Dataset1/Collective Remembering

From Jsarmi

Session 4 - Team 5

In the last session of one of team five, the facilitator produces a summary of the teams’ prior work and suggests that they continue from that point. However, the team has some new members and others who had missed the previous sessions, so this recommencement of the prior work was problematic. One of the participants who attended the last session attempts to remember what they were doing, and by doing so engages the group in the Figure 5. Shared whiteboard of Team 5, session 4. collective remembering of that prior work as can be seen in the following chat log:

 121 MFmod:      I think that the above section I wrote is where the group last was
 122 MFmod:      yes?
 123 drago:      well
 124 gdo:        i dont remember that
 125 drago:      actually, my internet connection broke on Tuesday
 126 drago:      so I wasn't here
 127 MFmod:      so maybe that is not the best place to pick up
 128 estrick:    i wasnt able to be here on tuesday either
 129 gdo:        how bout u meets
 130 meets:      uh...
 131 meets:      where'd we meet off....
 132 meets:      i remember
 133 gdo:        i was in ur group
 134 meets:      that we were trying to look for a pattern
 135 gdo:        but i didn't quite understand it
 136 gdo:        can u explain it to us again meets
 137 meets:      with the square, the 2by 2 square, and the 3by2 rectangle
 138 meets:      sure...
 139 meets:      so basically...
 140 gdo:        o yea
 141 gdo:        i sort of remember
 142 meets:      we want a formula for the distance between poitns A and B
 143 drago:      yes...
 144 meets:      ill amke the points
 145 MFmod:      since some folks don't remember and weren't here why don't you
                  pick up with this idea and work on it a bit
 146 meets:      okay
 147 meets:      so there are those poitns A and B
 148 meets:      (that's a 3by2 rectangle
 149 meets:      we first had a unit square
 150 meets:      and we know that there are only 2 possible paths......

One of the things that are remarkable about the way this interaction unfolds is the fact that although it might appear as if it is Meets who remembered what they were doing last time, the actual activity of remembering unfolds as a collective engagement in which different team members participate dynamically. In fact, later in this sequence there is a point where Meets remembers the fact that they had discovered that there are 6 different shortest paths between the corners of a 2-by-2 grid but he reports that he can only “see” four at the moment. Even though Drago did not participate in the original work leading to that finding, he was able to see the six paths when Meets presented the 2- by-2 grid on the whiteboard and proceeded to invent a method of labeling each point of the grid with a letter so that one can name each path and help others see it (e.g., “from B to D there is BAD, BCD …”). After this, Meets was able to see again why it is that there are six paths in that small grid and together with Drago, they proceeded to investigate, in parallel, the cases of a 3-by-3 and a 4-by-4 grid using the method just created. The result can be seen on the whiteboard:.

Despite the fact that this picture is a restrictively static representation of the team’s use of the whiteboard, it allows us to illustrate some unique aspects of this remarkable creative organization of their collective activity. First, we see again the crucial role of indexicals and referencing activity in the collective construction of the mathematical ideas of the team (e.g., through the use of labels, the witnessing of actions on the whiteboard, and the coordination of parallel activity).

The use of the whiteboard represents an interesting way of making visible the procedural reasoning behind a concept (e.g., shortest path). The fact that a newcomer can use the persistent history of the whiteboard to re-trace the team’s reasoning seems to suggest a possible strategy towards preserving complex results of problem-solving activities. However, the actual meaning of these artifacts is highly situated in the doings of the co-participants, a fact that challenges the ease of their reuse despite the availability of detailed records such as those provided by the whiteboard history.

Despite these technical limitations, we could view the artifacts created by this team as “bridging” objects which, in addition to being a representation of the teams’ moment-to-moment joint reasoning, could also serve for their own future work and for other members of the VMT online community. These particular objects are constructed in situ as a complex mix of resources that “bridge” different points in their own problem-solving and, potentially, those of others. As can be seen in Figure 4, the two team members combined the depiction of the cases being considered, the labeling and procedural reasoning involved in identifying each path, a summary of results for each case (i.e., the list of paths expressed with letter sequences) and a general summary table of the combined results of both cases. The structure of these artifacts represents the creative work of the team but also documents the procedural aspects of such interactions in a way that can be read retrospectively to document the past, or “projectively” to open up new possible next activities.