Troubles of Troubles of Understanding in Virtual Understanding in Virtual Math TeamsMath TeamsNan ZhouNan Zhou

PhD CandidatePhD Candidate

iSchool @ Drexel UniversityiSchool @ Drexel University

OutlineOutline

IntroductionIntroduction Research QuestionsResearch Questions Theoretical FrameworkTheoretical Framework MethodologyMethodology FindingsFindings Q & AQ & A

Information Behavior ResearchInformation Behavior Research

““the totality of human behavior in relation to the totality of human behavior in relation to sources and channels of information, including sources and channels of information, including both active and passive information seeking, both active and passive information seeking, and information use” (and information use” (Wilson, 2000Wilson, 2000) )

Triggered by problem situation (Triggered by problem situation (Belkin, Seeger, & Belkin, Seeger, & Wersig, 1983Wersig, 1983); knowledge deficiency (); knowledge deficiency (Belkin, Belkin, 19801980); gap in understanding (); gap in understanding (Dervin, 1983a; Itoga, Dervin, 1983a; Itoga, 1992; Dervin & Nilan, 19861992; Dervin & Nilan, 1986); uncertainty ); uncertainty ((Kuhlthau,1993; Wilson, 1999Kuhlthau,1993; Wilson, 1999) )

Dominated by cognitive viewpoint focused on Dominated by cognitive viewpoint focused on individualsindividuals

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

The Virtual Math Teams ProjectThe Virtual Math Teams Project

Joint research project between IST and the Math ForumJoint research project between IST and the Math Forum

Investigates the innovative use of online collaborative Investigates the innovative use of online collaborative environments to support effective K-12 mathematics discourse.environments to support effective K-12 mathematics discourse.

Design-based research approach (Brown, 1992; Collins, 1992; Design-based research approach (Brown, 1992; Collins, 1992; Design-based Research Collective, 2003) Design-based Research Collective, 2003) Addresses complexities in investigating designed artifacts contribute Addresses complexities in investigating designed artifacts contribute

to learning in naturalistic settings to learning in naturalistic settings Involves progressive improvement of instructional and technological Involves progressive improvement of instructional and technological

interventions and the theory informing their design interventions and the theory informing their design

Explores the nature of collaborative learning and small-group Explores the nature of collaborative learning and small-group interactions interactions

The VMT Chat EnvironmentThe VMT Chat Environment

(Illustration by courtesy of Murat Cakir)

Troubles of Understanding in Troubles of Understanding in Virtual Math TeamsVirtual Math Teams

In respect to mathematical concepts, reasoning In respect to mathematical concepts, reasoning procedures or problem solving procedures or problem solving

Ground for studying constructs in information behavior Ground for studying constructs in information behavior Important mechanism for collaboration and learningImportant mechanism for collaboration and learning

Social and situated views of learningSocial and situated views of learning (Piaget, 1932; Vygotsky, (Piaget, 1932; Vygotsky, 1930/1978; Lave & Wenger, 1991; Suchman, 1987; 1930/1978; Lave & Wenger, 1991; Suchman, 1987; Scardamalia & Bereiter, 1991) Scardamalia & Bereiter, 1991)

Shared understanding or meaningShared understanding or meaning (Koschmann, 2002; Stahl, (Koschmann, 2002; Stahl, 2006b; Suthers, 2006) 2006b; Suthers, 2006)

CollaborationCollaboration (Roschelle, 1992; 1996; Barron, 2003; Stahl, (Roschelle, 1992; 1996; Barron, 2003; Stahl, 2003, 2006b) 2003, 2006b)

Research QuestionsResearch Questions

RQ1RQ1:: How are How are troubles of understandingtroubles of understanding with with respect to mathematical concepts, reasoning respect to mathematical concepts, reasoning procedures or problem solving procedures or problem solving introducedintroduced and and made relevant to the ongoing interaction in the made relevant to the ongoing interaction in the group? group?

