
06617751
j
2016e.00543
Samper, Carmen
Perry, Patricia
Camargo, Leonor
S\'aenzLudlow, Adalira
Molina, \'Oscar
A dilemma that underlies an existence proof in geometry.
Educ. Stud. Math. 93, No. 1, 3550 (2016).
2016
Springer Netherlands, Dordrecht
EN
E50
G40
existence proofs
students' procedure to prove existence theorems
meaningmaking
teacher semioticmediation
doi:10.1007/s106490169683x
Summary: Proving an existence theorem is less intuitive than proving other theorems. This article presents a semiotic analysis of significant fragments of classroom meaningmaking which took place during the classsession in which the existence of the midpoint of a linesegment was proven. The purpose of the analysis is twofold. First follow the evolution of students' conceptualization when constructing a geometric object that has to satisfy two conditions to guarantee its existence within the Euclidean geometric system. An object must be created satisfying one condition that should lead to the fulfillment of the other. Since the construction is not intuitive it generates a dilemma as to which condition can be validly assigned initially. Usually, the students' spontaneous procedure is to force the conditions on a randomly chosen object. Thus, the second goal is to highlight the need for the teacher's mediation so the students understand the strategy to prove existence theorems. In the analysis, we use a model of conceptualization and interpretation based on the Peircean triadic SIGN.