Dataset1/SandLines
From Jsarmi
Bridging problem-solving perspectives: “…it's like, you can't walk in water, and the lines are dry lines …”
The further unfolding of the excerpt from team five in session one which we analized before provides some more evidence on how bridging activity affects a problem-solving interaction. Starting with mathwiz’s posting in line 314 (“would you want to keep as close to the hypotenuse as possible? or does it actually work against you in this case?) continues the bridging activity opened up by drago in a unique way. Mathwiz’s posting suggests an active way of orienting towards drago’s presentation of how the grid-world had been found to work, while at the same time ratifying drago's position as the one who is to respond to assessments of his report (i.e. testing whether this case “works against you”). In this way, mathwiz’ posting seems to actively situate drago’s narrative of the past by ratifying its relevance for their current problem solving and assessing its practical comprehensibility. The presentation of a “test case” by mathwiz follows gdo’s presentation of a general rule in a way that signals the sustainability of the team’s knowledge building. It is precisely because of this type of engagement that we do not see this interaction simply as a peer explanation nor do we label the relationship between prior members of the team and newcomers as an entirely asymmetrical one of explainer–audience. This short sequence signals only the beginnings of the type of interactional work necessary to fully bridge prior knowledge work into present joint activity, and yet it is sufficient to provide us with significant evidence of the nuanced aspects of this type of activity. Other researchers have pointed out that the management of attention and knowledge proposals as well as the roles of the co-participants in establishing join attention are consequential for the collective achievements of small groups (Barron, 2000) (Stahl, 2006b). Here we see how these interactional processes are especially important for the establishment of continuity of knowledge building over time.
One further aspect of the second session of team five is worth exploring. The excerpt below follows the one from session two presented earlier and it allows us to observe how this collectivity dealt with the uptake of drago’s presentation of the past finding about short distances in the grid-world.
323 drago: ok.... 324 drago: so 325 gdo: square root of 45 326 mathwiz: but you have to move on the grid lines, right? 327 gdo: 3^2+6^2=c^2 right? 328 drago: no 329 drago: you can't go diagonal 330 gdo: ok 331 drago: the problem before said so, but you weren't here 332 gdo: so the hypotenuse is not square root of 45? 333 gdo: i was on team 2 334 drago: I mean 335 drago: it is 336 gdo: but moved to team 5 337 gdo: since u guys didn't have enough people 338 drago: but, we can't move diagonally since that would be cutting through the grid 339 mathwiz: the hypotenuse is fine, but for the problem, you have to go on the grid lines 340 gdo: ok 341 drago: so 342 mathwiz: it's like, you can't walk in water, and the lines are dry lines 323 drago: ok....
Despite drago’s orientation to the recommencement of the prior work that he and estrick did before (and to a narrator-explainer framework of participation), gdo departs partially from that orientation in line 325 by making a solution proposal for the shortest path between the points they are currently examining (“square root of 45”). Consequently, the sequence of postings from 325 to 330 seems to indicate a local engagement with the problem as the present matter and no longer as a bridging move to re-use prior findings. However, in the sequence starting at line 331 drago uses, once again, elements of prior interactions (“the problem before said so but you weren’t here”) to address what appears to be a problem in gdo’s understanding (i.e. that you can’t go on the diagonal). This alternation between present and bridged resources for problem solving indicates a dynamic engagement by the group with its distributed history and its current problem-solving activity.
Also particularly interesting in this sequence are mathwiz’s postings in lines 339 and 342: “the hypotenuse is fine, but for the problem, you have to go on the grid lines…it's like, you can't walk in water, and the lines are dry lines.” These postings seem to do the unique work of ratifying gdo’s use of the hypotenuse —as well as his participation in the task— while at the same time offering him a new “rule” or perspective to manipulate the grid. It seems to us that this interactional move bears resemblance with the types of activities we have analyzed before and deserves the label of bridging work. By offering this new perspective on how to imagine and manipulate the grid, mathwiz identifies a boundary between different perspectives or forms of understanding (i.e. being able to use diagonals or not in the grid world) and goes beyond simply refuting it by offering a link or bridge between the two. This bridging of perspectives can naturally occur between different problem-solving episodes or collectivities but here we see it happening within the flow of a team’s interactions. With the dynamic changes in team membership that characterize naturalistic environments and the diversity of points of view among individuals and teams that are typical of online communities, sustained problem-solving work seems to require that co-participants also engage in this type of bridging of perspectives. Additional research is necessary to explore the range of resources produced by individuals and groups to overcome these types of perspectival boundaries which emerge as relevant during their interactions and which relate to overcoming challenges of continuity, coordination or affiliation. It is possible that the methods and processes of doing this kind of boundary work could characterize effective collaborative learning interactions, but this remains a notion to be investigated. So far, we have explored a few instances of bridging activity in the trajectory of a particular virtual math team in our experiment. In doing so, we have offered a preliminary analysis of how the collective engagement with past work is constituted across different interactions or episodes, how changes in the alignment of the participants signal various aspects of the sustained knowledge work of the teams, and how problem-solving perspectives are subject to bridging as well. Furthermore, our analysis seems to suggest that these attempts to establish continuity in collaborative problem solving involve the recognition and use of discontinuities or boundaries as resources for interaction (e.g. temporal or episodic discontinuity), changes in the participants’ relative positioning toward each other as a collectivity (e.g. narrators and interactive audience), and also the use of particular orientations towards specific knowledge resources (e.g., the problem statement, prior findings, what someone professes to know or remember, etc.). This initial analysis demonstrates that in interactional contexts where there are continual sequences of discrete problem-solving episodes and where the membership of a team might change over time, sustaining continuity of the team’s knowledge work becomes a particular challenge for which teams need to develop particular interactional strategies. In fact, the analysis of other instances of this type of activity could lead us to uncover a range of bridging mechanisms used as part of the teams’ engagement in this online learning community.
