VMT CSCL Workshop June 2004

Collaborative Problems and Pedagogy

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

VMT Workshop June 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 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 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 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 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 Gerry’s classes ISYS 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 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

VMT Workshop June 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 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 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 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 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

VMT Workshop June 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 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

VMT Workshop June 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

VMT Workshop June 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

VMT Workshop June 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

VMT Workshop June 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

VMT Workshop June 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?

VMT Workshop June collaborative problem solving in a classroom setting p_learning.shtm p_learning.shtm secondary teacher Gisele Glosser explains what CL looks like in her classroom and what how it works _new/math/tips298.shtm _new/math/tips298.shtm from PBS, tips for promoting positive interdependence within groups

VMT Workshop June collaborative problem solving in a classroom setting TeachingWithDG.html TeachingWithDG.html about teaching with the Discovering Geometry textbook, which encourages group work and collaboration h/class/cooplist.html h/class/cooplist.html 60 (research-supported) reasons why CL is a good idea, originally posted to a CL list