Troubles of Understanding in Virtual Math Teams Nan Zhou PhD Candidate Drexel University

Outline  Introduction  Research Questions  Theoretical Framework  Methodology  Findings  Q & A

Information Behavior Research  “the totality of human behavior in relation to sources and channels of information, including both active and passive information seeking, and information use” ( Wilson, 2000 )  Triggered by problem situation ( Belkin, Seeger, & Wersig, 1983 ); knowledge deficiency ( Belkin, 1980 ); gap in understanding ( Dervin, 1983a; Itoga, 1992; Dervin & Nilan, 1986 ); uncertainty ( Kuhlthau,1993; Wilson, 1999 )  Dominated by cognitive viewpoint focused on individuals

A model of information behavior (Adapted from Wilson 1999: Models in Information Behaviour Research, Journal of Documentation, 55(3))

The Virtual Math Teams Project  Joint research project between IST and the Math Forum  Investigates the innovative use of online collaborative environments to support effective K-12 mathematics discourse.  Design-based research approach (Brown, 1992; Collins, 1992; Design-based Research Collective, 2003)  Addresses complexities in investigating designed artifacts contribute to learning in naturalistic settings  Involves progressive improvement of instructional and technological interventions and the theory informing their design  Explores the nature of collaborative learning and small-group interactions

The VMT Chat Environment (Illustration by courtesy of Murat Cakir)

Troubles of Understanding in Virtual Math Teams  In respect to mathematical concepts, reasoning procedures or problem solving  Ground for studying constructs in information behavior  Important mechanism for collaboration and learning  Social and situated views of learning (Piaget, 1932; Vygotsky, 1930/1978; Lave & Wenger, 1991; Suchman, 1987; Scardamalia & Bereiter, 1991)  Shared understanding or meaning (Koschmann, 2002; Stahl, 2006b; Suthers, 2006)  Collaboration (Roschelle, 1992; 1996; Barron, 2003; Stahl, 2003, 2006b)

Research Questions  RQ1: How are troubles of understanding with respect to mathematical concepts, reasoning procedures or problem solving introduced and made relevant to the ongoing interaction in the group?  RQ2: How are the introduced troubles dealt with in the group and how is shared understanding co-constructed?

Theoretical Framework: Studies on Information Behavior  Focus on individuals ( Taylor,1968; Belkin, 1982; Wilson, 1981, 1996; Krikelas, 1983; Bates, 1989; Kuhlthau, 1993; Savolanein, 1995 )  Collaborative Information Behavior ( Maltz & Ehrlich, 1995; Twidale, Nicholas, & Paice, 1997; Sonnenwald and Pierce, 2000; Bruce et al, 2002; Prekop, 2002; Hyldegard, 2006 )  Dervin’s Sense-Making  Constructionism (Talja, Tuominen, and Savolainen): linguistic turns and discourse

Computer-Supported Collaborative Learning (CSCL)  “meaning and the practices of meaning-making in the context of joint activity, and the ways in which these practices are mediated through designed artifacts” (Koschmann, 2002b)  Interaction Paradigm calls for studying practices and processes (Roschelle, 1996; Roschelle & Teasley, 1995; Barron, 2003; Stahl, 2006b; Koschmann, Stahl & Zemel, 2007; Koschmann & Zemel, 2006)  Resolving troubles:  questioning (Graesser, 1994; Webb, Nemer, & Ing, 2006 )  peer explaining (Chi, 2000; Webb, 1989, 2003)  “grounding” (Clark & Brennan, 1991; Clark & Schaefer, 1989)  argumentation (Andriessen, Baker, & Suthers, 2003; Weinberger & Fischer, 2005);  intersubjectivie negotiation (Stahl, 2003, 2006b; Stahl & Herrmann, 1999)  convergence of conceptual change (Roschelle, 1992)

A social and interactional model of information behavior with the sequential team interaction in the center. ( Stahl, G. (2010) Guiding Group Cognition in CSCL. ijCSCL 5 (3). )

