TY - JOUR
TI - Knowing about “equal area” while proving a claim about equal areas
AU - Herbst, Patricio
T2 - Recherches En Didactique Des Mathématiques
AB - What role can proving play in the development of public knowledge in classrooms? This article shows how the activity of proving may not only engage students in making use of a base of public knowledge but also in extending and reorganizing the ideas that constitute such base of public knowledge. The article examines the role that mathematical reasoning played in shaping and making explicit a notion of area equivalence in eight American high school geometry classes as students worked in solving a problem that required making triangles of equal area and proving that their areas were equal. The various tasks involved in such work created conditions for observing four distinct conceptions of equal area, which are described in the article. The diversity of conceptions observed is used to bring to the fore a more general discussion on the role that proving can play in making a concept reasonable. It is also argued that neither final definitions for concepts nor stringent standards of proof are needed to engage students in proving particular claims about particular ideas. On the contrary, the activity of proving can elicit existing conceptions and develop them into more sophisticated conceptions. This can be done in the context of activities that, while relying on the standards of customary proving practices, also promote a negotiation of how those standards should apply on account of what is there to know with them.
DA - 2005///
PY - 2005
VL - 25
IS - 1
SP - 11
EP - 56
J2 - RDM
LA - FR
SN - 0246–9367
UR - https://revue-rdm.com/2005/knowing-about-equal-area-while/
ER -