A Dilemma That Underlies an Existence Proof in Geometry

Autor/inn/en	Samper, Carmen; Perry, Patricia; Camargo, Leonor; Sáenz-Ludlow, Adalira; Molina, Óscar
Titel	A Dilemma That Underlies an Existence Proof in Geometry
Quelle	In: Educational Studies in Mathematics, 93 (2016) 1, S.35-50 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-016-9683-x
Schlagwörter	Theories; Geometric Concepts; Validity; Concept Formation; Semiotics; Teacher Role; Teaching Methods; Mathematical Logic + Suchen Sie Ihr Suchwort? Theory; Theorie; Elementare Geometrie; Gültigkeit; Concept learning; Begriffsbildung; Semiotik; Lehrerrolle; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematical logics; Mathematische Logik
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01