Ming Ming Chiu State University of New York – Buffalo

1. 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

2. 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-creativity

3. Solving 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?

4. 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 )

5. What Affects Micro-creativity? • Social Metacognition? • Face / Rudeness?

6. 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 )

7. 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)

8. Face / Rude • Disagree Rudely • Excessive Agreement • Command !

9. 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 )

10. 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 )

11. 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 )

12. 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 )

13. Social Metacognition 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 …

14. 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 

15. 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

16. 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 ( _. )

17. 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)

18. Coded Transcript Add other variables at each speaker turn: Student: Gender, ethnicity, mid-year algebra grade, … Group: Group’s mean mid-year algebra grade, …

19. 4 types of AnalyticalDifficulties Time Outcomes Explanatory variables Data set Statistical Discourse Analysis

20. Statistical Discourse Analysis • Difficultiesregarding Time • Time periods differ (T2 T4) •  Serial correlation (t8→ t9) • Strategies • Breakpoint analysis

21. 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

22. Breakpoints in 1 group 100% 80% 60% % New ideas 40% 20% 0% 0 10 20 30 Time (mins) % Micro-creativity

23. 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)

24. Statistical Discourse Analysis • Outcome Difficulties  Discrete outcomes (Yes / No) • Multiple outcomes (Y1, Y2) New idea & Justify • Strategies  Logit / Probit • Multivariate, multilevel analysis

25. Statistical Discourse Analysis • Explanatory model Difficulties • People & Groups differ • Mediation effects (X→M→Y) • False positives (+ + + +) • Effect across turns (X6→Y9) 

26. Effects across several turns 2 speakers ago = (– 2) 1 speaker ago = (– 1) Ben: 10 times 18 is Eva: 28. Jay: Wrong, 180 dollars.

27. 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) 

28. VAR models effects across turns

29. 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

30. 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

31. 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

32. 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

33. 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.

34. 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

35. 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

36. Unsupported Hypotheses Questions were not linked to New idea or Justifications Rudely disagreements were not linked to Justifications

37. 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 

38. 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

39. 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?

40. Thank you!

42. Statistical Discourse Analysis 

43. 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

44. Mathematics Bayesian Information Criterion Regression specification