From Jsarmi

This dataset corresponds to 18 sessions held as part of the first VTM Spring Fest in 2005.
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Contents 1 Summary 2 Data Sources 3 Overarching Questions 3.1 Goals 3.2 Methods & Procedures 4 Trajectories 5 Summary of Cases 5.1 Other Cases? No uptakes

Summary

• Date: Spring of 2005
• Participants: Volunteer students, selected by invited teachers, grouped in 5 teams of 3 to 5 students
• Sessions: A series of 4 group chats per team lasting about one hour over a span of two weeks (Tuesday, Thursday, Tuesday, Thursday)
• Task: Open-ended mathematical task: Taxi-cab geometry
• Facilitation: A moderator was present in all sessions but tried not to participate in the math activity. Feedback was provided in between sessions

Data Sources

New VMT data site: http://vmt.mathforum.org/vmtdata/

Teams and Sessions

Team	Summary	Session 1	Session 2	Session 3	Session 4
Team 1	Summary	Transcript - Notes 0510g1.jno	Transcript - Notes 0512g1.jno	Transcript - Notes 0517g1.jno	Transcript - Notes 0519g1.jno
Team 2	Summary	Transcript - Notes 0510g2.jno	Transcript - Notes 0512g2.jno	Transcript - Notes 0517g2.jno	Transcript - Notes 0519g2.jno
Team 3	Summary	Transcript - Notes 0510g3.jno	Transcript - Notes 0512g3.jno	Transcript - Notes 0517g3.jno	Transcript - Notes 0519g3.jno
Team 4	Summary	Transcript - Notes 0510g4.jno	Transcript - Notes 0512g4.jno	Transcript - Notes 0517g4.jno	Transcript - Notes 0519g4.jno
Team 5	Summary	Transcript - Notes 0510g5.jno	Transcript - Notes 0512g5.jno	Transcript - Notes 0517g5.jno	Transcript - Notes 0519g5.jno

[data] (password protected)

Overarching Questions

• What are the interactional bridging methods that can be identified in these VMT online learning sessions?
• How can we effectively conceptualize these phenomena and analyze their interactional effects?
• How does bridging activity span across the teams' trajectories over time?

Goals

The central goal of this baseline design study is to reach an initial characterization of bridging phenomena and produce an initial survey of methods used by participants to engage in bridging activity. At this point, we define bridging as the interactional work that virtual math teams engage in when dealing with three specific discontinuities of their collective work: The discontinuity of their sequences of collaboration episodes (i.e. each online session they participate in), the discontinuities emerging from the different patterns of participation of individuals and collectivities (e.g. individual attendance to sessions, collective participation in relevant problem-solving work), and the discontinuities derived from diverse problem-solving perspectives brought forward during the collaborative interactions.

Methods & Procedures

The data for this study comes from 18 collaborative sessions held in the Spring of 2005 as part of the Virtual Math Teams project. Four teams of 3-5 secondary students. Recordings. The teams engaged in online math discussions for four hour-long sessions over a two-week period. We expect that the sequential nature of the mathematical tasks that will be utilized in addition to the collaborative nature of the multi-team setup will provide with a propitious setting for bridging work to be investigated.

• Team Composition and Evolution: Each team will be composed of three to four non-collocated, upper middle-school or high-school students. Participants will be recruited through the Math Forum online community and selected by volunteer teachers at different schools across the USA or abroad. To the extent possible, teams will be composed of students from different schools. Participants will use anonymous handles throughout the four sessions and will be encourage to behave in a natural way. Attendance to all sessions will be highly encouraged but because of the voluntary nature of the study and the naturalistic environment that the Math Forum entails, it is possible that changes in team composition will occur. However, we see these changes as propitious opportunities to study bridging and, as a result, they will be managed as such. Across the four sessions, we will encourage teams to stay together but changes in team membership might also occur due to attendance constraints or personal preference of the participants.

• Settings: The elements of the activity system that we expect to investigate in this study include the sequential structure of the task, the composition of the teams (as well as their development across sessions), and the online environment. We described these three elements below.

• The task: Teams will work on the “Grid world” mathematical task, which allows for both, collaborative problem finding and problem solving. In the first session, the teams will be given a brief description of this non-traditional geometry environment: a grid-world where one could only move along the lines of a grid. The students will be asked to generate and pursue their own questions about the grid-world, such as questions about the shortest distance between two points in this world.

Figure 2. Grid world task

The online sessions where facilitated by a member of the VMT research project team. In each session, the facilitator welcomed the students to the chat, introduced the task, and provided technical assistance regarding the special features of the collaboration environment. The facilitator did not actively participate in the team’s mathematical collaboration. After the first session, the teams received feedback on their prior work and the work of other teams. The instructions for each session directed teams to continue their prior work, consider the work of other teams or pursue new questions. We expect that these aspects of the task, including the feedback given to the teams, would promote sustained problem-solving work by the teams. The analysis of the data collect would then provide us with an opportunity to validate this expectation and analyze how continuity is established in interaction. The fact that the task is open for the team to find, formulate, and purse the questions that are of interest to the participants, leads us to predict that we will be able to observe a wide range of problem-solving activity including problem formulation, problem representation, strategic .

• Online Environment:. Participating teams will use the ConcertChat virtual room environment for their interactions. ConcertChat combines a persistent chat environment with a shared whiteboard and a set of special referencing tools to reduce ambiguity when referring to chat postings or objects on the whiteboard.

