TeamCDataSessionFindings

This is the wiki page for sharing our findings of Team C data for our data sessions Fall, 2008.

Please post your preliminary findings for the selected excerpt on Monday, prior to the Wednesday afternoon data session so others can read and come to the session prepared.

For example, you could say what you found interesting of the excerpt, why it is interesting, and what you think might be going on there.

For those who are working on their dissertation, write something that is related to your dissertation research.

The first data session will be held at noon, Wednesday, Oct 1st, 2008, at the Math Forum. We will start from the very beginning of Team C's first session to where ssjnish joins the group.

---

Excerpt 1 (Oct 1, 2008 data session) 6:24-6:34

[Notes from Data Session 1]

Comments from Gerry

6:24-6:26 normal greetings as people enter room

6:24 but Davidcl starts right away drawing on the whiteboard, building the pattern from the problem

6:25 137 starts to draw on the whiteboard for fun/practice

6:24-6:26 Davidcyl tells 137, to stop and erases 137's drawings to make room for his own on-topic math drawings

6:25:44-6:26:21 Jason introduces knowledge and terminology from his school experience outside the chat

6:26:21 Jason opens math discussion with a proposal for approaching/defining the problem, phrased as a question

6:26:25 Davidcyl now connects his drawings to the chat problem solving

there is visual reasoning, counting sticks and squares in drawings and translating this into sums and formulae

There are many proposals and questions, rapidly following parallel and intersecting threads

There is a mixture of exploratory interaction and explanatory discourse

Comments from Ramon

WHAT MAKES THIS SECTION INTERESTING 2006-05-09: 6:24:26 – 6:34:12

How Participation Begins

In the VMT-Chat environment, the presence of participants, but not the order in which they entered the room, is visible in the upper right corner of the screen.

Differences in how a participant ‘joins’ the interaction

-through the Chat Space

1. Upon entry into a room, a participant sees who are in the room through the listing mentioned, but has no idea of their chat activity until after the ‘recall’ button is pressed.

2. Even after the recall button has been pressed, a newly entered participant would not see fully see the unfolding of the previous activity because its possible replay is ‘approximate’ rather than at the speed at which it originally unfolded.

3. The chat activity which is seen by a participant is that which takes place after his entrance and he sees how it unfold.

4. Chat postings are preceded by the names of their posters.

5. Pressing the ‘Enter’ key puts a message in the chat window.

-through the Whiteboard space

1. Determining the identity of the poster of a whiteboard posting requires paying attention to the upper left edge of the whiteboard

2. The latest posted activity on the whiteboard can be seen by the newest entrant into the room.

3. Whiteboard activity become visible to all other participants when the poster clicks on the message typing box or begins typing there.

4. Previous instantiations of the whiteboard can be scrolled back to, but they are not replayable because a review cannot be run at the same speed at which the original event unfolded.

Possible consequences of the above

1. More recent entrants into the environment require ‘some’ time to sense the level of activity in the environment; their greater participation may require them to be ‘invited’ to ‘join in’ by those who have entered the room earlier.

2. ‘Acceptance’ of an invitation may consist in ‘some acknowledgment’ that the invitation has been seen. This may be some response which may be in the form of a reply to some question or some sign of attention to recent postings.

Observations

1. Though Jason was the first participant (with the exception of the facilitator Azemel) to enter, the first posting was by davidcyl and the posting was on the whiteboard.

2. The ‘attendance check’ at 6:24:39 may be a response to the whiteboard posting. It functions as an invitation to be active as ‘davidcyl’ has already begun to be active.

3. A question: do the entry times of the participants partially explain how they respond to the ‘attendance check’?

a. Jason is not in a position to know who should be there but he has probably noticed the system messages showing the entry of davidcyl and 137, hence the ‘hedging’ in the answer.

b. Davidcyl has been active on the whiteboard and is probably aware of the entry of 137. Thus he can declare his readiness without hedging.

c. 137 has seen the two previous responses, hence he can also declare his readiness without hedging

4. Since two other participants have declared their readiness, Jason is now in a position to declare how many are in the room and can be expected to ‘participate’ and not simply lurk.

5. The declaration that there are four participants now permits Azemel to close the ‘attendance check’ activity and permit the initiation of another activity, which is the introduction to where the offered problem is, some essential steps that the participants should engage in and (eventually as displayed in 6:25:54) limit his participation in the interaction.

Different Proposals for Problem of Interest and how they are presented (via whiteboard and via chat)

1. Presentation of resources precedes identification of the problem of interest!

a. Davidcyl has ‘prepared the whiteboard’ by putting up a still unidentified and unexplained representation and erasing 137’s ‘whiteboard greeting (6:25:22 – 6:25:44)’.

b. Jason offers a claim of expertise with the yet unidentified problem; 6:25:44 ‘we just did in this in math class a week ago’.

c. Davidcycl proposes his finished representations at 6:26:25.

2. Two problems of interest are eventually proposed.

a. Jason proposes the problem of sticks by soliciting other approaches for it at 6:26:21.

b. Davidcyl proposes the problem of squares at 6:27:32.

3. Distinct interaction spaces are used to propose an approach.

a. Jason uses the chat window.

b. Davidcyl uses the whiteboard space.

Interrelation of the proposals

1. Both Jason and davidcyl hand over their proposals for uptake but eventually ‘explain’ their solutions, through the presentation of examples of candidate answers.

2. 137 links the competing proposals by ‘connecting’ to each proposal though it is unclear which problem of interest he actually takes up.

3. 137’s apparent ‘confusion’ starting at 6:28:43 seems to create an opening for davidcyl to take up the ‘sticks’ problem after the ‘squares’ problem seems to have been answered through 137’s formula at 6:28:16.

Comments from Nan

6:26:21 Jason's question initiates the problem solving process by inviting people including himself to answer the question. Jason himself answers the question, providing his findings, making them available for others to assess.

6:29:05 137 makes a proposal, presumably a formula describing the pattern, in the form of question, calling for assessment from the group.

137's proposal does not get direct assessment. Instead, David directs people to the whiteboard and tries to provide some description of how the figure consists of sticks.

Seems like when a participant is engaged in exploratory work with other members, math proposal is often made in the form of question. Such questions serve to organize the participation of exploratory work. 137's proposal is an example of this. Another example:

6:32:02 Jason: well could you just use like

...

6:32；28 Jason: # sticks = N*(3+N)

Questions are used to do clarification. e.g. 6:30:50 would that be the number of sticks; 6:32:30 wait what are you working on?

To think about: are some of the proposals in analogy to "failed proposal"? what may consist of a successful math proposal?

Comments from Murat

MuratsNotesOct08

Comments from Johann

In my tracing of trajectories, usually first sessions don't register a lot of "bridging activity" but I had this in my notes for this team's initial phase:

Jason 5/9/06 6:25:44 PM EDT: ooh we just did this in math class about a week ago! :-)

Jason 5/9/06 6:25:55 PM EDT: well, not the exact thing, but sequences and series

These 2 posting are interesting to me because they seem "prepare" a participation framework (using reporting-like postings) and serve as a preface to this next posting:

Jason 5/9/06 6:26:21 PM EDT: so do we see how the number of sticks grows in a sequence?

What follows, to me, illustrates how Jason tries to get "us" to "see" how the number of sticks grows Question: Is some of this what you called "explanatory" Gerry? I kind of see a kind of "explanatory+exploratory" combination... but unfortunately not much visible uptake to Jason? I agree that there is a lot of parallel work here. Interestingly, no one is complaining about that. :)

Comments from ...

Comments from ...

---

Excerpt 2 (6:34-7:13:53)

[Notes from Data Session 2 Oct 8th]

[Notes from Data Session 3 Oct 14th]

[Notes from Data Session 4 Oct 22nd]

Comments from Gerry

Comments from Ramon

The gentle art of correcting a whiteboard object

Jason initiates the creation of a whiteboard object – a summation in sigma form – of the number of squares. At completion, his whiteboard object is ∑_(n=1)^∞▒n

Davidcyl makes corrections by replacing the formula n(n+3) with n. The ‘n’ is then replaced by ‘k’, ‘n = 1’ by ‘k = 1’ and finally the infinity symbol ‘∞’ is replaced by ‘k’ at 6:44:33. The ‘k’ is reverted to ‘n’ at 6:44:38.

The final form of the whiteboard object – ∑_(k=1)^n▒k - is highlighted by davidcyl at 6:44:50.

Jason initiates the whiteboard activity at 6:40:45 explaining what he is doing through chat postings and uses reference links to connect his postings to his whiteboard activity 6:42:31. After ‘finishing’ the whiteboard posting, he agrees with davidcyl’s offer to work on the wiki. Jason’s agreement takes place at 6:43:32 and 6:43:36.

davidcyl starts changing Jason’s whiteboard posting sometime after 6:43:37 and highlights an initial change he made through a reference link. The chat posting suggests a mitigated disagreement through the use of the hedge ‘I think’. Jason accepts the correction. Davidcyl continues to revise all other labels of the summation until 6:44:38. Finally, davidcyl highlights the whiteboard object at 6:44:50.

An initial ‘correction’ presented as a typo by the original poster, rather than treated as a mistake, results in a mutually acceptable resource, whose revision saves the ‘face’ of the original poster.

