Collaborating with Relational Reference= s

The previous chapter used a simple concept of reference in which an utterance refers to an identifiable object in the world—a specific rocket description in the simulation list. In this chapter, the analysis is deepened to reveal the same group’s learning= of a more sophisticated reference that involves pairs of objects compared in a subtle way. Mastering practices that define such references is necessary for conducting collaborative scientific experiments involving controlled variab= les. This accomplishment is achieved by the group of students as a whole, working with computer-based artifacts under the guidance of an adult mentor. In the previous chapter, the group of students encountered confusion about which r= ockets they were referring to in their talk-in-interaction. In this chapter, it becomes clear that their task of referring was complicated; it involved a n= ew way of looking at the meanings embedded in the simulation artifact.

This analysis provides a rich case study for the theoretical reflections of part III. By chapter 20, it is seen that the conceptual change that the students’ group cognition passed through in this chapter has important philosophical consequences. In chapter 21, the analysis of an excerpt from an online chat provides a complementary case to this one.

Embedding Meaning in Software

Several years ago I met Tony Petrosino at a conference and was intrigued by his research using model rockets to te= ach science to disaffected middle school students in Texas. He explained that the use of mo= del rockets is quite widespread in middle school curricula and that kits for building model rockets with a variety of rocket engines are readily availab= le. Because we were at a computer-oriented conference, Tony and I started talki= ng about developing a computer simulation of model rockets to supplement his curriculum.

When I returned to my office, I discussed the idea wit= h Alex Repenning, my officemate at the time and the developer of Agentsheets, a software environment= for the end-user programming of simulations. We decided that this would be a go= od exercise for me to undertake in order to learn more about Agent= sheets. So, I got some data from Tony about the effects of different rocket design options on the flight of model rockets and I programmed a simulation. Using= the Agentsheets visual programming language (Repenning & Sumner, 1995), I defined the behavior of rockets to correspond roughly to Newton’s l= aws, taking into account different air resistances due to rocket shape and textu= re (based on Tony’s data), the thrust of the different rocket engines and the force of gravity. I translated Newton’s laws into difference equations for computing a rocket height at every time slice of the simulation. Then I added a random factor (“weather conditions”) to make predictions more interesting. While middle-school students do not know the equations of physics, they can find averages on th= eir calculators to take into account the random noise.

At the time, I was working with two middle-school clas= ses to develop software for them with which to practice writing summaries (see cha= pter 2). In the spring, these classes broke into special science projects, for w= hich parents and community members were encouraged to volunteer. The classroom teachers I was working with invited me to mentor a model rocket group, and I proposed to spend two hour-and-a-half sessions with them using my new simulation.

On one level, I was curious to see what kids in the sp= ace age really understand about rockets and the scientific method. In particula= r, I wondered if they understood the basic principle of experimentation: varying only one attribute at a time while holding the others constant. So, I equip= ped the simulation with 7 rockets whose configurations would allow one to measu= re the effects of each rocket variable and then predict the behavior of an 8th rocket.

On another level, more than just being curious about w= hat a certain group of students knew, I was interested in studying how middle-sch= ool students would approach learning about a new software tool. I thought that having them work in a group would make their learning visible to me. I videotaped them in order to capture a record of their learning.

Of course, based on hours of time spent with video gam= es and similar devices, students these days are adept at using software and at discovering its functionality. However, what I was asking them to learn was different. They had to learn the structure of the list of rockets and learn= how to take advantage of that structure in order to complete certain computatio= nal tasks. In other words, I was embedding meaning in the simulation and they w= ould have to come to understand that meaning. An individual can conceptualize any software program as the embodiment of meanings that were programmed into its appearance and its behavior. For instance, the meaning of certain icons and menu items in a word processing program has to do with determining fonts for text. To understand that program, one must learn about fonts and their use,= as well as about how to manipulate fonts using the interface icons.

