as you come in… take a sheet think about what how you would answer the questions: as a sixth...
TRANSCRIPT
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
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
Questions (implicit and explicit)
asked during small group
discourse as pairs of middle
school students formulate
argumentations for carefully
designed probabilistic/ informal
inference tasks
Initial Research Focus
Data
10 day probability unit 6 separate tasks
Students Sixth grade Urban, public
middle school Pairs of students
3 focus groups by ability
Data
Classroom video Focus group video Screen Capture Focus group audio Written work
Process Convert to digital
format Line up audio/video Transcribe Code
Probability Explorer
Stohl (1999-2005)
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
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
What would you do?
What are your approaches?
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.
What would you do with this data?
What kinds of questions would come up in a discussion to answer these two questions?
How does that reflect on nature of discussion?
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.
Questions (implicit and explicit)
asked during small group
discourse as pairs of middle
school students formulate
argumentations for carefully
designed probabilistic/ informal
inference tasks
Initial Research Focus
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)
Questions (implicit and explicit)
asked during small group
discourse as pairs of middle
school students formulate
argumentations for carefully
designed probabilistic/ informal
inference tasks
Initial Research Focus
Argumentation Framework
Toulmin, 1969
ClaimData
Warrant
Qualifier
Backing
Rebuttal
Questions (implicit and explicit)
asked during small group
discourse as pairs of middle
school students formulate
argumentations for carefully
designed probabilistic/ informal
inference tasks
Initial Research Focus
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?
Bloom’s Taxonomy
Bloom’s Taxonomy Revised Bloom’s Taxonomy
Lorin Andersonhttp://www.odu.edu/educ/roverbau/Bloom/blooms_taxonomy.htm
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?”
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
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)
Teacher can quickly change the tone of a student-to-student conversation
Students ask: Verification
Questions Few high level
questions
Back to the Classroom: Discourse
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
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.