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Model for Analyzing Collaborative Knowledge Construction in a Quasi-Synchronous Chat Environment

Juan Dee WEE & Chee-Kit LOOI

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What might be new?

A graphical representation of chat flow

Example(s) where triangulation (through participants’ reflections) agreed and disagreed with model drawn by researchers

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Data collection in Singapore Junior college students from Singapore

(age 17) Groups of 3 worked together to solve

math problems on VMT-Chat Several chat transcripts in 2006 & 2007 Advantage: we have access to the

students Some new data since this paper’s online

discussion in early June

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Singapore Context:Briefing before VMT Session

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VMT Orientation Session in the Computer

Laboratory

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Opened Ended Mathematics Question placed on the shared whiteboard

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VMT Chat Interface

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Build on

Grounded Theory (Glaser & Strauss, 1967)

Interactional Analysis (Jordan & Henderson, 1995)

Meaning-making in a small group (Stahl, 2006)

Uptake analysis (Suthers, 2005; Suthers et al, 2007)

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Collaboration Interaction Model

We develop a method of analysis called Collaboration Interaction Model to study meaning-making paths

Adapted from the methodology of Grounded Theory

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Collaboration Interaction Model Seeks to trace the development of

knowledge construction. A analytical and representational tool.

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Constructing the CIM Chat posting and

whiteboard representations coded.

VMTplayer Individual Uptake

Descriptor TableIndividual Uptake Descriptor Table

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VMT Chat Transcript

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C87

Pivotal Contribution

C86

C90C88

C91 C92

C93

C94

C95

C96

C98

C97

C100

C99

C101

C102

C103

C104

Pivotal Contribution

C105

C106

C107 C108C109

Pivotal Contribution

C110

C112

C111

C114

C115 C113

Stage1: Making sense of part (e)

Stage 2: Finding the range or domain

Stage 3: Agreeing on the injective function Question

Question Student reading off from the question

weekheng

song sue

queklinser

This session was conducted during the June holidays. Students were accessing the VMT from home (geographically apart). The above CIM shows a 10 mins 11 seconds chat between 3 JC 1 students. The mathematics topic is function.

CIM before Triangulation with Uptake Descriptor Table

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Individual Uptake Descriptor Table

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Linser’s Uptake Descriptor Table

Each chat line you typed.

Whose and what chat lines did you see that

made you type the chat line?

What were your other thoughts?

61 No the domain of F

Wee Kheng: I think range is -2 to infinity

Wrong answer given by Wee Kheng.

62 That the domain of GF

Wee Kheng: I think range is -2 to infinity

63 Sorry if I write the word equal just now when I suppose to write subset. (C98)

For qn E, the range of F is the domain of G (C86)Songsue: I thought domain of GF equals to the domain of F. (C90)

I make a typing error.

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C87

Pivotal Contribution

C86

C90C88

C91

C92

C93

C94

C95

C96

C98

C97

C100

C99

C101

C102

C103

C104

Pivotal Contribution

C105

C106

C107 C108C109

Pivotal Contribution

C110

C112

C111

C114

C115 C113

Stage1: Making sense of part (e)

Stage 2: Finding the range or domain

Stage 3: Agreeing on the injective function Question

Question Student reading off from the question

weekheng

song sue

queklinser

This session was conducted during the June holidays. Students were accessing the VMT from home (geographically apart). The above CIM shows a 10 mins 11 seconds chat between 3 JC 1 students. The mathematics topic is function.

CIM after Triangulation with Uptake Descriptor Table

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Another VMT Math’s Problem

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VMT Chat Transcript

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C2

C3

C1

C6

Pivotal Contribution

C4

C5

C7

C8

C9

C10 C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

C24 C25

Pivotal Contribution

kentnee

Ma_China_Tor

chenchen

C11

CIM constructed based on Researcher’s interpretation of the chat transcript

Stage 1: How to f(x) is a 1-1 function

Stage 2: Using the knowledge of Composite Functions to find range/domain.