One can say that a computer software program is an art= ifact that embodies “inferred,” “referred,&= #8221; “derived” or “stored” intentionality. That i= s, the software designer programmed meanings or intentions into the software, = and these allow the software to behave in a meaningful way. A clear example of = this is given by artificial intelligence. An AI program is supposed to exhibit human-like intelligence in responding to inputs. Of course, that is only possible if the programmer reduced some limited domain of intelligent behav= ior to algorithmic rules (or heuristic rules that are able to mimic human decis= ions much of the time) and then programmed these into the software. The meaning = of the software’s behavior is derived from the human software designer’s symbolic external representations in the programming langu= age (Keil-Slawik, 1992). The user notices traces of the designer’s intention in the form of the operational software artifact. The meaning is referred from its source in t= he designer to its appearance in the interface, much as “referred pain” appears in a different part of the body from its causal source.= The AI software embodies its designer’s intelligence in a way that is analogous to how commodities and machinery embody “stored” or “dead” human labor that determine their exchange value accordin= g to Marx (1867/1976). In the case of the com= puter simulation, not only the temporal behavior of the rocket, but also the usef= ul arrangement of the rocket attributes in the list of rockets, are intentional artifacts whose meaning was structured by the designer.

Varieties of Meaningful Artifacts

We can distinguish different categories of meanin= gful artifacts:

· physical artifacts

· symbolic artifacts

· computational artifacts

· cognitive artifacts

By definition, an artifact is something man-made. We might typically think of an arrowhead, pot shard = or figurine unearthed by an archeologist. The physical artifact is made out of some material that has survived thousands of years. It has a form or outer appearance that displays some purpose or meaning, and that shows that it was made by a person, by a designer who embedded that meaning in it. We may not= be sure exactly how to interpret the meaning—whether a given figurine is religious, magical, fertility enhancing, artistic, a child’s doll, a = remembrance of an important individual or a decoration—but we know that we are in= the presence of a meaning and we know that someone at some time in the distant = past intended the artifact to have a meaning. We are tempted to attribute some interpretation to the meaning. With our interpretation comes a glimpse into= a faint and distant world: a culture within which this artifact was once transparently integrated.

A physical art= ifact embodies meaning in the physical world. Traditional western theories, influenced by Descartes’ conceptualizations, think of meanings as something purely mental, divorced from the physical world. According to this view, meanings are ideas we have in our heads about things in the world. Bu= t if we consider the nature of artifacts, we soon realize that the physical worl= d is full of mental meanings, or, the world is meaning-full; not because I as an observer apply values and meanings to things I see, but because practically everything in our world has been made by people, and has been designed to h= ave specific meanings. Our shared culture makes these meanings available to us = all. Even the rare glimpses we get of nature are imbued with historical or aesth= etic dimensions; they are measured by what it would take for us to climb or touc= h or paint them; they are framed by the eye of an architect, landscaper or urban planner who purposely left them for us to glimpse. The very concept of natu= re is so socially-mediated that any sharp separation of meaning and the physic= al object itself is misguided.

And vice versa. Symbolic artifact= s are not completely ethereal. Words appear in sounds, ink or pixels. They co= uld scarcely do their jobs as conveyors of meaning from one person to another if they did not appear in the physical world where they could be perceived and= shared. Symbols do not come from nowhere; nor are we born with them inside us, like= the neurons of our brains. We learn the meaning and use of symbolic artifacts—the words of our languages and of our language games—= from our activities in the world, primarily verbal interaction with our care-giv= ers, our siblings, our childhood best friends, our various teachers and other people.

Once embodied in an artifact, meaning may exceed the original designer’s intention. A book or poem may bring together words and images whose interactions and connotations exceed their author’s understandings. With computational artifacts, it is well known that softwar= e is used in ways never anticipated by the designers. Although meaning may have originally expressed a subjective interpretation, it takes on a life of its= own out in the shared world, subject to changing socio-historical conditions and open to interpretation from various perspectives by different people.

Artifacts have been around as long as humans, although= the concept of artifact-as-bridge across the mind/body distinction has only pla= yed a central role in philosophical ontologies since Heidegger (1927/1996), Benjamin (1936/1969) and Vygotsky (1930/1978). However, computational artifacts are a rela= tively new phenomenon. An artifact like the SimRocket simulation enlivens with computational power the meaning that is programmed into the software bits. The rocket icon moves with a behavior whose meaning= was programmed in by the designer, although carefully designed random and interactive elements make the precise behavior unpredictable, as well as dependent upon the user’s actions. The computational, interactive artifact has a different kind of complexity than the prehistoric arrowhead (although the crafting of some arrow heads may have been so skilled that th= ey are impossible to duplicate today). While it may be hard to specify precise= ly how meaning and physicality are merged in the bits of software that can be limitlessly duplicated and reconfigured, it seems clear that effective usage presupposes that the user recover (in his or her own way) the meaning of the software that was designed into the software to empower the user.

In educational contexts there is an expectation that t= he meaning will be taken a further step: that the lessons will be learned, that is, that whatever me= aning is unearthed in the artifacts will be internalized by the student. This expectation does not necessarily entail a return to the view that meanings exist in individual minds. Rather, the expectation is that the student will= be able to make use of a meaning that is learned from an encounter with a physical, symbolic or computational artifact when the student is in a new situation in which that meaning might again be relevant. Without speculating about what might be involved in the student internalizing a meaning, we sim= ply look at the student interpreting the meaning in the original situation and = then using this experience as a resource for constructing some similar form of m= eaning in a new situation in the world.

Vygotsky recognized that w= e do have an inner mental life and he succeeded in relating our mental life to o= ur social life in the world by arguing that our private mental world was an internalization of the primary, shared, social world. We learn to speak, act and be in the world by interacting with other people and by sharing a cultu= re and a meaningful world with them. As we begin to master these as a young ch= ild, we start to talk to ourselves—first out loud and then silently. We fo= llow a similar sequence with reading—and then with debate and other social skills. In each case, when we internalize a skill it undergoes a complex sequence of transformations, eventually becoming a cognitive artifact, a mental tool. For instance, an arrowhead m= ight allow us to kill our prey in the world, the language of hunting allows us to discuss group plans for an expedition, a computer lets us simulate hunting scenarios and the internalized language lets us imagine a glorious hunt. Th= e nature of the hunt is different depending on whether it is mediated by a physical, symbolic, computational or cognitive artifact. The silent self-talk that Vygotsky analyzed is the start of the stream of consciousness that forms our private mental life. Various skills like the ability to construct narratives (Bruner, 1990) and to give an account = of our actions (Garfinkel, 1967)<= !--[if supportFields]> enrich that life.

In this chapter we want to observe how a new cognitive artifact can evolve out of social interaction involving a computational artifact. How do the students develop the cognitive skill of comparing experimental cases having different attributes?

The Structure of the Rocket List

The SimRocket applet is a computational artifact<= /i>. It includes the simulation panel of the rocket flight and the rocket list describing the available rockets. Based on Tony’s model rocket kits, I designed the simulation rockets to have four variable attributes:

·        Nose cone shape (rounded or pointed)

·        Number of fins (3 or 4)

·        Surface texture of body (painted or sanded)<= /p>
·        Rocket engine (Big Bertha, Astro Alpha, Crazy Quasar, Giant Gamma)

The rockets are paired in the list of available r= ockets (see Figure 13-1). There are two rockets with each kind of engine. The first three pairs have identical attributes, except for one difference:

·        Rockets 1 and 2 differ in nose cone shape

·        Rockets 3 and 4 differ in number of fins

·        Rockets 5 and 6 differ in body texture

·        Rockets 7 and 8 differ in nose cone, fins and body

The computer simulation was carefully designed wi= th this particular set of rockets. This set of rockets allows the user to determine the effect of the different attributes on the flight of the rocket by, in effect, holding constant all variables, except one, each trial. Thus, one can determine the effect of nose cone shape by comparing the flights of rockets 1 and 2; of number of fins with rockets 3 and 4; of body texture wi= th rockets 5 and 6. These effects can then be combined to predict how rocket 8 will fly, given the flight of rocket 7, which differs from rocket 8 by thes= e three attributes. This describes, from the designer’s perspective, the mean= ing that was embedded in the simulation list artifact.

Figure 13-1 goes approximately here

There are other sets of configured rockets that would = allow similar calculations and predictions. Rather than varying attributes in pai= rs of rockets (let us call this “paired configurations”), one could compare a set of different rockets to= one common standard (call this “s= tandard configurations”). For instance, rockets 2, 3, and 4 could each di= ffer from rocket 1 by a different individual attribute. Then, rockets 5, 6 and 7 could be like rocket 1, but have the different engines. This would also all= ow one to compute the effects of each attribute singly and combine them to pre= dict any configuration of rocket 8. Either this standard configurations combinat= ion of rockets or the paired configurations combination above allows one to com= pute the dynamics of all 32 possible rocket configurations using a set of just 7 different rockets.

Using the contrast just made of paired configurations = to standard configurations, we can better understand the breakdown analyzed in= the previous chapter. The students discovered that rockets 3 and 4 could be compared to determine the best fin configuration because 4 was a variation = of 3. They then sought a variation of rocket 3 that could be analogously compa= red for nose cone shape. The students were assuming a standard configurations m= odel in which everything is compared to one standard rocket (rocket 3).

However, the rocket list was, in fact, structured with paired configurations. Brent’s gesture first drew attention to a pair with the needed difference, using a paired configurations model. The result= of the subsequent collaborative interaction was to reach a consensus in which = the whole group took a particular pair (rocket 1 and 2) as the focus of compari= son, rather than insisting on looking for a variation of the standard rocket-3 engine.

Uncovering Embedded Meaning

At this point it may seem obvious to the adult re= ader how one should compare rockets in the SimRocket list to find out the effects of the different attributes. However, it clear= ly was not obvious to the young students. We saw in the last chapter how their references to rockets to be compared became quite confused. This confusion presented an occasion for an exceptional interaction to occur among the students in order to sort out this breakdown in the references. They accomplished this efficiently, with the use of brief, productive utterances that are hard for an observer to interpret but proved to be incredibly effective within the discourse. Once the references were resolved and accep= ted as shared by the group, the students were able to quickly draw the scientif= ic conclusions about rocket characteristics. They then displayed in their talk their mastery of how to compare rockets. They accomplished this not by talk= ing about “controlling variables”—such adult (schooled, professional) terminology was never used—but by making the proper use= of their data. They learned the principle of scientific comparison in the practical, situated sense that they could actually carry out the appropriate operation= s on their data.

The learning that we uncovered in the collaborative mo= ment transcript in chapter 12 played a key role in the larger classroom session.= It is now possible to review the larger transcript and find statements in which learning associated with the issue addressed in the collaborative moment is also expressed—following the hermeneutic principle that interpretatio= n must go back and forth between part and whole.

During the ten minutes surrounding the thirty-second “collaborative moment” (from about 1:17:00 to 1:27:00), where t= he teacher and students discussed how to analyze their rocket data, the group understanding went from a rather naïve and vague sense of how to use t= he list artifact to a very clear and explicit appreciation of the meaning of t= hat artifact and a practical knowledge of how to use it to achieve useful and meaningful results. Following are a series of excerpts from the longer transcript that illustrate this development by presenting significant statements that expressed the evolving group understanding. They are given = here in ten stages:

·        Stag= e a, Chuck expressed the group’s assumption that one could simply adopt all the features of the rocket that flew the highest. When the teacher suggested that a particularly strong engine could mask the differences caused by the other features, the students were at a loss on how to proceed without strong guidance from the teacher, leading up to the collaborative moment with its breakthrough insight.

1:17:01

Chuck

We’ll just go with number one uh (.) a= n that did the best, (.) or something, out of all ours comp= a:red

·        Stag= e b, after some discussion of statistical analysis, Steven still articulated the same group position as Chuck had, to go with all the features of the best rocket.

1:17:44

Steven

Well we’d look at- (.) we’d look at the= graph that we do an see which has ( uh ) the = best. An whichever has the best like rocket= one two n three or- so on, (.) .h n whichever has the best we’d look to= see if it has a rounded, or a pointed, which (.) which ours shows so far, tha= t a = rounded, (.) that a rounded is better?

·        Stag= e c, Jamie suggested seeing whether the set of rockets with pointed noses does better overall than those with rounded noses, assuming that this kind of averaging will cancel the effects of the other features.

1:18:29

Jamie

Well what you do is you take every one that has a r= ounded nose an every one with a (.) pointed nose. (0.4) an you see which (0.2) one did better overall

·        Stag= e d, Chuck had the idea of manipulating one feature at a time while holding the others constant, but he wanted to do this on physical model rockets (made o= ut of soda pop bottles) rather than applying it to the data he just collected = from the simulation.

1:18:36

Chuck=

Yeah if you could bring in one that (.) like two= two liter pop bottles you know that’s (.) mak= e one with a pointed nosecone n one with a rounded nosecone. an see which one did better .hh so then we c&= #8217;d go with that one an then add the feature that was on that o= ne to the other one .hh an whatever featu= res you put on here, (.) you leave off of (1.0) that- uh off of the ot= her one .hh that way you c&#= 8217;n j’s see which one will fly. (.) ‘= F the features on this one didn’ work then we= take th’m off and then go from there.

·        Stag= e e, Jamie was ready to use the data from the simulation, but returns to the ide= a of finding which did “better overall.”

1:19:05

Jamie

You can use the simulation by .h finding out (.) j’st which one has a rounded nose and which o= ne has a pointed nose? (.) and which one did better overall. (0.8) Like w- (.) which (.) rockets like (.) if (.) only one<= /u> rocket with a rounded nose .h did good, then (.) a rounded nose (.= ) isn’t very good, (.) but like if. yeah but like if <= u>all the rounded noses are good, (.) compared to the pointed nose, then the rounded nose- noses are good.

·        Stag= e f, Chuck solved the problem for fins, using the simulation and identifying roc= kets 3 and 4 on the list as having the necessary characteristics for valid comparison.

1:20:30

Teacher

So how would you find out which is better four fins= or three fins. (1.0)

Chuck

By launching (&nbs= p; ) with two different things on it–

Teacher

–Which one—which two.

Chuck

one with fou::r (.) n one with three: like (0.6) rocket four an rocket o= ne. (0.8) Err no—(.) Ro:cke:ts= , (.) fou:r, n rocket three. Cuz they both have the same engine. (0.8) An they both have the same nosecones.

·        Stag= e g, Chuck wanted to change the simulation to create a comparable pair of rocket= s. He was willing to use the simulation, but has not looked carefully through = the list to find what he needs.

1:20:03

Chuck

see ‘f you guys c’= d make one .h wha– with an astro (.) alpha engine four fins and pointed nosecone, (1.6) w’ll see if you c’= d do, (.) uh cha:nge all this around n s= tuff so that .hh you might get ( ) you also—.hh have an option of a pointed nosecone like—((swallow)) .hh you could (.) kinda = like in HyperStudio .hh if you = were tuh (.) like (.) click on this .h it would <= u>give you (.) all kinds of things th’t= you (.) ought—like (.) on the (.) pointy nosecone (.) .h you c’d switch it to a rounded nosecone .h= and the fins,

·        Stag= e h was the collaborative moment we have analyzed in chapter 12. At 1:22:21, Ja= mie turned to his data sheet and compared the data for rockets 1 and 2, conclud= ing that because rocket 1 went higher than rocket 2 and the only difference bet= ween them is that rocket 1 has a rounded nose cone, a rounded nose cone is preferable.

·        Stage i, = Steven explicitly described the structure of the list for doing the task for all features of the simulation rockets. He said, “I think it (the structu= red list) is good how it is,” fully appreciating that the necessary pairs have been built into the list.

1:24:46

Steve= n

What we would do is test (.) test (.) uh- rocket th= ree and rocket four, (.) cuz they both have a rou= nded nose they both (.) have that astro alp= ha engine n they- (.) n one has three one has four fins. I think it’s good how it is because .hh every rocket has somep’n different. Lik= e if you tested (.) five and six, then it- (.) they have the crazy uh- (.) qua= sar engine, .h they both have the crazy quasar engine, they both have the rou= nded .h nose they both have three fins, except th’t= if- if we uh- if we tested those two, we’d be - testing for thuh- uh painted body or uh -- a sanded body= , (.) so I like it how it is.

·        Stag= e j, the whole group agreed about how to use the list and they were able to collaboratively draw scientific conclusions with its help.

1:26:46

Brent

I would say that éthree is bett= er than four

Jamie

       &nbs= p;            &= nbsp;     ëthree is better than four (       &nbs= p; )=3D

Chuck

Yeah, three is better than four so=3D

Teacher

=3DSo éyour rocketù

Chuck

     ë(we want)   û three fins n a rounded noseécone

Teacher

       &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;   ëYour rocket three goes up higher ‘n rocket four=3D

students

Yeah ((multiple voices))

Teacher

So that means that three fins i= s better ‘n four.

By solving a sequence of problems that the teacher gui= ded them through, the students developed an increasingly robust working knowled= ge of the fundamental principle of scientific experimentation that only one variable should be varied while the others are held constant. Although this principle was built into the simulation’s list of rocket descriptions= and although the students started the classroom session by reading this list al= oud and discussing it, they were not able to use this feature of the list to analyze the data they collected until they worked through the preceding ten stages. Even as bright, motivated, middle-school students, they were not developmentally able to grasp the principle individually. However, this abi= lity did lie within their zone of proximal development (Vygotsky, 1930/1978), and they succeeded in attaining it as a group through a scaffolded collaborative process.

