Lectures sur Embodiment, Cognition, Gestures

Présentation au sujet: "Lectures sur Embodiment, Cognition, Gestures"— Transcription de la présentation:

1 Lectures sur Embodiment, Cognition, Gestures
Mariam Haspekian, Jean-Baptiste Lagrange vendredi 5 février 2010

2 Plan Les travaux « en toile de fond » ESM 2004 ESM 2009
Présentation générale du numéro (Mariam) Présentation de 2 articles (JB, Mariam) ESM 2009 Complément théorique: tour des parties introductives et théoriques des articles (Mariam) Pour aller plus loin que ces numéros (JB) (Présentation détaillée d’un article d’IJCML 2008)

3 Le « background » (en toile de fond…)
Cahier 58 partie C.« De l’apprentissage situé à l’embodiment » Pour résumer: 2 façons différentes de se référer au corps embodiment= ’incorporation’ de concepts Tall: conceptcorps Nunes & al.: embodied cognition et enaction, corpsconcepts

4 Nunes & al (2003, ESM 39) Historique des approches:
classique (~70) cognition située (80/90) cognition incarnée Hypothèses sur la nature et le développement des mathématiques Comment les élèves construisent-ils du sens? Comment l’expérience peut initier de la connaissance? Ici: remettre en valeur le rôle de l’intuition et des expériences physiques dans l’abstraction

5 Tall (2006, Annales Did&Sces Cogn., n°11)
Cohérence et structure des Maths Développement biologique de l’esprit humain Compression d’idées en « concepts » pensables Connexions entre concepts: schémas d’actions et schémas de savoir 2+3: processus ou concept: « procept » Trois mondes mentaux: conceptuel/incorporé (conceptual embodied world) proceptuel-symbolique formel/axiomatique

6 L’ ESM 57.3 (2004) Imagination  perception physique
Objets mathématiquesperception et actions physiques 2 exemples: Rasmussen, C., et al. Arzarello & Robutti

7 «Approaching fonctions through motion experiments» Arzarello & Robutti
Thème Difficultés des élèves dans l’interprétation de graphes de fonctions Contexte Introduction notion de fonction auprès d’élèves de 14/15ans à travers une situation de modélisation (ici un graphe position-temps) Chaque groupe: calculatrice reliée à un capteur de mouvement Objectifs de la recherche Analyser processus cognitifs dans la construction de sens

8 La situation Comment les E, en se référant à l’expérience concrète, donnent du sens au graphe du mouvement enregistré par le capteur à la table de données correspondantes

9 Différents cadres théoriques
Dimension sociale (Vygotsky): construction sociale des connaissances et médiation par les artefacts culturels Approche instrumentale (Rabardel, 95) Embodied Cognition (Lakoff, Nunes, 2000) Analyse sémio-culturelle (Radford, 2003) Analyse des gestes (Mac Neill, Alibali): « Gestures together with langage help constitute thought » (Mac Neill, 92) « Gestures play a role in thinking » (Alibali et al. 2000) Gestes deictic/ iconic/ iconic physical/ iconic symbolic

10 « Intégration » des aspects cognitifs et instrumentaux
Objectivation (Radford, 2003) Genèse du concept de fonction: 2 pts de vue (conditionnés par la médiation de l’artefact utilisé) 3 vidéos: Vidéo 1: montre 3 étapes de cette objectivation Vidéo 2: la discussion collective en classe Vidéo 3: comparaison avec une autre classe

11 Vidéo 1 Début de l’Objectivation de connaissance:
Correspondance ligne horizontale du graphe  absence de mouvement Concept de « vitesse » Correspondance expérience physique et tables de données par le scrolling de la calculatrice

12 Vidéo 1 (suite) Utilisation de l’instrument similaire à l’expérience avec le graphe: « immobilité »  partie de la table de données correspondante extension aux autres parties de la table (mouvements uniformes) Signification plus claire du concept: le scrolling de la calculatrice a rendu visible les 2 variables, ce que n’avait pas permis la seule représentation graphique

