Papers by Kalliopi Siopi
HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017
The study presented in this report is part of a research project concerning the mediation of arti... more The study presented in this report is part of a research project concerning the mediation of artifacts in teaching and learning geometry. In this paper we analyze the first step of our research which concerns the student-pantograph interaction and the identification of the math laws incorporated in the machine. During this interaction we are specifically interested in arguments that students produce for supporting their claims. Tools, especially mathematical machines, may support argumentation processes focusing either on the structure of the machine, or to the embodied math concepts that emerge from the machine's movement. Our research has shown that these arguments hold mainly on the topological conception of geometric figures.
Le Centre pour la Communication Scientifique Directe - HAL - Archive ouverte HAL, Feb 1, 2017
The study presented in this report is part of a research project concerning the mediation of arti... more The study presented in this report is part of a research project concerning the mediation of artifacts in teaching and learning geometry. In this paper we analyze the first step of our research which concerns the student-pantograph interaction and the identification of the math laws incorporated in the machine. During this interaction we are specifically interested in arguments that students produce for supporting their claims. Tools, especially mathematical machines, may support argumentation processes focusing either on the structure of the machine, or to the embodied math concepts that emerge from the machine's movement. Our research has shown that these arguments hold mainly on the topological conception of geometric figures.
New perspectives for Geometry teaching : Mechanical linkages Technology
In this paper we try a brief presentation of mechanical linkages, and especially of the drawing m... more In this paper we try a brief presentation of mechanical linkages, and especially of the drawing machines. Our focus is on the pantograph, that incorporates mathematical properties and relationships in structure in such a way to allow the implementation one geometrical transformation, such as, symmetry, reflection, translation and homothety. In order to investigate subjects’ concepts/ theorems-in-action developed by investigating the structure of the pantograph, and especially the identification of the math concepts and laws incorporated in the machine, we selected a pantograph’s model and taught homothety to high school students for four hours (early 2016), in the framework of an attempt to incorporate artifacts with the characteristics geometrical machine’s in the instruction of Euclidean geometry.
In this paper we analyze the student-pantograph interaction and the identification of the math l... more In this paper we analyze the student-pantograph interaction and the identification of the math laws incorporated in the machine. During this interaction we are specifically interested in arguments that students produce for supporting their claims. Tools, especially mathematical machines, may support argumentation processes focusing either on the structure of the machine, or to the embodied math concepts that emerge from the machine’s movement.
In this paper we try a brief presentation of mechanical linkages, and especially of the drawing m... more In this paper we try a brief presentation of mechanical linkages, and especially of the drawing machines. Our focus is on the pantograph, that incorporates mathematical properties and relationships in structure in such a way to allow the implementation one geometrical transformation, such as, symmetry, reflection, translation and homothety. In order to investigate subjects’ concepts/ theorems-in-action developed by investigating the structure of the pantograph, and especially the identification of the math concepts and laws incorporated in the machine, we selected a pantograph’s model and taught homothety to high school students for four hours (early 2016), in the framework of an attempt to incorporate artifacts with the characteristics geometrical machine’s in the instruction of Euclidean geometry.
Paper (based on practice)
Conference Presentations by Kalliopi Siopi
This report is part of a research project concerning the mediation of artifacts in teaching and l... more This report is part of a research project concerning the mediation of artifacts in teaching and learning geometry. We analyze the first step of our research which concerns the student-pantograph interaction and the identification of the math laws incorporated in the machine. During this interaction we are specifically interested in arguments that students produce for supporting their claims. Tools, especially mathematical machines, may support argumentation processes focusing either on the structure of the machine, or to the embodied math concepts that emerge from the machine’s movement. Our research has shown that these arguments hold mainly on the topological conception of geometric figures.
The presentation examines the integration of an artifact in teaching Euclidean geometry at upper ... more The presentation examines the integration of an artifact in teaching Euclidean geometry at upper secondary school in Greece.
The physical and functional characteristics of the artifact allow students to reach geometric conclusions by induction and to device ways to prove their initial reasoning based on the mathematics the artifact incorporates. Because of non precise traces that the artifact produces students were obliged to “escape” from the pure observational records to a math way of reasoning.
Uploads
Papers by Kalliopi Siopi
Conference Presentations by Kalliopi Siopi
The physical and functional characteristics of the artifact allow students to reach geometric conclusions by induction and to device ways to prove their initial reasoning based on the mathematics the artifact incorporates. Because of non precise traces that the artifact produces students were obliged to “escape” from the pure observational records to a math way of reasoning.
The physical and functional characteristics of the artifact allow students to reach geometric conclusions by induction and to device ways to prove their initial reasoning based on the mathematics the artifact incorporates. Because of non precise traces that the artifact produces students were obliged to “escape” from the pure observational records to a math way of reasoning.