Secondary prospective teachers grappling with ordered dense or discrete denumerable number sets: a pilot study
Articolo
Data di Pubblicazione:
2023
Citazione:
Secondary prospective teachers grappling with ordered dense or discrete denumerable number sets: a pilot study / L. Branchetti, V. Durand-Guerrier. - In: RECHERCHES EN DIDACTIQUE DES MATHÉMATIQUES. - ISSN 2728-2422. - 43:1(2023), pp. 47-86.
Abstract:
In this paper we present a pilot study with master students, who are also
secondary prospective teachers in mathematics, where some cognitive
conflicts emerged on the issue of ordered number sets being at the same
time dense and denumerable. We first provide a literature review and
historical-epistemological background, then we carry out an institutional
overview related to these notions. Finally, we present qualitative analyses
of data collected in our universities: one case study regarding a student in
Italy, that made our main hypothesis emerge; a questionnaire to 30 French
students. We carried out the analyses under the lenses of concept image
and concept definition, which we use to analyse empirical data, collected
in both countries. The analysis revealed that the concept images of discrete
and dense sets in general are not connected by the students to formal
definitions, and conflict emerged at the level of concept images. Since the
articulation of definitions and images is crucial in the transition school-
university and these concepts are basic in advanced mathematics, we
discuss some implications of such conflicts and open new research
questions to better investigate the problem in future studies.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
L. Branchetti, V. Durand-Guerrier
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