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Each chat line you typed.

Whose and what chat lines did you see that

made you type the chat line?

What were your other thoughts?

1. kentnee, 7:36 (8.07): draw the graph y=f(x), then use horizontal line to prove is 1-1?

(stating answer after consideration of question) starting on the first question, explaining how to prove that the graph if 1-1.

2 kentnee, 7:36 (8.07): okay Ma_China_Tor, 7:36 (8.07): u dun have to solve the problem..just say how u gonna solve it

showing understanding that we need not work out the actual question

3 kentnee, 7:37 (8.07): yarkentnee, 7:37 (8.07): then (i) done

chenchen, 7:37 (8.07): Df inverse=range f showing agreement with what was stated

4 kentnee, 7:38 (8.07): domain of g = domain of f inverse g

chenchen, 7:38 (8.07): for finverseg(x) answering the question

Kentee’s Uptake Descriptor Table

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Each chat line you typed.

Whose and what chat lines did you see that

made you type the chat line?

What were your other thoughts?

5 kentnee, 7:39 (8.07): ops chenchen, 7:38 (8.07): its the subset slight misunderstanding about the formula

6 kentnee, 7:40 (8.07): formula of composite functions lol

Ma_China_Tor, 7:39 (8.07): dun draw such conclusionMa_China_Tor, 7:39 (8.07): like domain of g=domain of f inverse gMa_China_Tor, 7:40 (8.07): how u know?

explaining where I had gotten the conclusion from

7 kentnee, 7:41 (8.07): coz domain of f inverse g cannot exceed domain of g

(stating answer after consideration of question) further explanations about the conclusion

8 kentnee, 7:42 (8.07): no need to actually work out? so we state method le

(stating a query about our tasks) attempting to move on to the next question

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Ma_China_Tor’s Uptake Descriptor Table

Each chat line you typed.

Whose and what chat lines did you see that made you type

the chat line?

What were your other thoughts?

1 then take a horizontal line test

Chen chen :so we need to draw the fKen:Draw the graph y=f(x), then use horizontal line to prove is 1-1?

I want to suggest how to do the question

2 u dun have to solve the problem..just say how u gonna solve it

chenchen, 7:36 (8.07): hw to draw here Telling the criteria

3 i thk you have to test on the range of g and see if it fits the domain of f-1

chenchen, 7:37 (8.07): then rf inverse = domain of fchenchen, 7:37 (8.07): Df inverse=range fkentnee, 7:37 (8.07): yarkentnee, 7:37 (8.07): then (i) donechenchen, 7:38 (8.07): for finverseg(x)kentnee, 7:38 (8.07): domain of g = domain of f inverse gchenchen, 7:38 (8.07): its the subset

Suggesting some rule of function before solving

4 Kendun draw such conclusion

kentnee, 7:39 (8.07): opskentnee, 7:39 (8.07): ?kentnee, 7:39 (8.07): must test

I think ken was wrong. Just telling him.

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Each chat line you typed.

Whose and what chat lines did you see that made you type

the chat line?

What were your other thoughts?

5 OhThen I am wrong sorry

chenchen, 7:40 (8.07): Df inverse g(x)=Dg correct?chenchen, 7:40 (8.07): then we can solvekentnee, 7:40 (8.07): formula of composite functions lol kentnee, 7:41 (8.07): coz domain of f inverse g cannot exceed

domain of g

I thought about the question wrongly.

6 en kentnee, 7:42 (8.07): no need to actually work out? so we state method le

Agree with ken

7 1st one settleMove on

kentnee, 7:42 (8.07): ? we solved question 1. I suggest them to move on.

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Chenchen’s Uptake Descriptor Table

Each chat line you typed.

Whose and what chat lines did you see that made you type

the chat line?

What were your other thoughts?

