id: 06639326
dt: j
an: 2016f.00792
au: Richard, Philippe R.; Oller Marcén, Antonio Miguel; Meavilla Seguí,
Vicente
ti: The concept of proof in the light of mathematical work.
so: ZDM, Math. Educ. 48, No. 6, 843-859 (2016).
py: 2016
pu: Springer, Berlin/Heidelberg
la: EN
cc: E50 D20 C70
ut: didactics of mathematics; epistemic necessity; interactions; mathematical
working space; model reader and model user; proving in geometry;
tolerance analysis; valence of mathematical work; validation mode
ci:
li: doi:10.1007/s11858-016-0805-9
ab: Summary: Our article aims to show how illuminating mathematical work as a
concept from didactics of mathematics is useful in understanding issues
relating to proving and learning of proof, with or without technology.
After posing our hypotheses on the relationship of proof with
mathematical work, the pedagogical intent of historical elements of
geometry and the use of modern technical tools, we present reference
contexts and situations around the property of the tangent. These
contexts and situations allow for a comparison of the validation modes,
the type of epistemic necessity at stake and certain underlying
discourse peculiarities. We introduce the idea of a “valence of
mathematical work” and we interpret in an a priori approach the main
interactions that could maintain a model user-reader in a mathematical
working space. We pay special attention to an extract of {\it Elémens
de Géométrie} by Alexis Claude Clairaut, with one of the reference
contexts revisiting his problem with the assistance of dynamic geometry
software.
rv: