id: 06617751
dt: j
an: 2016e.00543
au: Samper, Carmen; Perry, Patricia; Camargo, Leonor; Sáenz-Ludlow, Adalira;
Molina, Óscar
ti: A dilemma that underlies an existence proof in geometry.
so: Educ. Stud. Math. 93, No. 1, 35-50 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: E50 G40
ut: existence proofs; students’ procedure to prove existence theorems;
meaning-making; teacher semiotic-mediation
ci:
li: doi:10.1007/s10649-016-9683-x
ab: Summary: Proving an existence theorem is less intuitive than proving other
theorems. This article presents a semiotic analysis of significant
fragments of classroom meaning-making which took place during the
class-session in which the existence of the midpoint of a line-segment
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.
rv: