VMT CSCL WorkshopJune 2004

VMT CSCL WorkshopJune 2004

Collaborative Problems and

Pedagogy

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overview Pedagogical purpose VMT Year I experiments Collaborative math problem solving in

classroom settings

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purpose - math collaborative learning current math pedagogy theory:

• students construct math understandings, not memorize facts & algorithms

• students discuss math understanding• build on everyday contexts: story settings

collaborative learning• shared representation & construction• learn by sharing/discussing/teaching

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purpose - why collaborative learning and problem solving? learn and practice the essential life skill of

working with others exposure to more ideas for solving problems students who are good in social situations can

gain confidence in their mathematical abilities students understand an idea more deeply if

they have to articulate it for someone else students learn to solve more complex

problems than they could on their own

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purpose - why do these experiments? observe collaboration in problem solving

using existing settings in order to understand the issues that might be addressed through the design of the software and the math problems

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VMT Year I experiments our own practice chats

• VMT folks explore Blackboard and AIM Sharswood Middle School

• 8th grade classroom in Philadelphia Gerry’s Drexel Classes

• undergrads and graduate students PoW-Wows

• middle and high school students taking Algebra and Geometry (mostly), advertised through our Problems of the Week

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Sharswood Middle School one observation visit, one “teaching” visit residue: videotape, audiotape observations:

• Observe detailed math practices of students• Collaboration as “parallel working”• Mutual help so all learn together

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Gerry’s classes ISYS 310 - Human Computer Interaction II

• undergraduates (seniors), design and evaluate prototypes for supporting student groups to collaboratively learn mathematics

INFO610 - Analysis of Interactive Systems• masters and doctoral students, analyze the support of

student teams collaboratively doing mathematics problem solving

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Gerry’s classes (continued) Circle Inscribed in a Triangle

• Blackboard, groups of 2-5• residue: logs• observations

• primary goal was to get used to working collaboratively and to try out the virtual classroom in Blackboard

• not enough time to make much progress on the math problem itself

• many people did not remember basic formulas from high school geometry and had to spend time searching the web for information about triangles

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Gerry’s classes (continued) Tangent Square and Circle

• Blackboard, 10 groups of 2-5• residue: logs• observations

• providing math facts did not help • range of problem-solving abilities• range of collaboration & math approaches

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Gerry’s classes (continued) Taxicab Geometry

• face-to-face, same groups• residue: videotapes, interviews, focus groups,

surveys• observations

• wide range of math skills: constructive/procedural• different collaboration styles, roles• video clips to analyze tomorrow morning

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Gerry’s classes (continued) Getting Your Ducks in a Row

• Blackboard, same groups• residue: logs• observations

• no math facts required• representations, crank out possibilities• different kind of math problem

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PoW-Wows based on the Math Forum’s existing

Algebra and Geometry Problems of the Week

20 dates, Sunday and Thursday nights used AOL’s Instant Messenger number of participants ranged from 1 to

7, so groups of 1 to 5

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Problems of the Week non-routine challenge problems posted bi-weekly in

Math Fundamentals, Pre-Algebra, Algebra, and Geometry

coordinated somewhat with school curriculum refined during “Math Monday” used by teachers in schools and individuals goals of problem solving and communication Dr. Math support sometimes provided sample submissions and comments are eventually

posted

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PoWs (continued) students can submit answers and request

mentoring from volunteers and (limited or subsidized) staff

scoring is done via a rubric which emphasizes problem solving and communication

an answer (no explanation) is provided, and revision is encouraged

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PoW-Wows Algebra and Geometry PoWs were used

for PoW-Wows students registered ahead of time initially students first saw the problem at

the PoW-Wow, later they got it beforehand

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PoW-Wows (continued) facilitators used a minimal script to

maintain consistency facilitator offered no math help, just

technical support students could IM the facilitator a picture,

which was put on the web

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PoW-Wows (continued) residue: logs—lots of logs!—and

followup forms observations:

• the amount of math varied greatly• decent sharing and helping, but not always a

lot of “collaborating”• learning did take place

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how collaboration can lookin a classroom setting grouping is sometimes random, sometimes not groups are often changed every 4-6 weeks, or

each quarter roles usually assigned with some explanation of

responsibilities (facilitator, recorder, reporter, etc.)

all individuals are responsible for learning the material and reporting back

teacher circulates to “poke and prod” as necessary when groups seem stuck

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how collaboration is different inthe PoW-Wows grouping is totally random at this point

and is limited by low participation registration process is unreliable (lots of

no-shows) students don’t know each other, for the

most part no intervention from facilitator

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questions we have aboutpossible future experiments would we attempt to create groups with varying

ability levels if we had longer term data from repeat participants?

“dummy” participants modeling better cooperative communication (questioning, explaining, confirming)?

starting with groups that have learned and used face-to-face collaborative learning, then moving them to the virtual environment?

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collaborative problem solving ina classroom setting http://www.mathgoodies.com/articles/

coop_learning.shtm• secondary teacher Gisele Glosser explains

what CL looks like in her classroom and what how it works

http://www.pbs.org/teachersource/whats_new/math/tips298.shtm• from PBS, tips for promoting positive

interdependence within groups

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collaborative problem solving ina classroom setting http://www.keypress.com/DG/

resources/TeachingWithDG.html• about teaching with the Discovering Geometry

textbook, which encourages group work and collaboration

http://www.wou.edu/las/natsci_math/math/class/cooplist.html• 60 (research-supported) reasons why CL is a

good idea, originally posted to a CL list