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------=_NextPart_01C5FA3E.0DF8E960 Content-Location: file:///C:/2CF61D13/icceslides_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C5FA3E.0DF8E960 Content-Location: file:///C:/2CF61D13/icceslides_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" ICCE 2005 Slides
1
Sustaining Online <= /span>Collaborative Problem Solving with Math Proposals
Gerry Stahl
Drexel University, Philadelphia, USA
Gerry.Stahl@drexel.edu
www.cis.drexel.edu/faculty/gerry
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Promoting Collaborative Learning
<= span class=3DBB style=3D'position:absolute;left:-3.88%'>ØHow can we promote collabora= tive learning?
ØFor example, math discourse = and math problem solving skills & discourse. ØHow can we create an online world-wide = community of students engagi= ng in chats about math with their peers?
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The VMT Project
ØVirtual Math Teams (VMT) at the Math Forum @ Drexel University. <= /span>
ØResearch project – groups of 3-6 algebra & geometry students in chat r= ooms with challenging problems of math worlds to explore.
Ø“= ;If two equilateral triang= les have edge-lengths of 9 cubits and 12 cubits, what is the edge-length of the equilateral triangle whose area is equal to the sum of the areas of the other = two?”= ;
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How Do Students Sustain Interactio= n?
ØHow do students “do math” together onlin= e in small groups?
ØHow do they get started, decide what to talk about, and keep the= interaction going?
ØAn empirical question!
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How Can We Help to Sustain their Knowledge Building?
<= span style=3D'font-size:88%'>ØInteraction ta= kes place in the moment.
ØLearning takes place over time, across interactions.&= #13;= ØHow can the software design and the curriculum scaffolding sustain t= he knowledge that= is built in brief moments of interaction? (Goals of VMT project)
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Proposals:
A Method for Susta= ining
ØWe will identify a “me= thod of interaction”: making proposals
ØWe will look at how one smal= l group did “making proposals” in a simple chat environment.
ØA “method” is a recurrent pattern of interaction, shared by members of the community.
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The Transcript
&O= slash;A 3 ½ minute excerpt from an hour chat
Ø =
&O= slash;Contains several proposals
–6 proposal bids that get taken up by others
–1 failed proposal that is ignored in the chat
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8
Example chat log
= Ø1. Avr (8:21:46 PM): Okay, I think we should start with the form= ula for the area of a triangle
2. Sup (8:22:17 PM): ok 3. Avr (8:22:28 PM): A =3D 1/2bh
4. Avr (8:22:31 PM): I believe
5. pin (8:22:35 PM): yes
6. pin (8:22:37 PM): i concue
7. pin (8:22:39 PM): concur*
8. Avr (8:22:42 PM): then find the area of each triangle
9. Avr (8:22:54 PM): oh, wait
10. Sup (8:23:03 PM): the base and heigth are 9 and 12 right?
11. Avr (8:23:11 PM): no
12. Sup (8:23:16 PM): o 13. Avr (8:23:16 PM): tha= t's two separate triangles
14. Sup (8:23:19 PM): ooo
15. Sup (8:23:20 PM): ok
16. Avr (8:23:21 PM): right
17. Avr (8:23:27 PM): i t= hink we have to figure out the height by ourselves
18. Avr (8:23:29 PM): if possible
19. pin (8:24:05 PM): i k= now how
20. pin (8:24:09 PM): draw the altitude'
