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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

mingchiu@buffalo.eduI appreciate the research assistance of Choi Yik Ting and Kuo Sze Wing

Under the UniversalTexting plan, each text message costs $.10. BudgetTexting costs $.01 per text message, but charges a monthly fee, $18.

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-creativitySolving problems & Micro-creativity

- Difficult problem for students learning algebra
- To solve this problem, novice students create new ideasandcheck/justify their utility (micro-creativity processes).
- More micro-creativity processes

Solve problem

- What group processes

micro-creativity processes?

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 )

What Affects Micro-creativity?

- Social Metacognition?
- Face / Rudeness?

Social Metacognition

Metacognition

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 )

Social Metacognition

Questions

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)

Face / Rude

- Disagree Rudely
- Excessive Agreement
- Command !

Face / Rude

Face = Public Self-image

Disagree rudely (attack face)

vs. Disagree politely (save face)

( Brown & Levinson, 1987 )

“Ten times two hundred.”

DisagreeRudely

“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 )

Face / Rude

Disagree 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 )

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 )

Face / Rude

Command !

- 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 )

Ask Questions (+)

Disagree (+)

Micro-creativity processes

New ideas

Justifications

Face / Rudeness

Politely Disagree (+)

Rudely Disagree (–)

Excessively Agree (–)

Command (–)

Control variables

Math grade

Peer Friendship

Gender, ethnicity, …

Group mean grade,

Group gender variance …

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

Content analysis

Jay: 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

Multi-dimensional Coding

Evaluation 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 ( _. )

Invitational Form Decision Tree

Minimize 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)

Coded Transcript

Add other variables at each speaker turn:

Student: Gender, ethnicity, mid-year algebra grade, …

Group: Group’s mean mid-year algebra grade, …

4 types of AnalyticalDifficulties

Time

Outcomes

Explanatory variables

Data set

Statistical Discourse Analysis

Statistical Discourse Analysis

- Difficultiesregarding Time
- Time periods differ (T2 T4)
- Serial correlation (t8→ t9)

- Strategies
- Breakpoint analysis

Identify Breakpoints

Breakpoints

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

Statistical Discourse Analysis

- Difficultiesregarding 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)

Statistical Discourse Analysis

- Outcome Difficulties

Discrete outcomes (Yes / No)

- Multiple outcomes (Y1, Y2)

New idea & Justify

- Strategies

Logit / Probit

- Multivariate, multilevel analysis

Statistical Discourse Analysis

- Explanatory model Difficulties
- People & Groups differ
- Mediation effects (X→M→Y)
- False positives (+ + + +)
- Effect across turns (X6→Y9)

Effects across several turns

2 speakers ago = (– 2)

1 speaker ago = (– 1)

Ben: 10 times 18 is

Eva: 28.

Jay: Wrong, 180 dollars.

Statistical Discourse Analysis

- Explanatory 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 variables
- e.g., Disagree (-1), Girl (-1)
- Disagree (-2)

Statistical Discourse Analysis

Data Difficulties

Missing data (101?001?10)

Robustness

- Strategies
- Markov Chain Monte Carlo

multiple imputation

- Separate outcome models
- Use data subsets
- Use unimputed data

Results: Breakpoints

2.65 new idea breakpoints per group

3.65 time periods per group (min=1; max =6)

2.05 justification breakpoints per group

3.05 time periods per group (min=1; max =6)

Number of breakpoints did not differ across groups that solved vs. did not solve the problem

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

Creativity generator

Ana 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

Creativity dampener

Kay 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.

Explanatory model: New Idea & Justify

Previous turn (-1)Current turnOutcomes

New Idea

Rudely Disagree (-1)

Rudely Disagree

Agree

Rudely Disagree (-1) * Unsolved

Rudely Disagree (-1) *Wrong (-2)

Command (-1)

Peer Friendship

Justify

Politely Disagree

Math grade (-1)

Math grade (-1) *Unsolved

Group + Time Period Differences

Unsuccessful 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

Unsupported Hypotheses

Questions were not linked to

New idea or Justifications

Rudely disagreements

were not linked to Justifications

Implications for Teachers & Students

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 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

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?

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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