The relation between mathematical object/mathematical name: Conceptual changes between designation, description, denomination and definition
Journal Title: European Journal of Science and Mathematics Education - Year 2018, Vol 0, Issue 0
Abstract
The actions of designation, description, denotation, denomination and definition are crucial in the didactic activity in the classroom (D'Amore and Fandiño Pinilla, 2012) since they embody different interplays between objects, representations, properties, names (in the sense of Duval (2008)). Switching from one action to the other may be the result of a conceptual change (diSessa, 2006). We present the result of a teaching experiment in classes of grades from 2 to 4 where the relation object/name is investigated in the case of the circle. The experiment makes use of a particular artefact, the Lénárt Spheres (Lénárt, 1996). Comparative geometry activities allow to deal with geometrical objects in a learning environment where the relations between objects, representations and properties are different from the usual ones, hence implying a restructuration of the interplays between them. As a result of the teaching experiment, as can be seen, in particular, from the comparison of initial and conclusive questionnaires, children started a change of their way of associating a name to an object. We argue that this is due also to a conceptual change and not only to “learning what was taught”.
Authors and Affiliations
Giorgio Bolondi| Department of Mathematics, Alma Mater Studiorum University of Bologna, Bologna, Italy, Federica Ferretti| Department of Mathematics, Alma Mater Studiorum University of Bologna, Bologna, Italy, For correspondence: federica.ferretti5@gmail.com, Alessandro Gambini| Department of Mathematics, University of Ferrara. Ferrara, Italy
Keywords
Related Articles
- EP ID EP8169
- DOI -
- Views 348
- Downloads 25
Student misconceptions about plant transport – a Sri Lankan example
Students bring with them their own misconceptions to the science classes and it becomes a barrier in developing new concepts. Therefore, identifying misconceptions is an essential component in teaching science. The obje...
Comparative effects of concept mapping and cooperative learning strategies on senior secondary school students’ achievement in mathematics-trigonometry in Kano State, Nigeria
This article presents the findings from an experimental study on the effectiveness of concept mapping and cooperative learning strategies on SSII students’ achievement in trigonometry in mathematics. The research design...
Conceptualizations of representation forms and knowledge organization of high school teachers in Finland: “magnetostatics”
One of the main components of teachers’ pedagogical content knowledge refers to their use of representation forms. In a similar vein, organizing concepts logically and meaningfully is an essential element of teachers’ s...
A workshop for high school students on naive set theory
In this article we present the prototype of a workshop on naive set theory designed for high school students in or around the seventh year of primary education. Our concept is based on two events which the author organiz...
Why do chemistry students need to take mathematics courses?
Students tend to ask why they should learn mathematics lessons or courses. This study investigates the perceptions of chemistry students and their instructors about the relevance of mathematics courses to their field of...