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 392
- Downloads 25
Identification of, and academic provision for high-ability science students: What does the literature say?
Over the last two decades, education inAustralia and New Zealand has focussed on improving student underachievement in schools. There is concern that this focus is having a negative impact on meeting the needs of high-ab...
Extreme Apprenticeship – Engaging undergraduate students on a mathematics course
This paper describes how an educational method called Extreme Apprenticeship has been used in teaching mathematics to undergraduates. The aim has been to facilitate the transition from secondary to tertiary education and...
A time profile of mathematics in a ‘gap year’ in Irish secondary schools
The Irish education system is unique in an international context as it sets aside a full school year for a transition and youth development programme in the middle of secondary education. The Transition Year (TY) program...
Students' views on mathematics in single-sex and coed classrooms in Ghana
In this study, we investigated students’ views on themselves as learners of mathematics as a function of school?by?sex (N = 2034, MAge = 18.49, SDAge = 1.25; 12th?grade; 58.2% girls). Using latent variable Structural Equ...
Perceived teacher factors in relation to students’ achievementrelated outcomes in science classrooms in elementary school
The purpose of the current study was to investigate the roles that perceived teacher affective support (PTAS), perceived teacher mastery goal orientation (PTMGO), academic emotions, self?efficacy and behavioural engageme...