Methodology - Ethnomethodological CA (EM/CA)  EM/CA as an approach in sociology  Explores the basic properties of practical reasoning and practical actions in everyday activities, including talk-in- interaction  The problem of social order was re-conceived as a practical problem of social action, as a members’ activity, as methodic and therefore analyzable  Assumes meaningful conduct is produced and understood based on shared procedures or methods  Sequential organization of action: “here and now”  turn-taking, adjacency pair, repair  Detailed analysis using logs of actual group discourse  Reliability/Validity:  Data sessions  Analysis subject to inter-subjective agreement  Data is presented as part of analysis

Data  2 teams each consists of 3 or 4 participants; 4 one-hour sessions across 2 weeks (from VMT Spring Fest 2006)  A few excerpts from sessions held in AOL Instant Messenger in 2004  Upper-middle school students, recruited via teachers through the Math Forum  A facilitator present in each session

Task for Spring Fest 06  How does the graphic pattern grow? Can your group see a pattern of growth for the number of sticks and squares?  What if instead of squares you use other polygons like triangles, hexagons, etc.? ….. What are the different methods (induction, series, recursion, graphing, tables, etc.) you can use to analye these different patterns?

The VMT Chat Environment (Illustration by courtesy of Murat Cakir)

The VMT Replayer

Findings 1.Three types of troubles a)epistemic differentials b)problems of indexicality c)conflicting understandings 2.Interactional Methods 1)Pose a question 2)Make a self report 3)Make an assertion  Certain methods are frequently associated with a particular type of troubles  Evolution of types of troubles  Traverse between methods

1)Pose a question: Question design  Demonstrate competency  Elicit an assessment of a candidate understanding of a matter previously put forward by another actor  Solicit a “reminder” of “forgotten” knowledge  Make a request for a demonstration  Provide information on what one already knows regarding the matter as a preface to a question  All involve designing a question for which the response is projected to be relatively unproblematic to produce

Procedures for question with candidate understanding 1)statement (such as proposal, idea, etc which contains the source of trouble) (A) 2)candidate understanding for assessment (B) 3)assessment (A) a)if positive, uptake the proposal/idea (B) END b)if negative, alternative understanding is produced (A) 4)assessment for the alternative/explanation (B) 5)demonstration of understanding (B) OR 6)problematizing move (B) goes to 3)

Example 1: Pose a Question Problem of indexicality

2) Make a self report  Elicits instructional work  Elicits inquiries from recipients to co- construct the question  Escalation structure

Example 2: Make a self report

Example 3: Escalation structure Epistemic differentials

3) Make an Assertion  Often uses Reversed Polarity Questions (RPQs) (Koshik, 2005)  E.g. “Wouldn’t that not work for that one?”  Calls for production of an account  When a negative assessment is made  Often comes after a question-answer sequence as a challenging or problematizing move  Can result in alternative proposals

Example 4: Conflicting understandings Make an assertion

3. Other methods when lack of competency  Presents what one knows  Defers question-asking by engaging others to “collaborate”  Both involve positioning self as peers to mitigate any epistemic differentials

4. Display/Demonstrate understanding  make a self-report regarding the achieved understanding on the matter of concern  apply what’s been explained to the problem solving and performing the next step  reformulate what’s been explained (elicit assessment)

Example 5: Display understandings

5. Organization of Participation  Yours or my problem: problems of indexicality vs. epistemic differentials  Mark competency issue by “bracketing relationship”  E.g. “hope this doesnt sound too stupid, but wuts a summation”  Co-construction of trouble  A self-report results in elicitation of a question  Intervention upon “failed” question  Prompts others to display understanding  Collaborative nature of response

Example 6: Co-construction of an inquiry: A “failed” question Epistemic differentials Problem of indexicality

6. Understanding work vs. lack of understanding work  Ways of dis-attending in chat  Initiate a separate thread  Make a dismissive comment  Make an alternative proposal  Evidence of good collaboration?

Conclusions  RQ1: How are troubles of understanding with respect to mathematical concepts, reasoning procedures or problem solving introduced and made relevant to the ongoing interaction in the group?  RQ2: How are the introduced troubles dealt with in the group and how is shared understanding co-constructed?

Contributions  Contribution to information behavior research  Offers an interactional approach using EM/CA  Information as process of informing  Contribution to CSCL  Questioning  “objectivism” and “structuralism” vs. interactional  Collaboration and learning  Where is shared understanding or meaning located? – in the methods and procedures in producing them – in the methods and procedures in producing them  Contribution to Conversation Analysis  Extends studies on repairs

Questions?