21. Avr (8:24:09 PM): how?
22. Avr (8:24:15 PM): right
23. Sup (8:24:19 PM): proportions?
24. Avr (8:24:19 PM): this is frustrating
25. Avr (8:24:22 PM): I don't have enough paper
26. pin (8:24:43 PM): i think i got it
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9
14
&= #13;
&= #13;
&= #13;
13
&= #13;
12
&= #13;
&= #13;
&= #13;
11
&= #13;
10
&= #13;
&= #13;
&= #13;
9
&= #13;
&= #13;
8
&= #13;
&= #13;
&= #13;
7
&= #13;
&= #13;
6
&= #13;
&= #13;
5
&= #13;
4
&= #13;
&= #13;
3
&= #13;
2
&= #13;
&= #13;
&= #13;
1
&= #13;
SUP
AVR
PIN
&= #13;
28
&= #13;
&= #13;
&= #13;
27
&= #13;
&= #13;
26
&= #13;
25
&= #13;
&= #13;
24
&= #13;
23
&= #13;
&= #13;
&= #13;
22
&= #13;
&= #13;
21
&= #13;
&= #13;
&= #13;
20
&= #13;
&= #13;
19
&= #13;
18
&= #13;
&= #13;
17
&= #13;
&= #13;
16
&= #13;
15
&= #13;
&= #13;
SUP
AVR
PIN
adjacency pair
other uptake
intersubjective <= /span>small-group meaning making
co-construction <= /span>of sequentiality in doing math
=
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=
“Math Proposal Adjacency Pairs”
ØWe define the method of group interaction in terms of a recurrent patt= ern of proposal bid/uptake
Ø= Proposals are only effective as interactional phenomena, not as “expressions of internal mental representations” of individuals
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<= ![endif]>
Structure of a Proposal
Ø1. A bid for a proposal is made by an individual for the group to work on: “I think we should= ….” =
Ø2. An acceptance, confirmation or up-take is made on behalf of the group by a second person: “Ok,” “right”= ;
Ø3. There is an elaboration of the proposal by members of the group. The proposed <= /span>work is begun, often with a secondary proposal for the first sub-step.
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A “Failed Proposal”
ØA failed attempt to initiate a proposal interaction
<= span class=3DBB style=3D'position:absolute;left:-5.2%'>ØA “breakdown” case
<= span class=3DBB style=3D'position:absolute;left:-5.2%'>ØHighlights conditions for success
<= span class=3DBB style=3D'position:absolute;left:-5.18%'>ØA promis= ing place to look closely
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=
Comparing Proposals
Ø17, 18. Avr (8:23= : 29 PM): i think we have to figure out the height by ourselves … if po= ssible
19. pin (8:24:05 PM): i know how
21. Avr (8:24:09 PM): how?
20. pin (8:24:09 PM): draw the altitude'
22. Avr (8:24:15 PM): right
24. Avr (8:24:19 PM): this is frustrating […]
<= span class=3DBB style=3D'position:absolute;left:-4.18%'>Ø23. Sup (8:24:19 PM): proportions?= <= /div> Ø25. Avr (8:24:22 PM): […] I don't have enough paper
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Problems with the Failed Proposal Bi= d
<= span class=3DBB style=3D'position:absolute;left:-4.31%'>ØA. No cl= ear semantic, syntactic structure
ØB. Timin= g within the flow of discussion
<= span class=3DBB style=3D'position:absolute;left:-4.79%'>ØC. No interruption of on-going work
<= span class=3DBB style=3D'position:absolute;left:-4.41%'>ØD. Doesn= ’t elicit some kind of response
<= span class=3DBB style=3D'position:absolute;left:-4.86%'>ØE. Doesn’t  specify work t= o be done
ØF.  Not based on a history of helpful work
<= span style=3D'visibility:hidden'>Ø
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What Methods Do Students Use?
ØTo form themselves into groups
ØDefine a problem to work on&= #13;
ØStart work
ØAgree on how to proceed =
ØBring in math resources =
ØAgree on solutions
ØClose the problem solving= 3;
ØGet to know each other
ØSocialize, have fun, flirt&#= 13;
ØAdapt to institutional setti= ng
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Conclusions:
Practical & Theoretical
ØA group can advance through math proposal adjacency pairs= 3;
Ø It would help to have support to <= /span>keep going without getting (a) stuck or (b) sidetracked
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Potential Helpful Computer Supports<= /span>
<= span class=3DBB style=3D'position:absolute;left:-4.1%'>Ø1. A pers= istent and visible list of proposals
<= span class=3DBB style=3D'position:absolute;left:-3.94%'>Ø2. A per= sistent and visible summary of work
<= span class=3DBB style=3D'position:absolute;left:-3.89%'>Ø3. Perha= ps a proof template that gets filled in
Ø4. Representations of the developing problem, such as a shared drawing whiteboard for geometry problems
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18
VMT-Chat Prototype
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