effects of social metacognition on micro-creativity : statistical discourse analyses of group...
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Effects of Social Metacognition on Micro-Creativity:
Statistical Discourse Analyses
of Group Problem Solving
Ming Ming ChiuState University of New York – Buffalo
[email protected] I appreciate the research assistance of
Choi Yik Ting and Kuo Sze Wing
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Under the Universal Texting plan, each text message costs $.10. Budget Texting costs $.01 per text message, but charges a monthly fee, $18.
1) How many text messages do you send each month?
2) Which company costs less for you?
3) How many texts should you send for the
Universal plan and the Budget plan
to cost the same?
Solving problems & Micro-creativity
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• Difficult problem for students learning algebra
• To solve this problem, novice students create new ideas and check/justify their utility (micro-creativity processes).
• More micro-creativity processes
Solve problem
• What group processes
micro-creativity processes?
Solving problems & Micro-creativity
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Micro-Creativity Processes • Creativity processes
–Generate ideas– Identify/Justify utility
( Sternberg & Lubart, 1999 )
• Big “C” creativity affects society• Small “c” creativity affects person
( Gruber & Wallace, 1999 )
• Micro-c creativity processes occur at a moment in time
( Chiu, 2008 )
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What Affects Micro-creativity?
• Social Metacognition?
• Face / Rudeness?
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Social MetacognitionMetacognition
Monitoring and control of one’s knowledge and actions
( Flavell, 1971; Hacker, 1998 )
Social Metacognition Group members’ monitoring and control of one another’s knowledge and actions
( Chiu, in press)
Most individuals have poor metacognition.( Hacker & Bol, 2004 )
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Social MetacognitionQuestions indicate knowledge gaps
Identifies gap in someone’s understanding Motivates and points out a way to fill the gap
to create a new idea (+) Use old or new info to explain/justify (+)
(Coleman, 1998; Webb, Troper & Fall, 1995; DeLisi & Goldbeck, 1999 )
Disagree Identify obstacles
Overcome via new ideas and/or justifications (+)
(Doise, Mugny & Perret-Clermont, 1975; Piaget, 1985)
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Face / Rude
• Disagree Rudely
• Excessive Agreement
• Command !
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Face / RudeFace = Public Self-image
Disagree rudely (attack face) vs. Disagree politely (save face)
( Brown & Levinson, 1987 ) “Ten times two hundred.”
Disagree Rudely “No, you’re wrong, it’s one tenth times two hundred.”
Previous speaker more likely to retaliate Emotional argument
Reduce new ideas & justifications () End cooperation
( Chiu & Khoo, 2003; Gottman & Krokoff, 1989 )
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Face / RudeDisagree politely “if we want it in dollars,
we can multiply two hundred by one tenth.”
• “if” – Hypothetical distances error away
• No “you” – No direct blame
• “we” – Shared positioning & common cause
Save previous speaker’s face Listen & understand obstacle Overcome via new ideas & justifications (+)
( Chiu & Khoo, 2003 )
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Face / Rude
Agree too much
Concern for social relationship
Reluctant to disagree with wrong ideas
Fewer new ideas & justifications (–)( Person, Kreuz, Zwaan, & Graesser, 1995; Tann, 1979; Tudge,1989 )
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Face / RudeCommand !
® Demand implementation of an old idea
® Suggest that speaker has higher status than audience
Ruder than question
Threaten face
Distract from problem solving
Fewer new ideas & justifications (–)(Brown & Levinson, 1987; Chiu,2008 )
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Micro-creativity processes
New ideas
JustificationsFace / RudenessPolitely Disagree (+)Rudely Disagree (–)Excessively Agree (–)Command (–)
Social MetacognitionAsk Questions (+)Disagree (+)
Control variablesMath gradePeer FriendshipGender, ethnicity, …Group mean grade, Group gender variance …
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Videotape Group Problem Solving
• 84 9th grade, average ability students in US city–Work in 21 groups of 4
• Not friends• Introducing 2 variable algebraic equations
– 1st day of group work– No group work preparation– Work on problem for 30 minutes
• Videotape & Transcripts– Two RAs coded each student turn – Krippendorf’s
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Content analysisJay: A hundred eighty dollars.
