VMT CSCL Workshop June 2004

1. VMT CSCL WorkshopJune 2004

2. VMT CSCL WorkshopJune 2004 Collaborative Problems and Pedagogy

3. overview • Pedagogical purpose • VMT Year I experiments • Collaborative math problem solving in classroom settings VMT Workshop June 2004

4. 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 VMT Workshop June 2004

5. 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 VMT Workshop June 2004

6. 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 VMT Workshop June 2004

7. 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 VMT Workshop June 2004

8. 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 VMT Workshop June 2004

9. 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 VMT Workshop June 2004

10. 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 VMT Workshop June 2004

11. 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 VMT Workshop June 2004

12. 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 VMT Workshop June 2004

13. 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 VMT Workshop June 2004

14. 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 VMT Workshop June 2004

15. 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 VMT Workshop June 2004

16. 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 VMT Workshop June 2004

17. 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 VMT Workshop June 2004

18. 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 VMT Workshop June 2004

19. 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 VMT Workshop June 2004

20. 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 VMT Workshop June 2004

21. 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 VMT Workshop June 2004

22. 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? VMT Workshop June 2004

23. 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 VMT Workshop June 2004

24. 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 VMT Workshop June 2004