# students’ gazes: new insights into students’ interactions

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STUDENTS GAZES: New Insights into Students Interactions. Peter Liljedahl - Simon Fraser University (Canada) Chiara Andr - University of Torino (Italy). P. the setting. Setting: series of four lessons on probability: grade 9 (14-15 year olds) - PowerPoint PPT Presentation

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STUDENTS GAZES: NEW INSIGHTS INTO STUDENT INTERACTIONS

STUDENTS GAZES: New Insights into StudentsInteractionsPeter Liljedahl - Simon Fraser University (Canada) Chiara Andr - University of Torino (Italy)

Pthe settingSetting:series of four lessons on probability:grade 9 (14-15 year olds) low socio-economic neighborhood in Bologna, ItalyData gathered:Probability task in the second lessonFour students (Luca, Fabio, Davide, and Marco) videotaped by a grade 12 student session lasted 50 minutes first 5 minutes were transcribed data selected for analysis:first 45 seconds were selectedThis subset of the data was selected because it exemplified individual intuitions within social interaction but that is not what we did with it!Cthe problemA robot walks along a corridor, it turns right with probability 1/3 and it turns left with probability 2/3. The map shows the labyrinth where the robot has to move. Compute the probability for the robot to be in each of the rooms.

Cwhat we did with it!some very interesting and turbulent undercurrents of group interactionsindividual and social engagement with the mathematics and a social interaction around the mathematics

we wanted to codify thisand to analyze thisto understand better the undercurrents of socio-mathematical interaction

Psocio-mathematical interactiondialogue as scaffolded metacognition (Sfard, 2001)but group interactions are complex socially and affectively charged environments we need to overcome the dualistic approach between the individuals interior space and his social interaction, and focus more on sociocultural conditions (Roth & Radford, 2011) Learning occurs in and through relations with others driven by collectively motivated activityactivity is a process with inner contradictions, differentiations, transformations, as well as emotionsnecessary for the activity and responsible of its developmentCsocio-mathematical interactionwe explore the role of emotions, motivation, as well as knowledge and learning visible, and invisible, within the group interaction

Pthe transcript

P

analysis 1.0students are making sense of the task. Marco is dealing with fractions, he is interested in the procedureLuca seems more interested in understanding the overall sense of the activity (Why dont we first compute how many probabilities are there in all? 00.36)Davide is still grasping the sense of the task (What do we have to compute? 00:28), and he is struggling to follow Marcos reasoning (Why? 00:37)Both Luca (00:11) and Marco (00:42) come to notice that the highest probability is related to the first room: Luca intuitionMarco computation

How is it that Marco does not see Lucas contribution?Cinteractive flowcharts

TWO TYPES OF SPEAKERS META-DISCURSIVE INTENTIONS: THE WISH TO REACT TO A PREVIOUS CONTRIBUTION OF A PARTNER OR THE WISH TO EVOKE A RESPONSE IN ANOTHER INTERLOCUTOR SFARD AND KIERAN, 2001

A VERTICALLY OR DIAGONALLY UPWARD ARROW IS CALLED A REACTIVE ARROW AND POINTS TOWARDS A PREVIOUS UTTERANCEA VERTICALLY OR DIAGONALLY DOWNWARD ARROW IS CALLED A PROACTIVE ARROW AND IT POINTS TOWARDS THE PERSON OR PEOPLE (RYVE, 2006) FROM WHOM A REACTION IS EXPECTED

Pinteractive flowchart

Panalysis 2.0proactive statements:Marco (n=7) Luca (n=3) Davide (n=0)reactive statements:Marco (n=5)Davide (n=5) Luca (n=1 not counting the self-talk as a reaction)statements made that are reacted to:Marco (n=6)Davide (n=3)Luca (n=1, not counting the self-talk)