13 Etapes dans la conceptualisation
VIDEO 1- EXTRAIT Etapes dans la conceptualisation Surprise face au graphe: le mouvement « devait » être uniforme Un pivot cognitif: la portion de ligne horizontale Tentatives d’interpréter les autres portions mais: difficultés verbales et conceptuelles face à la tâche d’interprétation du graphique (« décéléré » et « mouvement uniforme » sens vagues pour eux) L’expression « vitesse constante » émerge, avec un sens encore un peu flou Exploration des données numériques: « il a fait 4mètres! » Second pivot cognitif: les données constantes de la table Compréhension progressive des colonnes « temps » et « distance »: vision « variation » et « covariation » qui se met en place grâce au « scrolling » de la calculatrice, le concept de vitesse constante est enrichi

14 Analyse des auteurs Interprétation du scrolling en SU (Rabardel):
Exploratoire Vérification de conjecture et communication dans la classe Evolution des processus intellectuels selon la théorie de Vygotsky: L’interprétation du graphe a évolué en opérations médiées par l’usage de signes (comme la table numérique avec la modalité de scrolling) Le scrolling a transformé la calculatrice en outil psychologique (au sens de Vygotsky) par lequel les E ont pu objectiver une connaissance.

15 Vidéo 2 Discussion de classe: analyse du Langage (L) et des Gestes (G): 3 différentes façons de communiquer: L et G réfèrent à la situation concrète (« iconic gesture ») L et G réfèrent à une représentation de la situation concrète (graphe, table) (« iconic-symbolic gesture » L réfère au concrète et G à sa représentation (idem)

16 Vidéo 3: Protocole similaire dans une autre classe
Ex: les G incorporent de façon compressée des informations: qd la vitesse , la main bouge + vite La trajectoire de la main exprime la variation de la fonction (croissance/ décroissance) La vitesse de la main incorpore la vitesse du mouvement double embodiment de l’information, le geste: vu comme outil de médiation pour mieux appréhender la situation. Les concepts abstraits se forment à partir d’interprétations concrètes qui ont évolué et ont été compressées.

17 Chap 3: On Forms of Knowing: The Role of Bodily Activity and Tools in Mathematical Learning
Chris Rasmussen, Purdue University Calumet Ricardo Nemirovsky, TERC,Jennifer Olszewski, Kevin Dost, and James L. Johnson, Purdue University We analyze three undergraduate students' evolving ways of knowing ideas associated with system dynamics in a series of open-ended interviews as they work with a tool we call the “water wheel.” We characterize how bodily activity and emerging tool fluency combine in mathematical learning and how this combination suggests an alternative view on the nature of knowing. In particular we develop the idea of knowing-with, which characterizes aspects of meaning making as it relates to developing expertise with tools.

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19 For example, consider the system of differential equations, dR/dt = 0
For example, consider the system of differential equations, dR/dt = 0.2R – RF, dF/dt = -F + 0.8RF, intended to model the population of rabbits and foxes. Students in modern approaches to differential equations are often required to interpret the meaning of the individual terms in the equations (e.g., why does it make sense that the RF term in the first equation is subtracted, whereas it is added in the second equation?). We planned to invite students in this study to engage in similar interpretive analyses of the system of three differential equations that model the motion of the water wheel. Click here to open LWHEEL

20 Episode 2: Becoming Friends with Acceleration
We present Episode 2 in two parts, approximately three and six minutes long, respectively. In part (a), which occurred during the first interview, Monica synchronizes the rotation of the water wheel with a given graph of angular velocity versus time. In this excerpt Monica personifies the wheel and imaginatively experiences when the wheel will achieve its maximum and minimum velocity. In the process, she accounts for why these maximum and minimum velocities occur. In part (b), which occurred during the second interview, Monica predicts the angular acceleration versus time graph for the same angular velocity versus time graph discussed in part (a).