RQ2RQ2: : How are the introduced troubles dealt How are the introduced troubles dealt with in the group and how is with in the group and how is shared shared understandingunderstanding co-constructed? co-constructed?

Theoretical Framework: Studies on Theoretical Framework: Studies on Information BehaviorInformation Behavior

Focus on individuals (Focus on individuals (Taylor,1968; Belkin, 1982;Taylor,1968; Belkin, 1982; Wilson, 1981, 1996; Krikelas, 1983; Bates, 1989; Kuhlthau, Wilson, 1981, 1996; Krikelas, 1983; Bates, 1989; Kuhlthau,

1993; Savolanein, 19951993; Savolanein, 1995))

Collaborative Information BehaviorCollaborative Information Behavior ( (Maltz & Maltz & Ehrlich, 1995; Twidale, Nicholas, & Paice, 1997; Sonnenwald Ehrlich, 1995; Twidale, Nicholas, & Paice, 1997; Sonnenwald and Pierce, 2000; Bruce et al, 2002; Prekop, 2002; Hyldegard, and Pierce, 2000; Bruce et al, 2002; Prekop, 2002; Hyldegard,

20062006) )

Dervin’s Sense-MakingDervin’s Sense-Making ConstructionismConstructionism (Talja, Tuominen, and (Talja, Tuominen, and

Savolainen): Savolainen): linguistic turns and discourselinguistic turns and discourse

Computer-Supported Collaborative Computer-Supported Collaborative Learning (CSCL)Learning (CSCL)

““meaning and the practices of meaning-makingmeaning and the practices of meaning-making in the context of in the context of joint activity, and the ways in which these practices are mediated joint activity, and the ways in which these practices are mediated through designed artifacts”through designed artifacts” (Koschmann, 2002b) (Koschmann, 2002b)

Interaction Paradigm calls for studying practices and Interaction Paradigm calls for studying practices and processesprocesses (Roschelle, 1996; Roschelle & Teasley, 1995; Barron, 2003; Stahl, (Roschelle, 1996; Roschelle & Teasley, 1995; Barron, 2003; Stahl, 2006b; Koschmann, Stahl & Zemel, 2007; Koschmann & Zemel, 2006)2006b; Koschmann, Stahl & Zemel, 2007; Koschmann & Zemel, 2006)

Resolving troubles: Resolving troubles: questioningquestioning (Graesser, 1994; Webb, Nemer, & Ing, 2006 ) (Graesser, 1994; Webb, Nemer, & Ing, 2006 ) peer explainingpeer explaining (Chi, 2000; Webb, 1989, 2003) (Chi, 2000; Webb, 1989, 2003) ““grounding”grounding” (Clark & Brennan, 1991; Clark & Schaefer, 1989) (Clark & Brennan, 1991; Clark & Schaefer, 1989) argumentationargumentation (Andriessen, Baker, & Suthers, 2003; Weinberger & (Andriessen, Baker, & Suthers, 2003; Weinberger &

Fischer, 2005); Fischer, 2005); intersubjectivie negotiationintersubjectivie negotiation (Stahl, 2003, 2006b; Stahl & Herrmann, (Stahl, 2003, 2006b; Stahl & Herrmann,

1999)1999) convergence of conceptual changeconvergence of conceptual change (Roschelle, 1992) (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 Methodology - - Ethnomethodological CA (EM/CA)Ethnomethodological CA (EM/CA)

EM/CA as an approach in sociologyEM/CA as an approach in sociology Explores the basic properties of practical reasoning and Explores the basic properties of practical reasoning and

practical actions in everyday activities, including talk-in-practical actions in everyday activities, including talk-in-interactioninteraction

The problem of social order was re-conceived as a practical The problem of social order was re-conceived as a practical problem of social action, as a members’ activity, as methodic problem of social action, as a members’ activity, as methodic and therefore analyzableand therefore analyzable

Assumes meaningful conduct is produced and understood Assumes meaningful conduct is produced and understood based on shared procedures or methods based on shared procedures or methods

Sequential organization of action: “here and now”Sequential organization of action: “here and now” turn-taking, adjacency pair, repairturn-taking, adjacency pair, repair

