Abstract
This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero + 1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory of Semiotic Mediation. The paper focuses on the analysis of the semiotic potential of the pascaline and students’ instrumental genesis, on the functions of schemes and gestures of usage.
Highlights
Mankind has historically constructed and used tools to accomplish tasks (Norman, 1993; Vygotsky, 1934/1990)
The aim of this study is to deepen the understanding of the relationships between these two different theoretical frameworks, through the analysis of teaching experiments focused on the use of manipulatives, like the pascaline
In some institutional documents concerning mathematics curriculum in Italian schools, mathematics laboratory is considered as a didactical methodol-‐‐ ogy, based on various and structured activities, that aims at constructing mathematical meanings
Summary
The Theory of Semiotic Mediation (TSM) has been elaborated and applied to mathematics education by Bartolini Bussi & Mariotti (2008) within a Vygostkian perspective. If a link is established between use and meanings, the choice of which artefact is to be used represents the starting point of the whole didactic process of semiotic mediation It is made by the teacher according to the educational aims (related to the second component of the mediation) and the analysis of the semiotic potential of the artefact. The semiotic potential is defined as the double semiotic link established between the artefact and personal meanings, emerging in students’ mind from its use to accomplish a task (that has to be accessible for students), and, the artefact and mathematical meanings evoked by its use and recognisable as mathemat-‐‐ ics by an expert on the other hand In this kind of analysis, Bartolini Bussi and Mariotti exploit the notion of utilisation schemes (Mariotti, 2012). Different teaching experiments, carried out at different school levels, are discussed
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