21 Monica: Faster, uh, wait a minute, fast, fast, fast, fast, fast, fast, fast, fast. Peak, the fastest [points at the bottom of the wheel]. Right, right before that point. Critical point. Slowing down, slowing down, slowing down, slowing down, slowest [points at the top of the wheel]. Critical point. Speeding up, speeding up, speeding up, speeding up, speeding up, speeding uuuuup. Critical point. Starts slowing down. Slowing down. Slowing down, slowing down, slowing down. Critical point. Monica: Meaning, instead of calling it a critical point, we can even say, speeding up, speeding up, speeding up, speeding up, speeding up, speeding up. “Man, I’m no longer [pointing at bottom of the wheel] being pushed down. Now you want me to go back up. I don’t want to go up. So, I’m unhappy. But, I’m going to go up anyway because you’re pushing me.” From that initial speed. Chris: Wait, now you’re unhappy. I thought before you said you were happy down here [points to the bottom of the wheel]. Monica: No. I was happy down there. But, both of these are called critical points [points to the top and bottom of the wheel]. Chris: Oh, oh. I, Monica: Instead, instead of just using the word “critical,” because critical can sometimes seem to be technical, we can, we can use terms like, um, “place of satisfaction,” “place of not satisfied.” Monica: Um, I’m unhappy because I’m not in a place of satisfaction. Actually, I think this here is the only place of satisfaction [gestures on the left side of the wheel]. And this here is also, this here is not [gestures on the right side of the wheel]. Because...

22 Chris: What makes, what makes, what makes the wheel happy or satisfied
Chris: What makes, what makes, what makes the wheel happy or satisfied?[Monica laughs]. What’s the quality that makes, [both laugh]do you know what I’m asking? Monica: Yeah, um. Being able to go with the flow of, of motion and not going against. Being able to go with stuff and not have to go against stuff. So, being able to, to go with life and not have to go against it. [Laughter.]So, here [points to the left side of the wheel] gravity says go down [gestures in a downward pulling fashion]. And to be able to go with gravity makes us happy. Chris: So, on this side [points to the left side of the wheel] over here, I’m happy. Monica: We're going in this circle [draws a counter clockwise circle on top of the wheel]. Chris: Yeah, this direction. Monica: Yeah. This side here [points to the left side of the wheel], all of up in here, you real happy. Chris: And where am I happiest? Monica: Where you’re happiest, soon as you get, the moment before you hit the very bottom [points to the bottom of the wheel]. Chris: That helps me. OK. Monica: That mo[ment], that instant moment, right before you hit the bottom, you are just like, ah, loving it. [Chris laughs.]Because gravity, because you’re going with, with gravity [gestures on the left side of the wheel]. But, as soon as we have to fight against something [gestures on the right side of the wheel], we're not happy. And, it’s that time in between that’s critical. And it’s that time in the, in between [points to the bottom of the wheel] where we reach our peak points in our graph. Maximums and minimums. This is fun!

23 We trace how Monica, as she said, “became friends with acceleration” and highlight the centrality of bodily activity and emerging tool fluency in this process. We emphasize the role of bodily and emotionally dwelling in the tool, and illustrate knowing where and why acceleration is zero with the water wheel. Discussion. As illustrated in part (a), Monica uses her body to simulate the wheel, to make it move and talk for the purpose of telling the story of the wheel’s motion. She continues to tell the story of the wheel’s velocity in part (b) and by becoming the wheel (recall the shift from “it” to “I”) she begins to know acceleration with the wheel. Monica was initially “afraid” of acceleration and gradually becomes friends with acceleration. Being friends with acceleration does not mean that she knows all there is to know about acceleration. In fact, we would argue that Monica’s friendship with acceleration, her knowing acceleration with the wheel, is deeply rooted in where and when acceleration is zero. We think the analogy with friendship is an apt one because just as in the case of personal friends, one rarely or never knows everything about a person. Similarly, we have no evidence that Monica’s friendship with acceleration includes a deep understanding of where (and why) acceleration is maximum, for example.

24 Throughout this paper we have characterized how bodily activity and emerging tool fluency combine in mathematical learning and how this combination suggests a form of knowing we referred to as knowing-with; In particular, we summarize how knowing-with (1) engages multiple and different combinations of dwelling in the tool, (2) invokes the emergence of insights and feelings that are unlikely to be fully experienced in other ways, (3) is in the moment.

25 Some readers will wonder how it is possible that students, who are taking a differential equations course after passing calculus and physics courses, still seem to need revising what might be perceived as elementary ideas of acceleration or angular velocity. We think that this perception would be an artifact of unquestioned assumptions on what counts as advanced or elementary mathematics and how mathematics learning progresses. There is a widespread tendency to assume that, once a concept has been formally articulated and students have at one time proven fluent with the corresponding notation, the learning of this concept has been accomplished and a degree of readiness has been achieved for more advanced ones.