Detailed analysis using logs of actual group discourseDetailed analysis using logs of actual group discourse Reliability/Validity:Reliability/Validity:

Data sessionsData sessions Analysis subject to inter-subjective agreementAnalysis subject to inter-subjective agreement

Data is presented as part of analysisData is presented as part of analysis

DataData

2 teams each consists of 3 or 4 2 teams each consists of 3 or 4 participants; 4 one-hour sessions across participants; 4 one-hour sessions across 2 weeks (from VMT Spring Fest 2006)2 weeks (from VMT Spring Fest 2006)

A few excerpts from sessions held in A few excerpts from sessions held in AOL Instant Messenger in 2004 AOL Instant Messenger in 2004

Upper-middle school students, recruited Upper-middle school students, recruited via teachers through the Math Forumvia teachers through the Math Forum

A facilitator present in each session A facilitator present in each session

Task for Spring Fest 06Task for Spring Fest 06

How does the graphic pattern How does the graphic pattern grow? Can your group see a grow? Can your group see a pattern of growth for the number pattern of growth for the number of sticks and squares? of sticks and squares?

What ifWhat if instead of squares you  instead of squares you use other polygons like use other polygons like triangles, hexagons, etc.? triangles, hexagons, etc.? …….. What are the different .. What are the different methods (induction, series, methods (induction, series, recursion, graphing, tables, etc.) recursion, graphing, tables, etc.) you can use to analye these you can use to analye these different patterns?different patterns?

The VMT Chat EnvironmentThe VMT Chat Environment

(Illustration by courtesy of Murat Cakir)

The VMT ReplayerThe VMT Replayer

FindingsFindings

1.1. Three types of Three types of troublestroubles

a)a) epistemic differentials epistemic differentials

b)b) problems of indexicality problems of indexicality

c)c) conflicting conflicting understandingsunderstandings

2.2. Interactional Interactional MethodsMethods

1)1) Pose a questionPose a question2)2) Make a self reportMake a self report3)3) Make an assertionMake an assertion

Certain methods are frequently associated with a particular type of troubles

Evolution of types of troubles

Traverse between methods

1)1) Pose a question: Pose a question:

Question designQuestion design Demonstrate competencyDemonstrate competency

Elicit an assessment of a candidate understanding Elicit an assessment of a candidate understanding of a matter previously put forward by another actorof a matter previously put forward by another actor

Solicit a “reminder” of “forgotten” knowledgeSolicit a “reminder” of “forgotten” knowledge Make a request for a demonstration Make a request for a demonstration Provide information on what one already knows Provide information on what one already knows

regarding the matter as a preface to a question regarding the matter as a preface to a question All involve designing a question for which the All involve designing a question for which the

response is projected to be relatively response is projected to be relatively unproblematic to produceunproblematic to produce

Procedures for question with Procedures for question with candidate understandingcandidate understanding

1)1) statement (such as proposal, idea, etc which statement (such as proposal, idea, etc which contains the source of trouble) (A)contains the source of trouble) (A)

2)2) candidate understanding for assessment (B)candidate understanding for assessment (B)3)3) assessment (A)assessment (A)

a)a) if positive, uptake the proposal/idea (B) ENDif positive, uptake the proposal/idea (B) ENDb)b) if negative, alternative understanding is produced (A)if negative, alternative understanding is produced (A)

4)4) assessment for the alternative/explanation (B)assessment for the alternative/explanation (B)5)5) demonstration of understanding (B) ORdemonstration of understanding (B) OR6)6) problematizing move (B) goes to 3)problematizing move (B) goes to 3)

Example 1: Pose a Question Example 1: Pose a Question Problem of indexicality Problem of indexicality

2) Make a self report 2) Make a self report

Elicits instructional workElicits instructional work Elicits inquiries from recipients to co-Elicits inquiries from recipients to co-

construct the question construct the question Escalation structureEscalation structure

Example 2: Make a self reportExample 2: Make a self report

Example 3: Escalation structureExample 3: Escalation structureEpistemic differentialsEpistemic differentials

3) Make an Assertion3) Make an Assertion

Often uses Reversed Polarity Questions Often uses Reversed Polarity Questions (RPQs) (Koshik, 2005)(RPQs) (Koshik, 2005) E.g. “Wouldn’t that not work for that one?” E.g. “Wouldn’t that not work for that one?”