Ben: If we multiply by ten cents, don’t we get
a hundred and eighty cents?• Ben
– Disagrees politely– New information– Correct– Justifies– Question
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Multi-dimensional CodingEvaluation of the previous action
– Agree ( + ), Neutral ( n ), Ignore/New topic ( * ), Disagree rudely (––), Disagree politely (–)
Knowledge content regarding problem– New idea, Old idea, Null-content ( {} )
Validity– Correct ( ), Wrong ( X ), Null-content ( {} )
Justification – Justify ( J ), No justification ( [] ), Null-content ( {} )
Invitation to participate– Command ( ! ), Question ( ? ), Statement ( _. )
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Invitational Form Decision TreeMinimize Number of Coding Decisions to inter-coder reliability
• Minimize Depth of decision tree • Put highly likely actions at the top
Do any of the clauses proscribe an action?• Yes, code as command (imperative)• No, is the subject the addressee?
– No, are any of the clauses in the form of a question?• No, code as statement (declarative)• Yes, code as question (interrogative)
– Yes, is the verb a modal?• No, should the described action have been performed, but not
done? – Yes, code as a command– No, code as a question
• Yes, Is it a Wh- question (who, what, where, why, when, how)?– Yes, code as an question– No, is the action feasible?
• Yes, code as a command• No, code as an question Based on Labov (2001), Tsui (1992)
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Coded TranscriptID Action EPA KC Valid? Justify IF
Fay Do ten times eighteen. * C !
Ben Ten times eighteen is– + R _.
Eva Twenty-eight. + C X _.
Jay Wrong. A hundred eighty dollars. — C X _.
Ben If we multiply by ten cents, don’t we get a hundred and eighty cents?
- C J ?
Fay Yep. + _.
Add other variables at each speaker turn: Student: Gender, ethnicity, mid-year algebra grade, … Group: Group’s mean mid-year algebra grade, …
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4 types of Analytical Difficulties
• Time
• Outcomes
• Explanatory variables
• Data set
Statistical Discourse Analysis
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Statistical Discourse AnalysisDifficulties regarding Time
· Time periods differ (T2 T4)
Serial correlation (t8 → t9)
Strategies· Breakpoint analysis
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Identify BreakpointsBreakpoints• Critical events radically change interactions
• Statistically identify breakpoints– Test possible combinations of breakpoints– Model with smallest Bayesian Info Criterion (BIC)
Explain the most variance w/ fewest breakpoints
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Breakpoints in 1 group%
Mic
ro-c
reat
ivit
y
0%
20%
40%
60%
80%
100%
0 10 20 30Time (mins)
% N
ew id
eas
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Statistical Discourse AnalysisDifficulties regarding Time
· Time periods differ (T2 T4)
Serial correlation (t8 → t9)
Strategies· Breakpoint analysis
· Multilevel analysis (MLn, HLM)
· Test with Q-statistics
Model with lag outcomes
e.g. Justify (-1)
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Statistical Discourse AnalysisOutcome Difficulties
Discrete outcomes (Yes / No)
· Multiple outcomes (Y1, Y2)New idea & Justify
Strategies
Logit / Probit
· Multivariate, multilevel analysis
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Statistical Discourse AnalysisExplanatory model Difficulties
· People & Groups differ
· Mediation effects (X→M→Y)
· False positives (+ + + +)
· Effect across turns (X6→Y9)
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Effects across several turns
Ben: 10 times 18 is
Eva: 28.
Jay: Wrong, 180 dollars.
2 speakers ago = (– 2)
1 speaker ago = (– 1)
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Statistical Discourse AnalysisExplanatory model Difficulties
· People & Groups differ
· Mediation effects (X→M→Y)
· False positives (+ + + +)
· Effect across turns (X6→Y9)
Strategies
· Multilevel cross-classification Multilevel mediation tests
· 2-stage linear step-up procedure
· Vector Auto-Regression (VAR)Lag explanatory
variablese.g., Disagree (-1), Girl
(-1) Disagree (-2)
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VAR models effects across turnsID Action Justify Disagre
eDisagree (-
1)
Fay Do ten times eighteen. 0 0 -
Ben Ten times eighteen is– 0 0 0
Eva Twenty-eight. 0 0 0
Jay Wrong. A hundred eighty dollars.
0 1 0
Ben If we multiply by ten cents, don’t we get a hundred and eighty cents?
1 1 1
Fay Yep. 0 0 1
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Statistical Discourse AnalysisData Difficulties
Missing data (101?001?10)
Robustness
Strategies
· Markov Chain Monte Carlo
multiple imputation
· Separate outcome models
· Use data subsets
· Use unimputed data
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Results: Breakpoints
• 2.65 new idea breakpoints per group3.65 time periods per group (min=1; max
=6)
• 2.05 justification breakpoints per group3.05 time periods per group (min=1; max
=6)
• Number of breakpoints did not differ across groups that solved vs. did not solve the problem
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3 Types of Breakpoints• Creativity process generators
– Sharply increase new ideas or justifications
• Creativity process dampeners– Sharply decrease new ideas or justifications
• On-task Off-task transitions
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Creativity generatorAna How can they be equal?
