New Frameworks for Looking at Student Interactions - PowerPoint Presentation

Slide1

New Frameworks for Looking at Student Interactions

Peter Liljedahl

-

Simon

Fraser University (Canada)

Chiara

Andrà

-

University

of Torino (Italy)Slide2

An introduction

Luca Fabio

Davide

MarcoSlide3

the problem

A 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.Slide4

the transcript

HOW DO WE EXPLAIN THIS?Slide5

how do we explain this?

some

very interesting and turbulent undercurrents of group

interactions

individual and social engagement with the mathematics

and

a social interaction around the mathematics

we wanted to codify this

… and to analyze this

… to understand better the

socio-mathematical interactionSlide6

socio-mathematical interaction

we

need to overcome the dualistic approach between the individual’s interior space and his social interaction, and focus more on sociocultural conditions (Roth & Radford, 2011) Slide7

socio-mathematical interaction

Learning

occurs in and through relations with others driven by collectively motivated

activity

activity

is a process with inner contradictions, differentiations, transformations, as well as emotions—necessary for the activity and responsible of its

development

group

interactions are complex socially and affectively charged environments

So, how

do we codify this?Slide8

the transcriptSlide9

analysis 1.0

students

are making sense of the task.

Marco

is dealing with fractions, he is interested in the

procedure

Luca seems

more interested in understanding the overall sense of the activity (“Why don’t 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 Marco’s 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 – intuition

Marco – computation

How

is it that Marco does not see Luca’s contribution

?Slide10

interactive flowcharts

TWO TYPES OF SPEAKER’S 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 UTTERANCE

A 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

SOLID ARROWS ARE ON-TOPIC AND DASHED ARROWS ARE OFF-TOPICSlide11

interactive flowchartSlide12

analysis 2.0

proactive 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?Slide13

Flowchart +

Gazes

where the speaker is looking

where non-speaker is looking

P paper (new

interlocutor

)Slide14

analysis 3.0

Luca

is

NOT

being ignored by

marco

00:25

Davide

is asking a question while

gazing

at the paper. But Marco is not looking at Davide

– he

is looking

at

Luca

00:27 Marco responds to

Davide’s

question while he continues to look at Luca

00:34

Marco responds to

Davide’s

question

while

he

is looking

at

Luca

Luca is

ignoring (avoiding

)

Marco

00:15

luca

looks at

marco

while reacting to him

00:25

luca

looks at

marco

while

Davide

is

asking

a

question

00:36 while

Marco is looking at the

paper

Why

is Marco so intent on

Luca?

why

is Luca ignoring Marco? Slide15

flowchart + intensity gazes

casual glances

intense and longer gazes (stares)Slide16

analysis 3.1

something

interesting happening at

00:25 – 00:45

00:25

Davide

a question; Luca looks at

marco

;

marco stares intently at

luca → luca looks away

00:34

marco

stares

intently at

luca

00:36

luca

glances at

marco

while

marco

is looking at the paper

00:37

marco

stares intently at

luca

00:42

marco

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. Slide17

fictional writing

Fictional 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

student

creating

likely impressions, and connections that do not exist in the original

data

subjective

in

nature – but not

wholly

so

can help shed light on the students’ emotional disposition, attitudes and beliefs about mathematics

good

data

+

extensive analysis

→

inner

monologue

consistent

with the empirical

data Slide18

fictional writing Slide19

analysis 4.0

luca

feeling

a sense of avoidance about fractions

tries to think

on another level—a level that provides him with an overarching view of the

task

Any

time Marco uses fractions, Luca

escapes

avoiding Marco’s gazes

marco

has a

procedural view of

mathematics

is

concerned mostly with computations with

fractions—the

whole sense of the task is to do

computations

computation provides

him with a sense of likely

success—a sense

of self-confidence and

pleasure

pretends

to have understood everything and spread his knowledge to his

classmates

davide

is

aware that he is not a good student in

math

has

a willingness to

understandSlide20

analysis 4.0

Marco vs.

Davide

Davide

gives in to Marco

luca

vs. Marco

Luca is not prone to concede to Marco

differing views of mathematics

students’ gaze to each other but do not listen to each other

impede the interaction between Marco and Luca

Marco trying to catch

luca’s

attention and willing him to agree

luca

trying to avoid

marco

and not willing to bend to him

they cannot really interactSlide21

discussions

different codifications of the data allow us to see different things in the data:

Transcript

observing

the students’ utterances from a cognitive

perspective

inferred

their emotional dispositions

how knowledge

emerges and is shared amongst the group is seen by means of the words the students

say

interactive flowchart (+ gazes)

looked

at the students’

interactions through a behavioral

lens

and from an embodied

mind

paradigm

students

’ gestures, postures and glances are seen as constitutive components of the meaning making

process

the

ideas that emerge from the activity

are

in their gestures and glances––to the point that if we discard these elements as we did at the beginning of the paper we miss many relevant

facts

fictional writing

provides a

lens that helps us go deeper inside the students’ thoughts and

will

in

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

posturesSlide22

conclusions

Knowledge and emotions are distributed throughout the students’ hands, eyes, mind, and body, and

are inseparable from the

development of the

activity

Gazes

give us insights into this inner world and allow us to write a version of the inner monologues of each

participant

Other

monologues can be constructed from the data just like other conclusions can be extracted from different

analyses

Regardless

of what monologues result, however, one thing is clear—the interactions between these four students have a turbulent undercurrent of emotions and

intentions

The

use of interactive flowcharts documenting the verbal interactions and the gazes gives a window into these emotions and

intentions

Consciousness is in the first place not a matter of 'I think that' but of 'I can'.Slide23

thank you

liljedahl@sfu.ca