Calls for production of an accountCalls for production of an account When a negative assessment is madeWhen a negative assessment is made

Often comes after a question-answer sequence Often comes after a question-answer sequence as a challenging or problematizing move as a challenging or problematizing move

Can result in alternative proposals Can result in alternative proposals

Example 4: Conflicting understandingsExample 4: Conflicting understandingsMake an assertionMake an assertion

3. Other methods when lack of 3. Other methods when lack of competencycompetency

Presents what one knowsPresents what one knows Defers question-asking by engaging Defers question-asking by engaging

others to “collaborate” others to “collaborate” Both involve positioning self as peers to Both involve positioning self as peers to

mitigate any epistemic differentials mitigate any epistemic differentials

4.4. Display/Demonstrate Display/Demonstrate understandingunderstanding

make a self-report regarding the make a self-report regarding the achieved understanding on the matter of achieved understanding on the matter of concernconcern

apply what’s been explained to the apply what’s been explained to the problem solving and performing the next problem solving and performing the next step step

reformulate what’s been explained (elicit reformulate what’s been explained (elicit assessment)assessment)

Example 5: Display understandingsExample 5: Display understandings

5. Organization of Participation5. Organization of Participation

Yours or my problem: problems of indexicality Yours or my problem: problems of indexicality vs. epistemic differentialsvs. epistemic differentials

Mark competency issue by “bracketing Mark competency issue by “bracketing relationship”relationship” E.g. “hope this doesnt sound too stupid, but wuts a E.g. “hope this doesnt sound too stupid, but wuts a

summation”summation” Co-construction of troubleCo-construction of trouble

A self-report results in elicitation of a questionA self-report results in elicitation of a question Intervention upon “failed” question Intervention upon “failed” question Prompts others to display understandingPrompts others to display understanding

Collaborative nature of response Collaborative nature of response

Example 6: Co-construction of an Example 6: Co-construction of an inquiry: inquiry: A “failed” A “failed” questionquestion

Epistemic differentials Epistemic differentials Problem of indexicalityProblem of indexicality

6. Understanding work vs. 6. Understanding work vs. lack of understanding work lack of understanding work

Ways of dis-attending in chatWays of dis-attending in chat Initiate a separate threadInitiate a separate thread Make a dismissive commentMake a dismissive comment Make an alternative proposalMake an alternative proposal

Evidence of good collaboration? Evidence of good collaboration?

ConclusionsConclusions

RQ1RQ1:: How are How are troubles of understandingtroubles of understanding with with respect to mathematical concepts, reasoning respect to mathematical concepts, reasoning procedures or problem solving procedures or problem solving introducedintroduced and and made relevant to the ongoing interaction in the made relevant to the ongoing interaction in the group? group?

RQ2RQ2: : How are the introduced troubles dealt How are the introduced troubles dealt with in the group and how is with in the group and how is shared shared understandingunderstanding co-constructed? co-constructed?

ContributionsContributions

Contribution to information behavior researchContribution to information behavior research Offers an interactional approach using EM/CAOffers an interactional approach using EM/CA Information as process of informing Information as process of informing

Contribution to CSCLContribution to CSCL QuestioningQuestioning

““objectivism” and “structuralism” vs. interactionalobjectivism” and “structuralism” vs. interactional Collaboration and learningCollaboration and learning

Where is shared understanding or meaning located? Where is shared understanding or meaning located? – – in the methods and procedures in producing themin the methods and procedures in producing them

Contribution to Conversation AnalysisContribution to Conversation Analysis Extends studies on repairs Extends studies on repairs

Questions?Questions?