Luca and his solution are being ignored! or is he?CFlowchart + Gazes

where the speaker is looking where non-speaker is looking P paper (new interlocutor)Panalysis 3.0Luca is NOT being ignored by marco00:25 Davide is asking a question while gazing at the paper. But Marco is not looking at Davide he islooking at Luca00:27Marco responds to Davides question while he continues to look at Luca00:34Marco responds to Davides question while he is looking at Luca

Luca is ignoring (avoiding) Marco00:15luca looks at marco while reacting to him00:25 luca looks at marco while Davide is asking a question00:36while Marco is looking at the paper

Why is Marco so intent on Luca?why is Luca ignoring Marco? Cflowchart + intensity gazes

casual glances intense and longer gazes (stares)Panalysis 3.1something interesting happening at 00:25 00:4500:25Davide a question; Luca looks at marco; marco stares intently at luca luca looks away00:34marco stares intently at luca 00:36luca glances at marco while marco is looking at the paper00:37marco stares intently at luca00:42marco stares intently at luca

there is an affective aspect to the interaction between Luca and Marco. There are emotions, efficacy, will, and motivation in how Luca and Marco are interacting with each other.

but, what are the emotions, efficacy, will, and motivation?Cfictional writingFictional writing is a technique that can help the researcher to go beyond the external and visible into the students inner subjective experience - Hannula, 2003

envisioning the inner monologue of the studentcreating likely impressions, and connections that do not exist in the original datasubjective in nature but not wholly socan help shed light on the students emotional disposition, attitudes and beliefs about mathematics

good data + extensive analysis inner monologue consistent with the empirical data

Pfictional writing

Panalysis 4.0lucafeeling a sense of avoidance about fractions tries to think on another levela level that provides him with an overarching view of the taskAny time Marco uses fractions, Luca escapesavoiding Marcos gazes

marcohas a procedural view of mathematicsis concerned mostly with computations with fractionsthe whole sense of the task is to do computationscomputation provides him with a sense of likely successa sense of self-confidence and pleasurepretends to have understood everything and spread his knowledge to his classmates

davideis aware that he is not a good student in mathhas a willingness to understand

C18analysis 4.0Marco vs. DavideDavide gives in to Marco

luca vs. MarcoLuca is not prone to concede to Marcodiffering views of mathematicsstudents gaze to each other but do not listen to each otherimpede the interaction between Marco and LucaMarco trying to catch lucas attention and willing him to agreeluca trying to avoid marco and not willing to bend to himthey cannot really interact

Cdiscussionsthis presentation has a rather methodological soul: we are exploring a set of methodologies to be able to see what is invisible at a first glance

Transcriptobserving the students utterances from a cognitive perspectiveinferred their emotional dispositions how knowledge emerges and is shared amongst the group is seen by means of the words the students sayinteractive flowchart (+ gazes)looked at the students interactions through a behavioral lens and from an embodied mind paradigmstudents gestures, postures and glances are seen as constitutive components of the meaning making processthe ideas that emerge from the activity are in their gestures and glancesto the point that if we discard these elements as we did at the beginning of the paper we miss many relevant factsfictional writingprovides a lens that helps us go deeper inside the students thoughts and willin order to open a window on the students inner world it is necessary to repeatedly, patiently, and carefully look at their interactions, their words, and their postures

PconclusionsKnowledge and emotions are distributed throughout the students hands, eyes, mind, and body, and are inseparable from the development of the activityGazes give us insights into this inner world and allow us to write a version of the inner monologues of each participantOther monologues can be constructed from the data just like other conclusions can be extracted from different analysesRegardless of what monologues result, however, one thing is clearthe interactions between these four students have a turbulent undercurrent of emotions and intentionsThe use of interactive flowcharts documenting the verbal interactions and the gazes gives a window into these emotions and intentionsConsciousness is in the first place not a matterof 'I thinkthat' but of 'I can'.

CconclusionsConsciousness is being-towards-the-thing through the intermediary of the body. To movethe body is to allow oneself to respond to the call.- Merlau-Ponty 2002

thank youliljedahl@sfu.cachiara.andra@gmail.com

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