Dataset1/D1T5S1n

From Jsarmi

“I remember that I proved this once but I forgot...”

In addition to following the prospective unfolding of the particular instance of a team’s recommencement, we can also investigate retrospectively drago’s “bridging post” in session two (line 306: “you always have to move a certain amount to the left/right and a certain amount to the up/down”). We could do this by analyzing his prior work with estrick a few days back and explore the genesis of the reported finding. This approach would allow us to stretch the scope of our analysis not only from one problem-solving episode into another but also from one particular collectivity (drago-estrick-gdo-mathwiz) into a different one (the dyad drago-estrick). In essence, line 306 in session two appears as a re-statement of something that drago and estrick discovered in the first session that they held as a team. The following excerpt illustrates how this idea was articulated then:

 168 	estrick: well, judging by my calculations, any root that does not go along a diagonal is the same length   
 169 	drago: it should be (Points to line 168) 
 170 	drago: except if you go some extra long way for no reason 
 171 	estrick: haha, precisely 
 172 	drago: but why are they the same? I remember that I proved this once but I forgot... 
 173 	estrick: because you will alsways have to go down and to the right the same amount of times 
 174 	drago: oh, seems reasonable (Points to line 173) 
 175 	drago: so...any more questions you can think of? 
 176 	estrick: but i am not sure of the correct proof 
 177 	drago: well...I guess its because whatever path you take, you will make tiriangles (Points to line176 

The relationship between line 173 in this excerpt of session one and line 306 of session two appears significant. On the one hand, the use of the adverb “always” in both postings seems to suggest a rule-like statement (or a conjecture) aimed at capturing a constructed understanding about the way the grid-world works (from the participants’ perscpective). The fact that the creator of this text changes from estrickm in session one to drago in session two could be taken as an indicator that this rule is a collaborative understanding achieved by the dyad which is, later on, projected into a new collectivity and a “bridged” problem-solving context. Based on this observation, we could construe the re-statement of prior findings and the change in authorship as indicators of sustainability in the co-construction of knowledge as the history of multiple teams in an online community evolves. Although not entirely conclusive, these two conditions certainly seem to point in that direction despite the fact that in small-group interactions the notion of authorship needs to be analyzed critically. For instance, if line173 is a response to line 172 and proceeds from the flow of the interaction, isn’t it really the dyad who should be credited with having produced the original rule about the grid-world? These kinds of interactions point to the need to carefully redefine the notion of authorship as we navigate individuals, small-groups and larger collectivities engaged in knowledge building.

Beyond the apparent changes in authorship, it is interesting to note how drago’s text in line 306 of session two, differs from estrickm’s original posting from session one. Originally, there was only mention of moving “down and to the right,” but in drago’s restatement, one has to move a certain amount “to the left/right and a certain amount to the up/down.” Why has drago modified the original rule by adding the “/up” and “left/” elements? At this point, we need to mention that the environment in which these teams are interacting is much more complex than what is captured by the transcripts we have presented. In addition to the chat interface, a shared whiteboard is available to the participants in the virtual room provided. At the moment in session two when the exchanges that we have presented took place, the whiteboard in this team’s meeting room contains the picture in Figure 2. We can see in this snapshot the points that they selected to explore the grid-world and also some elements of how they have graphically presented their reasoning about it. Interestingly, a very similar diagram was used by estrick and drago in session one, as can be seen in Figure 3. However, in that case the diagram only included two points similar in their arrangement to points A and B in the diagram from session two. The arrangement of points used in session one matches estrick’s original rule that “you will always have to go down and to the right.” On Figure 2, there are two arrangement of points being considered: The one involving points A and B where the shortest path would be achieved by going down and to the right and another in which the movement would be up and to the right (linking the points labeled with circles). One can then read drago’s modification to the original rule as indication that he has adapted it to make it applicable to all arrangements of points based on the cases used by the team in this session.

Figure 2. Snapshot of Team 5’s whiteboard, Session 2.

Figure 3. Snapshot of Team 5’s whiteboard, Session 1

It is possible that drago realized this generalization via further individual work in between team sessions, or that the position on the grid of the points that the team has selected in session two provided the need for the generalization to happen. Whatever the actual motive, drago is presenting in session two a modified version of the finding previously constructed suited to the current circumstances. Beyond simply citing prior findings, drago has in fact bridged two problem-solving contexts in an attempt to construct continuity To further qualify this observation, we can contrast drago’s tentative reasoning for why the rule works presented in line177 of session one (well...I guess its because whatever path you take, you will make tiriangles) with the sense of confidence that his presentation conveys in session two. This subtle change could illustrate a change in the strength of his understanding of the grid-world. Observations like these, although requiring further verification through triangulation and further analyses, start to point to critical interactional aspects of how knowledge work is sustained over time and hint towards longitudinal aspects of collaborative learning interactions. Furthermore, they reveal the need to understand how bridging interactions span across the individual and the different collectivities involved in an online community.