As you come in…

1. As you come in… • Take a sheet • Think about what how you would answer the questions: • As a sixth grade student • With what you know now

2. Analysis of Middle Grades Students' Questions During Probabilistic Tasks Cindy Goodson and Dr. Todd Lee Elon University North Carolina Council of Teachers of Mathematics October 29, 2009

3. Initial Research Focus • Questions (implicit and explicit) asked during small group discourse as pairs of middle school students formulate argumentations for carefully designed probabilistic/ informal inference tasks

4. Data • 10 day probability unit • 6 separate tasks • Students • Sixth grade • Urban, public middle school • Pairs of students • 3 focus groups by ability

5. Data • Classroom video • Focus group video • Screen Capture • Focus group audio • Written work • Process • Convert to digital format • Line up audio/video • Transcribe • Code

6. Probability Explorer • Stohl (1999-2005)

7. Initial Research Focus • Questions (implicit and explicit) asked during small group discourse as pairs of middle school students formulate argumentations for carefully designed probabilistic/ informal inference tasks

8. Informal Inference and PE Tasks • Definition • Mystery Fish in the Lake task • 2 days (Friday and Monday) • Determine the probability of catching a Blue Bass • Endless supply of fish to draw from

9. What would you do?

10. What are your approaches?

11. Transcription of video • DK: And we’re doing number of ten? • LK: Umm…I guess. • DK: Do you wanna try like fifteen or twenty? • LK: Hmm…Okay. (Runs trial of twenty, 6BB 14GG) • DK: Golly! Six…umm…blue fish. And…one, two, three, four, fourteen I think. One, two, three… • LK: Yeah that looks right on the bar graph. Copy. Save. • DK: Yeah. Do we have to do that? I mean they said write it down. • LK: No. Yeah. Okay, don’t do it then. • DK: Okay. • LK: I thought we were supposed to. (Runs trial of twenty, 6BB 14GG) • DK: Is it the same? • LK: That looks like six. • DK: One, two, three, four…It is. It’s the exact same thing. (Runs trial of twenty, 6BB 14GG) • DK: Okay, now this one's different...I hope. One, two... • LK: Six. • DK: Gee. I think we found our answer.

12. What would you do with this data?

13. What kinds of questions would come up in a discussion to answer these two questions? • How does that reflect on nature of discussion?

14. Just so you know… • LK: We could do like the average score, that might… • DK: What do you mean? • LK: Like the average out of these. That could be a way we find it. • DK: Like…add them and then divide by how many? • LK: Yeah.

15. Initial Research Focus • Questions (implicit and explicit) asked during small group discourse as pairs of middle school students formulate argumentations for carefully designed probabilistic/ informal inference tasks

16. Discourse • Why do we want students to talk? • “Builds meaning and permanence” (NCTM Standards) • Two minds are better than one • Why do researchers care about discourse? • Insight into formation of knowledge • Insight into thinking process • Thinking is discourse with oneself (Sfard, 2001)

17. Initial Research Focus • Questions (implicit and explicit) asked during small group discourse as pairs of middle school students formulate argumentations for carefully designed probabilistic/ informal inference tasks

18. Argumentation Framework • Toulmin, 1969 Rebuttal Qualifier Data Claim Warrant Backing

19. Initial Research Focus • Questions (implicit and explicit) asked during small group discourse as pairs of middle school students formulate argumentations for carefully designed probabilistic/ informal inference tasks

20. Lens of Questions • Current literature focuses on teacher questions • Quality of questions for education • Task development (Bloom’s taxonomy) • Our focus in student-to-student questions • How is this different?

21. Bloom’s Taxonomy Bloom’s Taxonomy Revised Bloom’s Taxonomy Lorin Anderson http://www.odu.edu/educ/roverbau/Bloom/blooms_taxonomy.htm

22. What Do Students Ask? • Classroom vs. Tutorial Setting (Graesser & Person, 1994) • Small groups • Questions of confirmation from partner • “Blue Bass are the small one, right?” • Questions to create common ground • “Okay, and how did we get that?”

23. Graesser & Person, 1994 • Question Mechanisms • Knowledge deficit • Common ground • Social-coordination • Conversation-control • Types of information-seeking questions • Verification • Disjunctive • Concept completion • Feature specification • Quantification • Definition • Example • Comparison • Interpretation • Causal antecedent • Causal consequence • Goal orientation • Instrumental/procedural • Enablement • Expectational • Judgmental • Assertion • Request/Directive

24. Categorizing Student Questions • Development of useful categories for student-to-student questions • Explicit/Implicit • Audience • Part of the argument addressed • Type of information seeking question (Graesser & Person, 1994)

25. Back to the Classroom: Discourse • Teacher can quickly change the tone of a student-to-student conversation • Students ask: • Verification Questions • Few high level questions

26. Back to the Classroom: Informal Inference Tasks Large trials are for play If there is a perceived formal method, students gravitate towards it and there is less informal statistical inference

27. Questions? Comments? cgoodson@elon.edu

28. References • Graesser & Person, 1994 • Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1), 13-57. • Toulmin, S. (1969). The uses of argument. Cambridge: Cambridge University Press.