26 We conclude with a comment about the significance of this research for mathematics teaching and learning more broadly. In an era of mathematics education that is increasingly attuned to the use of tools (concrete manipulatives, physical devices, computer software, etc.), the analysis in this paper highlights the role and centrality of bodily activity and emerging tool fluency. As teachers and instructional designers seek to integrate a variety of tools in their students’ learning environments, the construct of knowing-with may prove to be a useful idea for guiding and informing such efforts by helping to focus one’s attention on what are the mathematical ideas with which students are expected to engage and on what will students be using as part of their subsidiary awareness as they engage in these ideas.

27 1. L’ ESM 70. 2 (2009): Présentation générale du n° 2
1. L’ ESM 70.2 (2009): Présentation générale du n° 2. Complément théorique 3. Présentation détaillée d’un article en lien Contre le dualisme séparant corps et pensée Explorer les différentes façons dont l’embodiment intervient en maths Construction de modèles théoriques, notamment la MULTIMODALITE: Ressources cognitives Mais aussi perceptives ET physiques (corporelles) Inclut: communication symbolique orale et écrite, dessins, gestes, manipulation d’artefacts mécaniques et informatiques, mouvements corporels (« bodily motions »)

28 L’introduction Husserl (1931), Gelhen (1988), Merleau-Ponty (1945):
La connaissance est bien plus que le résultat de mécanismes déductifs formels et abstraits Nature multimodale de la cognition (tactile, sensorielle, perceptuelle, kinesthésique…) Analyse des gestes physiques: reconnus comme éléments clés dans la communication et la conceptualisation en maths.

29 L’étude des gestes en général
Exemple: Mac Neill (1992): propose une classification des gestes: Deixis Metaphoricity Iconicity Temporal highlighting Et gestes pour moduler l’interaction sociale « Hand and mind: what gestures reveal about thought » A ces cadres généraux, les didacticiens des maths ajoutent leurs propres outils théoriques:

30 L’étude des gestes dans les 6 articles
Arzarello & al.: semiotic bundle et semiotic game Radford: objectification process, rapprochement sensoriel et culturel Edwards: conceptual integration (discours et gestes) Maschietto&Bussi: médiation sémiotique Nemirovsky&Ferrara: utterances Roth et Thom: incarnation, contextualisation des mathématiques

31 1. Arzarello & al. Le paradigme de multi modalité vient de plusieurs champs Les neurosciences montrent que le système sensori-moteur du cerveau est multimodal Le langage exploite ce caractère multimodal Notion de  «Semiotic bundle » (=speech+ gestures+ inscriptions…) qui élargit les « registres sémiotiques » de Duval structure dynamique qui évolue dans le temps=> 2 façons de l’analyser: Analyse synchronique Analyse diachronique  Découverte de « semiotic game » chez l’enseignant

32 2. Radford Débats et controverses sur le rôle du geste:
Simples facilitateur du langage? Ou fenêtre sur nos pensées (G et L issus d’une même source cognitive)? Ou encore intrinsèquement consituants de la pensée? Liens avec nos conceptions de «l’acte de penser»: ‘mental’? ou ‘mental +…’ ? Prise en compte du langage et du social

33 3. Edwards La question des « gestes spontanés » lors de discours concerne la recherche en didactique Gestes: sources d’information sur notre façon de penser ET contributeurs à la pensée et à la communication mathématique elles-mêmes: Conservation de volume (Alibali & al, etc.) Apprentissage du comptage (Alibali, Graham,…) Résolution d’équation (Glodwin-Meyer, …) Mouvement et tracé de graphes (Némirovski, Radford, Robutti…) Undergradutes mathematics (Nunes) Résolution de problèmes (Reynolds et Reeve) Pensée humaine incarnée dans : les gestes, l’image, les mouvements, l’expérience quotidienne et des capacités biologiques spécifiques.

34 Exemple: dans l’article Arzarello
Gestes et Langage forment un « package » complémentaire utilisable pour préciser sa pensée ou résoudre des problèmes L’apprenant est souvent capable d’exprimer sa compréhension d’un nouveau concept à travers le geste avant d’être capable de l’exprimer dans le discours.