Comments from Nan

• The group tries to catch the new comer ssjnish up upon request of the moderator by giving him instructions on reloading the messages. davidcyl gives a report of what the group has got so far, which does not receive any response from ssjnish.
• 6:45:11 How ssjnish sets up the context for asking a question by making a report of his math ability in comparison to rest of the group.
• There is significant silence following ssjnish's posting, which indicates interactional trouble of some sort.
• The "question" regarding the derivation of the number of the squares is constructed by ssjnish responding to the moderator's solicitation.
• The group encounters trouble in providing appropriate answer to ssjnish's question. The question is reformulated.
• The group engages in co-construction of a response to the reformulated question.
• The group shuts down ssjnish when their answer to the question does not receive preferred response from the questioner. The participation is changed.

Comments from Murat

• The joint reflection on the past work seems to be initiated by two factors (a) Jason’s post that he might have missed a relevant past discussion (b) the arrival of ssjnish as a newcomer.
  • When Jason proposed the team to move on the task of finding the formula for the number of squares at 6:35:36, other team members responded that they have already done that part of the problem. Jason’s next post states that he must have missed that part of the discussion. Then Davidcyl posts a message stating “look up” with a reference pointing several lines back in the history. The message is linked to the statement where Davidcyl made the proposal that the formula for the number of squares is n(n+1)/2. I think his choice for marking which message Jason should be looking at gives significance to the result. Davidcyl’s message not only locates the episode in chat history where the relevant discussion happened, but also pinpoints a statement including the formula.
    • In this episode group members explicitly orient to the task of making relevant a past result by making use of the referencing tool and taking advantage of the persistent storage of chat messages.
  • Next Jason asks one of the team members to post the formula on the whiteboard in a textbox. Jason posted the formula for the number of sticks earlier. Jason’s suggestion for posting group findings to the whiteboard as textboxes indicates that users attend to these dual spaces in different ways. This may also be a convention Jason is bridging back from his past experience in SF05 where we asked them to use textboxes to post team questions etc.
  • Next Davidcyl and 137 both post a textbox each. David’s box appears first including the formula n(n+1)/2. 137’s box overlaps with David’s and contains the text n(n+2). They both seem to target the space below the existing textbox as a relevant spot to post these findings, which is revealing in terms of how participants decide where to put things and organize their shared space. Moreover, the temporal proximity of these actions to Jason’s request for posting textboxes suggest that they are taking up on this request by acting on the other interaction space.
  • Following the textbox postings Jason moves 137’s box to the right and eliminates the overlap. Then 137 drags this box all the way to the right so that part of the box becomes invisible. This may be considered as an attempt to delete or get rid of that object.
  • Jason’s subsequent moves of the remaining textbox can be seen as an attempt to locate the other box posted earlier. He later posts a message in chat stating that he is sorry for moving the box around. This shows us that group members treat such movements of shared objects as a delicate, accountable matter.

• At 6:38:30 Davidcyl begins to provide a summary of the group's findings. In this posting and the next one the use of the pronouns "we" and "I" caught my eye. The plural "we" is used as part of the result about the number of squares (where 137 was participating and Jason seemed to have missed it completely). In his next posting Davidcyl seems to attribute the idea of splitting the shape into horizontal and vertical sticks to himself.

• Ramon noted this already but I would like to mention another aspect of the same exchange.
  • At 6:40:45 Jason begins to do some drawing work. He adds a summation sign and adds a textbox stating n=1 beneath it. Then he posts a chat message that glosses his drawing work as an attempt to write the team's formulas in summation form since that would be more "formal". Then he adds two overlapping ellipses and posts a chat message referring to that new shape stating that what he is pointing at should be read as an infinity sign. Finally he adds a textbox with the label n(n+3)to the right of the sigma sign. In this episode Jason consistently provides a narrative gloss after each of his drawing actions to describe the symbols he is using.
  • At 6:43:39 Davidcyl changes n(n+3) to n and shortly after that he posts a message pointing to the textbox he has just modified and stating that you (Jason) meant n. Jason seems to agree in the next line. Then Davidcyl makes further changes by changing the index variable to k and the upper bound to n. Finally at 6:44:50 Daidcyl posts a message pointing to the whole summation expression where the message does not have any text. This seems like a move to get the attention of others to the new form of the formula.
  • Overall, the point I am trying to make here is that, here Jason and Davidcyl provided an account for making a change on a whiteboard object in the chat space. The narrative accounts followed the drawing actions (i.e. the accounts presumed an action so that they can be seen as a response to some change made in the other interaction space).

Comments from Johann

Comments from ...

Comments from ...

---

Excerpt 3 (Nov 5th, 2008 data session) 5/11/06 7:26:32 - 7:31:22

[Notes from Data Session 6 Nov 5th]

Comments from Gerry

Comments from Ramon

Comments from Nan

Comments from Murat

Comments from Johann

Comments from ...

Comments from ...

---

Excerpt 4 (Nov 12, 2008 data session) 5/11/06 7:33:06 - 7:43:51

[Notes from Data Session 7 Nov 12th]

Comments from Gerry

Comments from Ramon

Comments from Nan

Comments from Murat

Comments from Johann

Comments from ...

Comments from ...