
06639326
j
2016f.00792
Richard, Philippe R.
Oller Marc\'en, Antonio Miguel
Meavilla Segu\'{\i}, Vicente
The concept of proof in the light of mathematical work.
ZDM, Math. Educ. 48, No. 6, 843859 (2016).
2016
Springer, Berlin/Heidelberg
EN
E50
D20
C70
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
doi:10.1007/s1185801608059
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 userreader in a mathematical working space. We pay special attention to an extract of {\it El\'emens de G\'eom\'etrie} by Alexis Claude Clairaut, with one of the reference contexts revisiting his problem with the assistance of dynamic geometry software.