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Effects of Social Metacognition on Micro-Creativity : Statistical Discourse Analyses of Group Problem Solving Ming Ming Chiu State University of New York – Buffalo mingchiu@buffalo.edu 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 Metacognition Metacognition Monitoring and control of ones knowledge and actions ( Flavell, 1971; Hacker, 1998 ) Social Metacognition Group members monitoring and control of one anothers knowledge and actions ( Chiu, in press) Most individuals have poor metacognition. ( Hacker & Bol, 2004 )

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Social Metacognition Questions indicate knowledge gaps Identifies gap in someones 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 / Rude Face = Public Self-image Disagree rudely (attack face) vs. Disagree politely (save face) ( Brown & Levinson, 1987 ) Ten times two hundred. Disagree Rudely No, youre wrong, its 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 / 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 speakers 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 / 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 )

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Micro-creativity processes New ideas Justifications Face / Rudeness Politely Disagree (+) Rudely Disagree (–) Excessively Agree (–) Command (–) Social Metacognition Ask Questions (+) Disagree (+) Control variables Math grade Peer Friendship Gender, ethnicity, … Group mean grade, Group gender variance …

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Videotape Group Problem Solving 84 9 th 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 –Krippendorfs

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Content analysis Jay: A hundred eighty dollars. Ben: If we multiply by ten cents, dont we get a hundred and eighty cents? Ben –Disagrees politely –New information –Correct –Justifies –Question

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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 ( _. )

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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)

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Coded Transcript IDActionEPAKCValid?JustifyIF FayDo ten times eighteen.*C ! Ben Ten times eighteen is – +R _. EvaTwenty-eight.+CX_. JayWrong. A hundred eighty dollars. CX_. Ben If we multiply by ten cents, don t we get a hundred and eighty cents? -C J? FayYep.+ _. Add other variables at each speaker turn: Student: Gender, ethnicity, mid-year algebra grade, … Group: Groups 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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Difficulties regarding Time Time periods differ (T 2 T 4 ) Serial correlation (t 8 t 9 ) Strategies Breakpoint analysis

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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

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Breakpoints in 1 group % Micro-creativity 0% 20% 40% 60% 80% 100% 0102030 Time (mins) % New ideas

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Statistical Discourse Analysis Difficulties regarding Time Time periods differ (T 2 T 4 ) Serial correlation (t 8 t 9 ) 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 Analysis Outcome Difficulties Discrete outcomes (Yes / No) Multiple outcomes (Y 1, Y 2 ) New idea & Justify Strategies Logit / Probit Multivariate, multilevel analysis

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Statistical Discourse Analysis Explanatory model Difficulties People & Groups differ Mediation effects (XMY) False positives (+ + + +) Effect across turns (X 6Y 9 )

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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 Analysis Explanatory model Difficulties People & Groups differ Mediation effects (XMY) False positives (+ + + +) Effect across turns (X 6Y 9 ) 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)

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VAR models effects across turns IDActionJustifyDisagreeDisagree (-1) FayDo ten times eighteen.00- Ben Ten times eighteen is – 000 EvaTwenty-eight.000 JayWrong. A hundred eighty dollars. 010 BenIf we multiply by ten cents, don t we get a hundred and eighty cents? 111 FayYep.001

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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

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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

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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 generator AnaHow can they be equal? BobI dont know CateTry another number? DanWhich number? [8 seconds of silence; each student looks at own paper] Cate[looks at Anas paper] Yours is much closer. So, try a number close to yours Dan[looks at Anas paper] Mines even closer Ana[looks at Dans paper] Oh! More messages get us closer

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Creativity dampener KayLets try a hundred. LeeOk. Thats a thousand. TomAnd thats one, so nineteen. KayThats like over nine hundred away. JanMaybe its one of those trick questions. TomYeah, like it cant be done. KaySo, maybe theres no answer. LeeThen, were 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 Outcomes Explanatory model: New Idea & Justify

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Group + Time Period Differences Unsuccessful groups: Negative effect of Rudely disagree (-1) on new ideas Negative effect of Math grade (-1) on justifications Mathematics grades 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 peoples behaviors over time during … –Classroom conversations? –Online discussions? –A students think-aloud problem solving? –An infants learning of a new word? –Basketball games? –Stock market transactions? –Wars?

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Thank you!

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IDActionTurn #Valid? Previous Turn Valid (-1) AnaDo three times four.1 –– BenThree times four is seven2X1 EvaThree times four is nine.3X2X JayThree times four is twelve.4 3X IDActionTurn #Valid? Respond to turn #? Valid (-1) AnaDo three times four.1 –– BenThree times four is seven2X1 EvaThree times four is nine.3X1 JayThree times four is twelve.4 3X

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Statistical Discourse Analysis Analytical Difficulty Differences across topics Time periods differ (T 2 T 4 ) Serial correlation (t 8 t 9 ) Parallel talk ( ) Strategy Multilevel analysis Breakpoint analysis & Multilevel analysis I 2 index of Q-statistics; Model with lag variables Store path: ID prior turn, Vector Auto-Regression Discrete outcomes (Yes / No) Multiple outcomes (Y 1, Y 2 ) Infrequent outcomes (00010) Logit / Probit Multivariate outcome models Logit bias estimator People & Groups differ Mediation effects (XMY) 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

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