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A dilemma that underlies an existence proof in geometry

Samper, Carmen; Perry, Patricia; Camargo, Leonor; Sáenz-Ludlow, Adalira; Molina, Óscar (2016). A dilemma that underlies an existence proof in geometry. Educational Studies in Mathematics, 93(1), pp. 35-50 .

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Resumen

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 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.

Tipo de Registro:Artículo
Términos clave:14. Matemáticas superiores > Geometría (matemáticas superiores)
06. Aprendizaje > Procesos cognitivos > Procesos de justificación
Nivel Educativo:Formación Profesional
Código ID:9439
Depositado Por:Patricia Inés Perry
Depositado En:06 Nov 2017 09:07
Fecha de Modificación Más Reciente:06 Nov 2017 09:07
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Personal del repositorio solamente: página de control del documento


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