master)
Subjects: Formazione - Apprendimento
Divisions: Dipartimento formazione e apprendimento > Scuola media (secondario 1)

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