A dilemma that underlies an existence proof in geometry
A dilemma that underlies an existence proof in geometry
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几何存在性证明背后的困境
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Oscar Molina
中科院分区：
文献类型：
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作者：
C. Samper;Patricia Perry;Leonor Camargo;A. Sáenz;Oscar Molina
证明一个存在定理不如证明其他定理直观。本文提出了一个符号学分析的显着片段的课堂意义的制造过程中发生的课堂会话中，线段的中点的存在被证明。分析的目的是双重的。首先，了解学生在建构一个几何对象时，概念化的发展，这个几何对象必须满足两个条件，以确保它在欧几里德几何系统中的存在。一个对象必须被创造出来，满足一个条件，并导致另一个条件的实现。由于这种构造不是直观的，它产生了一个两难的境地，即最初可以有效地分配哪个条件。通常，学生的自发过程是将条件强加于随机选择的对象。因此，第二个目标是强调教师的调解，使学生理解的策略，以证明存在定理的需要。在分析中，我们使用的概念化和解释模型的基础上皮尔斯三元符号。
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.