Meaning Construction Through Semiotic Means: The Case of the Visual Pyramid (original) (raw)
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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.
Educational Studies in Mathematics, 2008
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.
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 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).
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.
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...
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.
Signs, gestures, meanings: Algebraic thinking from a cultural semiotic perspective
In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello, F. (Eds.), Proceedings of the Sixth Conference of European Research in Mathematics Education (CERME 6) (pp. XXXIII – LIII). Université Claude Bernard, Lyon, France., 2010
In this presentation I will deal with the ontogenesis of algebraic thinking. Drawing on a cultural semiotic perspective, informed by current anthropological and embodied theories of knowing and learning, in the first part of my talk I will comment on the shortcomings of traditional mental approaches to cognition. In tune with contemporary research in neuroscience, cultural psychology, and semiotics, I will contend that we are better off conceiving of thinking as a sensuous and sign-mediated activity embodied in the corporeality of actions, gestures, and artifacts. In the second part of my talk, I will argue that algebraic thinking can be characterized in accordance with the semiotic means to which the students resort in order to express and deal with algebraic generality. I will draw upon results obtained in the course of a 10-year longitudinal classroom research project to offer examples of students’ forms of algebraic thinking. Two of the most elementary forms of algebraic thinking identified in our research are characterized by their contextual and embodied nature; they rely extensively upon rhythm and perceptual and deictic (linguistic and gestural) mechanisms of meaning production. Furthermore, keeping in line with the situated nature of the students’ mathematical experience, signs here usually designate their objects in an indexical manner. These elementary forms of algebraic thinking differ from the traditional one—based on the standard alphanumeric symbolism—in that the latter relies on sign distinctions of a morphological kind. Here signs cease to designate objects in the usual indexical sense to give rise to symbolic processes of recognition and manipulation governed by sign shape. The aforementioned conception of thinking in general and the ensuing distinction of forms of algebraic thinking shed some light on the kind of abstraction that is entailed by the use of standard algebraic symbolism. They intimate some of the conceptual shifts that the students have to make in order to gain fluency in a cultural sophisticated form of mathematical thinking. Voice, gesture, and rhythm fade away. Embodied and contextual ways of signifying are then replaced with a perceptual activity where differences and similarities are a matter of morphology, and where meaning becomes relational.