Bob I don’t know
Cate Try another number?
Dan Which number?
[8 seconds of silence; each student looks at own paper]
Cate [looks at Ana’s paper] Yours is much closer.
So, try a number close to yours
Dan [looks at Ana’s paper] Mine’s even closer
Ana [looks at Dan’s paper] Oh! More messages get us
closer
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Creativity dampenerKay Let’s try a hundred.
Lee Ok. That’s a thousand.
Tom And that’s one, so nineteen.
Kay That’s like over nine hundred away.
Jan Maybe it’s one of those trick questions.
Tom Yeah, like it can’t be done.
Kay So, maybe there’s no answer.
Lee Then, we’re done.
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New Idea
Justify
Agree
Rudely Disagree
Politely Disagree
Peer Friendship
Rudely Disagree (-1) * Unsolved
Rudely Disagree (-1) *Wrong (-2)
Rudely Disagree (-1)
Math grade (-1)
Math grade (-1) *Unsolved
Command (-1)
Previous turn (-1) Current turn OutcomesExplanatory model: New Idea & Justify
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Group + Time Period DifferencesUnsuccessful groups:
Negative effect of Rudely disagree (-1) on new ideas
Negative effect of Math grade (-1) on justifications
Mathematics grade’s effect on justifications
Differed across both time periods and across groups
-2% to +1% in unsuccessful groups
-1% to +3% in successful groups
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Unsupported Hypotheses
Questions were not linked to
New idea or Justifications
Rudely disagreements
were not linked to Justifications
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Increase Group Micro-creativity
• Ask questions rather than issue commands !
• Disagree politely to encourage justifications
• Listen to rude disagreements and use the content
to develop new ideas
Implications for Teachers & Students
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Implications for Researchers• Statistically identify critical moments
(breakpoints) that radically change subsequent processes
• Effects differ across groups, time periods, turns– Use statistical model to compute specific effect
• Effects of sequences – Look beyond the effects of single actions
• New method for statistically modeling
conversations
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Further applications… What major or momentary events affect
people’s behaviors over time during …–Classroom conversations?–Online discussions?–A student’s think-aloud problem solving? –An infant’s learning of a new word?–Basketball games?–Stock market transactions? –Wars?
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Thank you!
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ID Action Turn # Valid?Previous
TurnValid (-1)
Ana Do three times four. 1 – –
Ben Three times four is seven 2 X 1 Eva Three times four is nine. 3 X 2 X
Jay Three times four is twelve. 4 3 X
ID Action Turn # Valid?Respond
to turn #?Valid (-1)
Ana Do three times four. 1 – –
Ben Three times four is seven 2 X 1 Eva Three times four is nine. 3 X 1 Jay Three times four is twelve. 4 3 X
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Statistical Discourse AnalysisAnalytical Difficulty
Differences across topics
Time periods differ (T2 T4)
Serial correlation (t8 → t9)
Parallel talk (→→ )
Strategy
Multilevel analysis
Breakpoint analysis & Multilevel analysis
I2 index of Q-statistics; Model with lag variables
Store path: ID prior turn, Vector Auto-Regression
Discrete outcomes (Yes / No)
Multiple outcomes (Y1, Y2)
Infrequent outcomes (00010)
Logit / Probit
Multivariate outcome models
Logit bias estimator
People & Groups differ Mediation effects (X→M→Y) False positives (+ + + +)
Multilevel analysis Multilevel mediation tests 2-stage linear step-up procedure
Missing data (101?001?10)
Robustness
Markov Chain Monte Carlo multiple imputation
· Separate outcome models; Data subsets & unimputed data
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Knowledge content, Validity, and Justification
Does the speaker express any mathematics or problem-
related information?• No, code as null content• Yes, is all the info on the group's log/trace of problem
solving?– Yes, code as repetition– No, code as contribution and write specific info in
group's log– Does this info violate any mathematics or problem
constraints?• Yes, code as incorrect• No, code as correct
– Does the speaker justify his or her idea? • Yes, code as justification• No, code as no justification
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Mathematics
Bayesian Information Criterion
Regression specification
n
nk
n
L )ln(2
ijk = F(0 + f0jk + g00k+ 00sS00k +00tT00k+ujkUijk
+ vjkV(i-1)jk +vjkV(i-2)jk +vjkV(i-3)jk +vjkV(i-4)jk)