Troubles of Understanding in Virtual Math Teams

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Troubles of Understanding in Virtual Math Teams

• Nan Zhou
• PhD Candidate
• iSchool _at_ Drexel University

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Outline

• Introduction
• Research Questions
• Theoretical Framework
• Methodology
• Findings
• Q A

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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

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

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

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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?

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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)
• Dervins Sense-Making
• Constructionism (Talja, Tuominen, and
  Savolainen) linguistic turns and discourse

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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)

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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). )
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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

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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

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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?

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

• Three types of troubles
• epistemic differentials
• problems of indexicality
• conflicting understandings

• Interactional Methods
• Pose a question
• Make a self report
• Make an assertion

• Certain methods are frequently associated with a
  particular type of troubles
• Evolution of types of troubles
• Traverse between methods

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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

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Procedures for question with candidate
understanding

• statement (such as proposal, idea, etc which
  contains the source of trouble) (A)
• candidate understanding for assessment (B)
• assessment (A)
• if positive, uptake the proposal/idea (B) END
• if negative, alternative understanding is
  produced (A)
• assessment for the alternative/explanation (B)
• demonstration of understanding (B) OR
• problematizing move (B) goes to 3)

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Example 1 Pose a Question Problem of
indexicality
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2) Make a self report

• Elicits instructional work
• Elicits inquiries from recipients to co-construct
  the question
• Escalation structure

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Example 2 Make a self report
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Example 3 Escalation structure Epistemic
differentials
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3) Make an Assertion

• Often uses Reversed Polarity Questions (RPQs)
  (Koshik, 2005)
• E.g. Wouldnt 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

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Example 4 Conflicting understandings Make an
assertion
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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

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4. Display/Demonstrate understanding

• make a self-report regarding the achieved
  understanding on the matter of concern
• apply whats been explained to the problem
  solving and performing the next step
• reformulate whats been explained (elicit
  assessment)

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Example 5 Display understandings
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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

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Example 6 Co-construction of an inquiry A
failed question Epistemic differentials
Problem of indexicality
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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?

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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?

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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
• Contribution to Conversation Analysis
• Extends studies on repairs

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Questions?