1 chenchen, 7:35 (8.07): so we need to draw the f

Ma_China_Tor, 7:35 (8.07): lets start Solving the qn

2 chenchen, 7:36 (8.07): hw to draw here

Don't know where to draw don't know where to draw

3 chenchen, 7:37 (8.07): then rf inverse = domain of f

Ma_China_Tor, 7:36 (8.07): u dun have to solve the problem..just say how u gonna solve it

Since don't need to solve, I just state the method

4 chenchen, 7:37 (8.07): Df inverse=range f

Answering the qn Answering the qn

5 chenchen, 7:38 (8.07): for finverseg(x)

kentnee, 7:37 (8.07): then (i) done Answering the next part

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Each chat line you

typed.

Whose and what chat lines did you see that made you

type the chat line?

What were your other thoughts?

6 chenchen, 7:38 (8.07): its the subset

kentnee, 7:38 (8.07): domain of g = domain of f inverse g I thought ken was wrong

7 chenchen, 7:40 (8.07): Df inverse g(x)=Dg correct?

Asking whether I’m correct To solve the qn

8 chenchen, 7:40 (8.07): then we can solve

The qn can be solved if it is correct So we can move on

9 chenchen, 7:43 (8.07): it shd be the subset?

kentnee, 7:40 (8.07): formula of composite functions lol I thought he was wrong

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C2

C3

C1

C6

Pivotal Contribution

C4

C5

C7

C8

C9C10

C12

C13

C14

C15

C16

C17

C18

C19a

C20a C21

C22

C23

C24 C25

Pivotal Contribution

C11

C20b

kentnee

Ma_China_Tor

chenchen

Stage 2: Using the knowledge of Composite Functions to find range/domain.

Stage 1: How to f(x) is a 1-1 function

C19b

CIM constructed based on researcher’s interpretation of the chat transcript and the participant’s individual descriptor table

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Uptakes of Contribution Situations where

participants are manipulating previous contributions (Suthers 2005,2006) by the group.

Adaptation of the notation of Uptakes:

Two types of uptakes: Intersubjective and Intrasubjective.

Interpretation of Contribution motivates the manipulation

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Our Constructs

Contributions consist of chat postings (Chat), artifact construction and manipulation (Shared Whiteboard).

Stages consist of several contributions which are anchored by pivotal contributions.

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Our Constructs

Pivotal Contributions serve as a boundary of any stage, commencing the shaping or changing of direction of the discourse.

Uptakes Arrows represent individual’s interpretations on prior contribution constructed group members including self.

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Stages in the CIM Events in temporal and spatial

orientation can be segmented in some way (Kendon, 1985; Jordan & Henderson, 1995)

Negotiation across segment boundaries.

This is known as stages in the CIM ABRUPT verses SEAMLESS stage

transition

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Pivotal Contribution Contribution pivoting the discourse a particular

direction. Motivated by observation of contributions that

are fundamentally critical.

Stage 1 Stage 2

Stage 3

Stage 4Stage 5

Start of Chat End of Chat

Pivotal Contributions

CIM Vector Diagram

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Selection Criteria (1) Researcher’s perspective to map

out boundaries in the CIM. (2) Identify one Contributions that sit

on the boundaries. (Chat line or Shared whiteboard)

(3) Interrater reliability – Cohen’s Kappa>0.8.

Pivotal Contribution

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Generality of the CIM Data Session Unit of Analysis

Discussion

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Stages in the CIM Problem Design Level of Analysis

Discussion

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Conclusion

A structural view of interaction across the chat transcript (shared whiteboard and chat line).

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Conclusion

CIM is constructed based on the triangulation three data sources

1. VMTplayer2. Individual Uptake Descriptor Table3. Focus Group

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Future Work

Theoretical grounding of the concepts and methodology

Operationalizing these concepts Apply CIM to many transcripts to test

out the generality of the model. Using the CIM to aid educators in

understanding the students’ problem-solving and collaboration.