Roy D. Pea, Stanford University; Shelley V. Goldman, Stanford University; Kristen Pilner Blair, Stanford University; Osvaldo Jimenez, Stanford University

How and when do families collaborate on math?

• family as cultural context for doing math
• design points of synergy - math at family and math at school
• families are the first, effective learning settings
• thought as a solitary endeavour - understand math as concerted activity and problem-solving
• family as unit of analysis
• math that families encounter in their daily life

23 families

• interviewed at home
• together choose a cell-phone plan

Findings

• families learn and do math in a number of contexts
• ongoing activities, home improvement, work, game play
• math organized by problems they have to solve
• problems tackled with resources that are ready at hand
• difference between family math and school math
  • at school
    • math for math's sake
    • focus on one kind of math at a time
    • one correct solution, answer right or not, avoid error
    • evaluation by others
  • home
    • solving problems
    • multiple kinds of math
    • multiple solutions and levels of precisions
    • multiple solution attempts
    • self-perceived confidence, and being able to move on

Our environments need to

• be driven by situations
• promote enjoyment of math
• demonstrate value of mathematizing experience
• compelled by values
• use family as a social unit
• complement school
• use affordances of mobiles
• based on family math research

Hypothesis: family interactions + mobile apps → collaborations around math

Building on family communications

• active and intimate participation
• time spent together
• turn taking and conversational participation

Mobiles

• short activity bursts
  • down-time play
  • families in each other's business
  • game-like features and problem solving
• mobile affordances
  • anytime, anywhere
  • social uses

Go Roadtrip! (app)

Study tensions and findings

• families eager to join study, yet find it difficult to organize study-related time on their own
• access to phone not a given - apps are on mother's phone, doesn't want to give it to the kids
• pre-survey of kids reveals view of math as solitary activity
• kids mostly playing a certain of the games in the suite - the most game-like and fast-moving one

Carmen Julia Petrick, The University of Texas at Austin; Taylor Martin, The University of Texas - Austin; Matthew W. Berland, The University of Texas - San Antonio; Tom Benton, The University of Texas - Austin

How does physical embodiment change the way students learn to program

• actions
• perspective taking

Literature review

• Papert had kids who had problems with programming Turtle actually act out the path of the turtle (body syntonicity)
• Act our programs vs imagine acting out programs (actually acting out - more complex programs in the future)
• Physical robots vs virtual robots - physical robots more likely to take agent based, virtual robots more likely to take top-down perspective

Ideas

• perspective taking
  • first person perspective, getting into the action
• collaboration
  • 3rd person perspective
• students need to be able to take information from one perspective to translate it to another context

IPRO - programming game, students program virtual robots to play soccer

• mobile (iPod) - take their program with them
• social - walk over and show my friend my code, etc.

Data

• video
• log data (every time they made a change)
• student interview
• pre/post-test

Analysis

• case study of one specific student
• sequence
  • talking to another student - 3rd person perspective
  • steps back, moving this way and that way, pretending to be the robot - 1st person
  • walks back over to Roger, explain change she has made, 3rd person

Lee Michael Martin, University of California - Davis; Pamela R. Gourley-Delaney, University of California - Davis

Photo sort task

• does it involve math or not?
• disposable camera - take photos of math things
• upload photos, caption and choose to share
• view classmates' photos and comment on them
• small group discussions
• photo sort task again

• level of experience with an activity predicted students' judgment on whether that activity “involved math”
• compared with undergraduate rations
• variation in expansive or narrow stance on “what counts as math” - possibility vs necessity of math

Steven Edward Higgins, Durham University; Emma M. Mercier, Durham University; Elizabeth Louise Burd, Durham University

Four multi-touch tables (MTT), easily send things between tables, from teacher to tables, or to the projector (networked).

Questions

• how do tables support small-group collaborations
• how does inter-group collaboration and whole classroom context work

Framework (for CSCL research/design)

• technology
• teams
• tasks
• teachers (could be more-expert peers, facilitators, something in the technology itself etc)

Technology and teams

• MTT: more joint attention, more quickly developed a joint problem space

Room orientation

• more talk in centered room (and teachers didn't like it)
• more correct answers in traditional room
• BUT no difference in off-topic talk - they're talking more about the tasks, but not solving them any faster
• maybe higher levels of participation in centered room, front-facing room leaving it to top two-three students

Teams & tasks

• emergent roles
  • type of leadership that emerged during different tasks
  • person identified as leader changed from history to math tasks
  • more leadership moves during math than history (they know who is good at math)

Technology & teachers

• really disliked separate desk in the front of the classroom, want to be able to walk around
• group in front of the teacher table gets almost no attention from teacher
• put it on an iPad, kind of liked it, still complained (don't like to hold onto something)
• looking into using Kinect to let teacher use gestures

Technology, team and tasks

• within and between group math learning
• nice examples of learning / getting spurred on from other group

Summary

• multi-touch supports joint attention
• room orientation changes interaction
• content area influences emergent roles
• access to teacher controls is an important feature of development work
• within and between group learning

Mike Tissenbaum, University of Toronto; James D. Slotta, University of Toronto; Michelle Lui, OISE/University of Toronto

• discourse patterns
• distributed expertise

• KCI dimension
• epistemological commitments
• pedagogical affordances
• technology elements