1. 1 Model for Analyzing Collaborative Knowledge Construction in a Quasi- Synchronous Chat Environment Juan Dee WEE & Chee-Kit LOOI

2. 2 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

3. 3 Quasi-Synchronous Chat Environment  Participants work as a group to solve maths problem  VMT-Chat consists of a shared whiteboard and chat tool Math Forum (www.mathforum.org) andwww.mathforum.org the College of Information Science and Technology at Drexel University (Stahl, Shumar &Weimar, 2004).

4. 4 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

5. 5 Singapore Context: Briefing before VMT Session

6. 6 VMT Orientation Session in the Computer Laboratory

7. 7 Opened Ended Mathematics Question placed on the shared whiteboard

8. 8 VMT Chat Interface

9. 9 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)

10. 10 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

11. 11 Collaboration Interaction Model  Seeks to trace the development of knowledge construction.  A analytical and representational tool.

12. 12 Constructing the CIM  Chat posting and whiteboard representations coded.  VMTplayer  Individual Uptake Descriptor Table Individual Uptake Descriptor Table

13. 13 VMT Chat Transcript

14. 14

15. 15 C87 Pivotal Contribution C86 C90C88 C91C92 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 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

16. 16 Individual Uptake Descriptor Table

17. 17 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? 61No the domain of F Wee Kheng: I think range is -2 to infinity Wrong answer given by Wee Kheng. 62That the domain of GF Wee Kheng: I think range is -2 to infinity 63Sorry 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.

18. 18 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 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

19. 19 Another VMT Math’s Problem

20. 20 VMT Chat Transcript

21. 21 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.

22. 22 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. 2kentnee, 7:36 (8.07): okayMa_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 3kentnee, 7:37 (8.07): yar kentnee, 7:37 (8.07): then (i) done chenchen, 7:37 (8.07): Df inverse=range fshowing agreement with what was stated 4kentnee, 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

23. 23 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? 5kentnee, 7:39 (8.07): opschenchen, 7:38 (8.07): its the subsetslight misunderstanding about the formula 6kentnee, 7:40 (8.07): formula of composite functions lol Ma_China_Tor, 7:39 (8.07): dun draw such conclusion Ma_China_Tor, 7:39 (8.07): like domain of g=domain of f inverse g Ma_China_Tor, 7:40 (8.07): how u know? explaining where I had gotten the conclusion from 7kentnee, 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 8kentnee, 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

24. 24 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? 1then take a horizontal line test Chen chen :so we need to draw the f Ken:Draw the graph y=f(x), then use horizontal line to prove is 1-1? I want to suggest how to do the question 2u dun have to solve the problem..just say how u gonna solve it chenchen, 7:36 (8.07): hw to draw hereTelling the criteria 3i 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 f chenchen, 7:37 (8.07): Df inverse=range f kentnee, 7:37 (8.07): yar kentnee, 7:37 (8.07): then (i) done chenchen, 7:38 (8.07): for finverseg(x) kentnee, 7:38 (8.07): domain of g = domain of f inverse g chenchen, 7:38 (8.07): its the subset Suggesting some rule of function before solving 4Ken dun draw such conclusion kentnee, 7:39 (8.07): ops kentnee, 7:39 (8.07): ? kentnee, 7:39 (8.07): must test I think ken was wrong. Just telling him.

25. 25 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? 5Oh Then I am wrong sorry chenchen, 7:40 (8.07): Df inverse g(x)=Dg correct? chenchen, 7:40 (8.07): then we can solve kentnee, 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. 6enkentnee, 7:42 (8.07): no need to actually work out? so we state method le Agree with ken 71 st one settle Move on kentnee, 7:42 (8.07): ?we solved question 1. I suggest them to move on.

26. 26 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? 1chenchen, 7:35 (8.07): so we need to draw the f Ma_China_Tor, 7:35 (8.07): lets startSolving the qn 2chenchen, 7:36 (8.07): hw to draw here Don't know where to drawdon't know where to draw 3chenchen, 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 4chenchen, 7:37 (8.07): Df inverse=range f Answering the qn 5chenchen, 7:38 (8.07): for finverseg(x) kentnee, 7:37 (8.07): then (i) doneAnswering the next part

27. 27 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? 6chenchen, 7:38 (8.07): its the subset kentnee, 7:38 (8.07): domain of g = domain of f inverse gI thought ken was wrong 7chenchen, 7:40 (8.07): Df inverse g(x)=Dg correct? Asking whether I’m correctTo solve the qn 8chenchen, 7:40 (8.07): then we can solve The qn can be solved if it is correctSo we can move on 9chenchen, 7:43 (8.07): it shd be the subset? kentnee, 7:40 (8.07): formula of composite functions lolI thought he was wrong

28. 28 C2 C3 C1 C6 Pivotal Contribution C4 C5 C7 C8 C9 C10 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

29. 29 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

30. 30 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.

31. 31 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.

32. 32 Contributions  Coding of Chat posting and whiteboard artifact construction/manipulation  Sequential Order  A logical unit from participants perspective  Interrater reliability – Cohen’s Kappa >0.8)

33. 33 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

34. 34 Pivotal Contribution  Contribution pivoting the discourse a particular direction.  Motivated by observation of contributions that are fundamentally critical. Stage 1Stage 2 Stage 3 Stage 4 Stage 5 Start of Chat End of Chat Pivotal Contributions CIM Vector Diagram

35. 35  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

36. 36  Generality of the CIM  Data Session  Unit of Analysis Discussion

37. 37  Stages in the CIM  Problem Design  Level of Analysis Discussion

38. 38 Conclusion  A structural view of interaction across the chat transcript (shared whiteboard and chat line).

39. 39 Conclusion  CIM is constructed based on the triangulation three data sources 1. VMTplayer 2. Individual Uptake Descriptor Table 3. Focus Group

40. 40 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.