Working with artefacts: gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid (original) (raw)
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Educational Studies in Mathematics, 2009
This paper reports a part of a study on the construction of mathematical meanings in terms of development of semiotic systems (gestures, speech in oral and written form, drawings) in a Vygotskian framework, where artefacts are used as tools of semiotic mediation. It describes a teaching experiment on perspective drawing at primary school (fourth to fifth grade classes), starting from a concrete experience with a Dürer’s glass to the interpretation of a new artefact. We analyse the long term process of appropriation of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech and drawings under the teacher’s guidance.
International Group for the Psychology of …, 2005
This paper presents some elements of our study on the construction of mathematical meanings in terms of development of semiotic systems (gestures, speech in oral and written form, drawings) in a Vygotskian framework with reference to cultural artefacts (Wartofsky). It concerns with a teaching experiment on perspective drawing at primary school (4th-5th grade classes). We analyse the appropriation of an element of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech and drawings, starting from a concrete experience with a Dürer’s glass to the interpretation of a new artefact as a concrete model of that mathematical object.
Meaning Construction Through Semiotic Means: The Case of the Visual Pyramid
2005
This paper presents some elements of our study on the construction of mathematical meanings in terms of development of semiotic systems (gestures, speech in oral and written form, drawings) in a Vygotskian framework with reference to cultural artefacts (Wartofsky). It concerns with a teaching experiment on perspective drawing at primary school (4th-5th grade classes). We analyse the appropriation of an element of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech and drawings, starting from a concrete experience with a Dürer's glass to the interpretation of a new artefact as a concrete model of that mathematical object.
International Group for the Psychology of M athematics …, 2005
We shall summarize some findings of two studies (Bartolini et al., 1999; Bartolini et al. in press) concerning primary school. In the former we have studied the genesis of a germ theory of the functioning of gears. In the latter we have studied the construction of the meaning of painting as the intersection between the picture plane and the visual pyramid. The studies have been carried out in a Vygotskian framework that has been gradually enriched with contributions of other authors. As a result, classroom activity has been designed and orchestrated by the teacher in order to foster the parallel development of different semiotic means (language, gestures, drawing), which form a dynamic system (Stetsenko, 1995).
Drawings, Gestures and Discourses: A Case Study with Kindergarten Students Discovering Lego Bricks
2018
This chapter presents a study aimed at investigating the didactic potentiality of the use of an artefact, useful to construct mathematical meanings concerning the coordination of different points of view, in the observation of a real object/toy. In our view, the process of meaning construction can be fostered by the use of adequate artefacts, but it requires a teaching/learning model that explicitly takes care of the evolution of meanings, from those personal, emerging through the activities, to the mathematical ones, aims of the teaching intervention. The main hypothesis of this study is that the alternation between different semiotic systems, graphical system, verbal system and system of gestures can determine the evolution of the learning objectives that are the coordination of different points of view. The Theory of Semiotic Mediation offers the theoretical framework suitable to design the teaching sequence and to analyse the collected data. The study involved 15 Kindergarten st...
Artifacts and signs after a Vygotskian perspective: the role of the teacher
ZDM, 2009
The notion of mediation, widely used in the current mathematics education literature, has been elaborated into a pedagogical model describing the contribution of integrating tools to the human activity, and to teaching and learning mathematics in particular. Following the seminal idea of Vygotsky, and elaborating on it, we postulate that an artifact can be exploited by the teacher as a tool of semiotic mediation to develop genuine mathematical signs, that are detached from the use of the artifact, but that nevertheless maintain with it a deep semiotic link. The teaching organization proposed in this paper is modeled by what we have called the didactical cycle. Starting from assuming the centrality of semiotic activities, collective mathematical discussion plays a crucial role: during a mathematical discussion the intentional action of the teacher is focused on guiding the process of semiotic mediation leading to the expected evolution of signs. The focus of the paper is on the role of the teacher in the teachinglearning process centered on the use of artifacts and in particular a dynamic geometry environment. Some examples will be discussed, drawn from a long-term teaching experiment, carried out over the past years as part of a National project. The analysis is accomplished through a Vygotskian perspective, and it mainly focuses on the process of semiotic mediation centered on the use of artifacts and on the role of the teacher in this process.
The role of gestures in the mathematical practices of those who do not see with their eyes
Educational Studies in Mathematics, 2011
In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the appropriation of practices associated with the sets of artefacts that have historically come to represent the body of knowledge we call mathematics. This process of appropriation involves a coordination of a variety of the semiotic resources—spoken and written languages, mathematical representation systems, drawings, gestures and the like—through which mathematical objects and relationships might be experienced and expressed. To highlight the connections between perceptual activities and cultural concepts in the meanings associated with this process, we concentrate on learners who do not have access to the visual field. More specifically, we present three examples of gesture use in the practices of blind mathematics students—all involving the exploration of geometrical objects and relationships. On the basis of our analysis of these examples, we argue that gestures are illustrative of imagined reenactions of previously experienced activities and that they emerge in instructional situations as embodied abstractions, serving a central role in the sense-making practices associated with the appropriation of mathematical meanings.
Gestures as semiotic resources in the mathematics classroom
Educational Studies in Mathematics, 2009
In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching–learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.
The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning
Educational Studies in Mathematics, 2013
This study identifies forms of interactions with diagrams that are involved in conjecturing; more specifically, how students display their thinking publicly through using multimodal representations. We describe how students interact with diagrams in both gestural and verbal forms, and examine how such multimodal interactions with diagrams reveal their reasoning about diagrams. We hypothesize that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making conjectures. As a byproduct, the study also proposes a set of graphical representations of gestures that have been identified as important for geometrical reasoning. These can be employed to codify the gestural interactions and to depict the practices of teaching and learning in geometry classrooms.