Figure 2. ConcertChat collaboration environment with references from chat to whiteboard

• In this study, the teams will be provided a new ConcertChat room for each one of the sessions. Teams will not have direct access to the persistent records of their interactions from previous sessions or those of other teams and will only learn about them in a direct way through the feedback provided by the facilitators. No additional information will be available directly in the system about the members of the teams, their meetings and results. We expect that the setup of the online environment can be considered one with no explicit computational supports for bridging. ConcertChat also provides a detailed and timed log of the room activity which includes a transcript of the chat discourse, a recording of all public activity performed on the whiteboard, and a detailed log of other interactional events such entering or exiting the room. This log can be replayed on a special research tool developed as part of the Virtual Math Teams project in order to have a naturalistic view of how the interaction was performed from the participants’ point of view.

Trajectories

Summary of Cases

By type, cases with uptake (16):

Reporting	Reconstructing	Projecting
[T1,S3] ITS A PERMUTATION!!! [T2,S2] we already did that yesterday [T4,S2] as we discussed on Tuesday [T4,S4] IH: So i thought of another question [T5,S2] last time, me and estrick came up / that [T5,S2] I think - it *was* [T5,S4] we arent getting anything done [T5,S4] permutation? i suggested that last time	[T2,S3] i'm not too sure what the formula i made up last week is [T2,S3] so do we go through the same steps again? [T2,S4] you do the same thing you did with the circle/so should I make the bird's eye view? [T5,S4] I remember…we were trying to look for a pattern…	[T2,S2] I guess we should ask him next time... [T4,S3] then we may be able to find out a formula [T5,S2] could solve that next time [T5,S3] ok so ... 1 by 1 --> 2…

By Team and Session, all cases

Team 1	Team 2	Team 3	Team 4	Team 5
[T1,S2] x M1 [T1,S3] Rw ITS A PERMUTATION!!! nu [T1,S3) Rw so lets draw some points on two diagonal corners (same arrangement as S2) lc [T1,S3] Local: mm: i didnt understand the reasoning for this [T1,S4] x	M1 [T2,S2] we already did that yesterday M3 [T2,S2] mathfun: I guess we should ask him next time... (him=bob1) M2 [T2,S3] bob1: i'm not too sure what the formula i made up last week is / i got it/ but then i forgot it / give me 5 minutes to reget it... M2 [T2,S3] so do we go through the same steps again? M2 [T2,S4] so should I make the bird's eye view? (bird's eye view was developed in S3) nu [T2,S4] LOTS OF IMPLICIT REFERENCES TO PRIOR WORK (e.g. "again")	[T3,S2] (cancelled) ne [T3,S3] (interrupted) Tp moves to T1 with his cylinder idea presented implicitly not explicitly [T3,S4] x	M3 [T4,S1] projecting? Fo remarks that one thing she noticed was "That no matter what kind of path you use, in the pretend world, the shortest is always 10 units" M2 [T4,S2] Fo: yes, except there is another path of the same distance/ Ja:sure, there are several more / as we discussed on Tuesday nu [T4,S3] so last week, we found out that if moving only right and down, it will always be 10 moves frm a to b / yea i got that - so wa do we do now??? nu [T4,S3] ssjnish, 20:45: we did a problem like this in class except you could only go east or south lc [T4,S3] ...then we may be able to find out a formula for the number of possibilities M1 [T4,S4] IH: So i thought of another question nu [T4,S4] IH: (collumns+1)(rows)(2)...the # of short paths (reintroduced from S3 where "(# of columns minus 1)*(# of rows)*2= all ways to walk" was found not to work)	M3 [T5, S1] projecting? well, judging by my calculations, any root that does not go along a diagnol is the same length/.../because you will alsways have to go down and to the right the same amount of times M1 [T5,S2] last time, me and estrick came up / that ... M1 [T5,S2] oh - ok - I get it now - I think - it *was* absolute value x1-x2, absolute value y1-y2 M3 [T5,S2] projecting? we could solve that next time M1 [T5,S3] want to first see the distance between points A and B first? M3 [T5,S3] ok so ... 1 by 1 --> 2, 2 by 2 --> 6 ... M2 [T5,S4] we were trying to look for a pattern / with the square...  ? [T5,S4] we arent getting anything done M1 [T5,S4] permutation? i suggested that last time (fa)

M1= reporting past, M2 = collective remembering, M3 = projecting nu= no uptake, lc = local continuity, ? = related activity, unclear

Other Cases? No uptakes

T#/S2 ModeratorX: So, last Tuesday, all groups generated a number of questions about the world that we had and we collected some of them for you to consider today. I am going to paste then on the whiteboard for you to look at

[T2/S2] mathisfun, 20:05 (12.05): though we already discuss the 8th with number 4 we this one uses more thinker involved

[T5/S2] dragon, 20:26 (12.05): the ones I thought of are already on the list from other group

[T5/S2] mathwhiz: ARE THERE defined points a and by ... drago: there were definite points originally

[T5/S2] Moderator: Drago and Es can fill (Gdog) in... dragon, 20:31 (12.05): basically, we worked on a problem...

[T5/S2] gdog, 20:37 (13.05): what are the points? / dragon, 20:32 (12.05): I don't remember

[T5/S2] dragon: but the question asked if there were solutions or an equation to find A and B if they had any location

[T5/S2] dragon, 20:50 (12.05): the shortest distance was 6 over and three down...

Theoretical memo