35 4. Maschietto & Bartolini-Bussi 5. Némirovski-Ferrra:
Rejettent l’opposition perceptive-moteur/ mental Prennent en compte , en plus des travaux précédents, l’imagination. 6. Roth et Thom Notre conception des Maths repose sur une épistémologie constructiviste (Kant et Piaget) où le sujet « abstrait » ses connaissances indépendantes de l’expérience sensorielle Au contraire: Van Hiele (86) développe un modèle de l’apprentissage dépendant des stades d’évolution, des langages correspondants, etc. Nature incarnée et incorporée des mathématiques

36 Botzer, Yerushalmy IJCML (2008) 13:111–
Embodied Semiotic Activities and Their Role in the Construction of Mathematical meanings of Motion Graphs Botzer, Yerushalmy IJCML (2008) 13:111– This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of interaction: 2D freehand motion and 2D synthesized motion, designed by the composition of single variable function graphs. Our theoretical framework combines two perspectives: the embodied approach to the nature of mathematical thinking and the Vygotskian notion of semiotic mediation. The article describes in detail the actions, gestures, graph drawings, and verbal discourse of one pair of high school students and analyzes the social semiotic processes they experienced. Our analysis shows how the computerized artifacts and the students’ gestures served as means of semiotic mediation. Specifically, they supported the interpretation and the production of motion graphs; they mediated the transition between an individual’s meaning of mathematical signs and culturally accepted mathematical meaning; and they enable linking bodily actions with formal signs

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39 Embodied cognition Nevertheless, a claim about the embodied nature of mathematical thinking must take into account the relationship between the body as a locus for the constitution of an individual’s subjective mathematical meanings and the historically constituted cultural system of meanings conveyed by mathematical signs and existing before the particular individual’s actions (Radford et al. 2005). Radford et al. present the example of an interpretation of a Cartesian graph: ‘‘the Cartesian graph is a complex mathematical sign whose objective cultural meaning was elaborated in the course of centuries. The alignment of subjective and cultural meanings involved a profound active re-interpretation by the students, framed by the teacher and the particular context of the classroom’’

40 Mediation sémoitique Learning mathematics with technological artifacts enables the integration of embodied concrete action with semiotic activities. Technological artifacts can enable perceptual-motor ways of learning because they are grounded in actions, perceptions, and reactions to the feedback received from using the artifacts (Bartolini Bussi et al. 2004). Computer technology has proved to be a powerful tool for physical interaction. Interaction is the phenomenological experience that according to Mariotti (2002) includes user actions and feedback from the environment. Studying their own movements, students confront subtle relations between their kinesthetic sense of motion and graphic notations (Stylianou et al. 2005). Microworlds enable students to formulate conjectures, test them, and elaborate their conception about motion by using computerized artifacts. Kaput and Roschelle (1997) argue for ‘‘the important role of physical motion in understanding mathematical representations…[whereby] students confront subtle relations among their kinesthetic sense of motion, interpretations of other objects’ motions, and graphical, tabular, and even algebraic notations’’.

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43 In addition to the use of the technological artifacts, the students used gestures as an important means of semiotic mediation. Gestures played integral role in the communication between the students and enabled them to share the information embedded in the graphs. Gestures mediated the production of socially constructed meaning for the motion graphs, as for example when they used gestures to represent the slope of the graph and identified zero slope with zero velocity. Gestures also accompanied the elaboration of the meaning of graphic signs, as for example when the students represented physical features of the motion by gestures and related them to mathematical features of the graphs.

44 Gestures serve to organize spatial information (e. g
Gestures serve to organize spatial information (e.g., the direction of motion), and thus support conceptualization. Gestures also provided access to meaning that lay beyond the given representations, lending support to Goldin-Meadow’s (2003) claim that gestures convey information through imagery. But whereas Stephens and Clement (2006) refer to gestures as indicators of imagery processes, we suggest that the role of gestures is broader and extends to such student activities as thinking, communicating, and making sense of the graphs. For example, by tracing the graphs with their fingers in the signature exploration activity, the students were able to reconstruct the concrete motion that the graph represented.

45 Discussion Sur le terme « geste » Sur le rôle des instruments
Sur des questions plus « hors sujet » mais néanmoins en toile de fond: Comment conçoit-on l’apprentissage des concepts mathématiques? Comment conçoit-on la pensée humaine? Qu’est-ce qui la rend unique?