1. VMT CSCL Workshop June 2004

2. Collaborative Problems and Pedagogy

3. VMT Workshop June 20043 overview Pedagogical purpose VMT Year I experiments Collaborative math problem solving in classroom settings

4. VMT Workshop June 20044 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

5. VMT Workshop June 20045 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

6. VMT Workshop June 20046 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

7. VMT Workshop June 20047 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

8. VMT Workshop June 20048 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

9. VMT Workshop June 20049 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

10. VMT Workshop June 200410 Gerry’s classes (continued) Circle Inscribed in a Triangle Blackboard, groups of 2-5 residue: logslogs 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

11. VMT Workshop June 200411 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

12. VMT Workshop June 200412 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

13. VMT Workshop June 200413 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

14. VMT Workshop June 200414 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

15. VMT Workshop June 200415 Problems of the Week non-routine challenge problems posted bi-weekly in Math Fundamentals, Pre-Algebra, Algebra, and GeometryAlgebra coordinated somewhat with school curriculum refined during “Math Monday” refined 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

16. VMT Workshop June 200416 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

17. VMT Workshop June 200417 PoW-Wows Algebra and Geometry PoWs were used for PoW-Wows students registered ahead of timeregistered initially students first saw the problem at the PoW-Wow, later they got it beforehand

18. VMT Workshop June 200418 PoW-Wows (continued) facilitators used a minimal script to maintain consistencyscript facilitator offered no math help, just technical support students could IM the facilitator a picture, which was put on the webpicture

19. VMT Workshop June 200419 PoW-Wows (continued) residue: logs—lots of logs!—and followup formslogs observations: the amount of math varied greatly decent sharing and helping, but not always a lot of “collaborating” learning did take place

20. VMT Workshop June 200420 how collaboration can look in 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

21. VMT Workshop June 200421 how collaboration is different in the 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

22. VMT Workshop June 200422 questions we have about possible 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?

23. VMT Workshop June 200423 collaborative problem solving in a classroom setting http://www.mathgoodies.com/articles/coo p_learning.shtm http://www.mathgoodies.com/articles/coo p_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 http://www.pbs.org/teachersource/whats _new/math/tips298.shtm from PBS, tips for promoting positive interdependence within groups

24. VMT Workshop June 200424 collaborative problem solving in a classroom setting http://www.keypress.com/DG/resources/ TeachingWithDG.html 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/mat h/class/cooplist.html http://www.wou.edu/las/natsci_math/mat h/class/cooplist.html 60 (research-supported) reasons why CL is a good idea, originally posted to a CL list