A dilemma that underlies an existence proof in geometry

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...

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Autores:
Samper, Carmen
Perry, Patricia
Camargo, Leonor
Sáenz-Ludlow, Adalira
Molina, Óscar
Tipo de recurso:
Article of journal
Fecha de publicación:
2016
Institución:
Universidad de los Andes
Repositorio:
Séneca: repositorio Uniandes
Idioma:
eng
OAI Identifier:
oai:repositorio.uniandes.edu.co:1992/32353
Acceso en línea:
http://hdl.handle.net/1992/32353
http://funes.uniandes.edu.co/9439/
Palabra clave:
Geometría (matemáticas superiores)
Procesos de justificación
Educación / Licenciaturas
Rights
openAccess
License
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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dc.title.none.fl_str_mv A dilemma that underlies an existence proof in geometry
title A dilemma that underlies an existence proof in geometry
spellingShingle A dilemma that underlies an existence proof in geometry
Geometría (matemáticas superiores)
Procesos de justificación
Educación / Licenciaturas
title_short A dilemma that underlies an existence proof in geometry
title_full A dilemma that underlies an existence proof in geometry
title_fullStr A dilemma that underlies an existence proof in geometry
title_full_unstemmed A dilemma that underlies an existence proof in geometry
title_sort A dilemma that underlies an existence proof in geometry
dc.creator.fl_str_mv Samper, Carmen
Perry, Patricia
Camargo, Leonor
Sáenz-Ludlow, Adalira
Molina, Óscar
dc.contributor.author.none.fl_str_mv Samper, Carmen
Perry, Patricia
Camargo, Leonor
Sáenz-Ludlow, Adalira
Molina, Óscar
dc.subject.keyword.none.fl_str_mv Geometría (matemáticas superiores)
Procesos de justificación
topic Geometría (matemáticas superiores)
Procesos de justificación
Educación / Licenciaturas
dc.subject.themes.none.fl_str_mv Educación / Licenciaturas
description 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.
publishDate 2016
dc.date.issued.none.fl_str_mv 2016-09
dc.date.accessioned.none.fl_str_mv 2020-06-04T21:33:42Z
dc.date.available.none.fl_str_mv 2020-06-04T21:33:42Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.citation.none.fl_str_mv 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.
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/1992/32353
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dc.identifier.instname.spa.fl_str_mv instname:Universidad de los Andes
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identifier_str_mv 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.
instname:Universidad de los Andes
reponame:Repositorio Institucional Séneca
repourl:https://repositorio.uniandes.edu.co/
url http://hdl.handle.net/1992/32353
http://funes.uniandes.edu.co/9439/
dc.language.iso.none.fl_str_mv eng
language eng
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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. 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