Articulating Meaning

How was the meaning of the rocket list as a set of paired configurations constructed by the group of students? In reviewing the ten stages of understanding that evolved in the group during the ten minute= s surrounding the half-minute moment of collaboration, we have seen that the group went f= rom simply wanting to identify the “best overall” rocket, to propos= ing various methods of comparing rockets, and then—after the intensive collaborative moment—to understanding the paired configuration and us= ing it to complete their task.

Let us return to the transcript in chapter 12 to see i= n some detail how the pivotal insight developed. Consider the significant pauses o= f a second or two in the interaction at 1:21:54, 1:22:03 and 1:22:07.

1:21:53

Teacher

And (0.1) you don’t have anything like that t= here?

1:21:54

(2.0)=

1:21:56

Steven

I don’t think so

1:21:57

Jamie

Not with the same engine

1:21:58

Steven

┌ No

Jamie

└ Not with the same

1:21:59

Teacher

With the same engine … but with a different (= 0.1) … nose cone?=3D

1:22:01

Chuck

┌ =3Dthe same=3D

Jamie

└ =3DYeah,

1:22:02

Chuck

These are both (0.8) the same thing

1:22:03

= ;

(1.0)=

1:22:04

Teacher

Aw┌ right

1:22:05

Brent

   = └ This one&#= 8217;s different

1:22:06

Jamie

Yeah, but it has same no…

1:22:07

= ;

(1.0)=

The teacher started with a question that referenced the r= ocket list in order to reorient the group to the computational artifact, which Chuck’s speculations about alternative software obscured. The students did not respond immediately, but the teacher used “wait time”; waiting out a long silence, thereby encouraging students to take the floor. Steven began hesitantly to reject the implication of the teacher’s question, hedging his “No” as “I don’t think soR= 21; at first, but then confirmed it when backed up by Jamie. Jamie justified or clarified the negative response with, “Not with the same engine.̶= 1; Jamie then repeated his utterance up to the word “same,” making that term focal.

The teacher picked up on Jamie’s term “same” to explicate his term “like.” By asking, “And you don’t have anything like that here?” the teacher= was asking if there was a pair of rockets in the list on the computer monitor t= hat could be used to determine the effect of the nose cone shape the way that C= huck’s proposed software variation of rocket 3 or 4 would. Jamie’s response pointed out that there was no rocket in the list that could be paired with rocket 3 or 4 for this purpose because none of the other rockets had the sa= me engine as rockets 3 and 4. So, the teacher added the clarification: “= With the same engine, but with a different nose cone,” repeating JamieR= 17;s “same” as applied to the engine, and introducing the term “different” applied to the nose cone.

Of course, this expanded version of the question was s= till ambiguous: it could have been applied to either a list of paired configurat= ions or one of standard configurations. After Chuck and Jamie made unsuccessful attempts to respond to the issue of “the same,” the group fell silent. This is the point of aporia that Plato (350 BC/1961) considered the catalyst= of insight: silent wonder in the presence of a question that one finally understands to be a captivating mystery.

As if suddenly aroused from his intellectual slumber b= y a muse of scientific thought, Brent dramatically broke the silence with “This one’s different.” Jamie did not see what was differ= ent and repeated what was the same. Another pause.
Then, Steven and Jamie—but not yet Chuck—demonstrated a change of interpretive perspective:

1:22:07

(1.0)

1:22:08

Chuck

Pointy nose cone=3D

1:22:09

Steven

=3DOh, yeah=3D

1:22:10

Chuck

=3DBut it’s not the same engine

1:22:11

Jamie

Yeah, it is, =3D

1:22:12

Brent

=3DYes it is,

1:22:13

Jamie

┌ Compare two n one

Brent

└ Number two

At first, they simply registered a change of view= and alignment with Brent. Then, Jamie and Brent made the new comparison explici= t: “Compare two and one,” “Number two.” They continued= to explicate, saying, “Are the same,” “It’s the same engine,” “So if you compare two and one,” until Chuck saw things their way: “Oh yeah, I see, I see, I see.” The crucial m= ove was to look at rockets 1 and 2 as a paired configuration. Then, one could s= ee that they both had the same engine (and the same other attributes, except n= ose cone), so they could be compared for different nose cones.

In this analysis, we see that the terms same, different and= compare became focal to the discourse. These are terms that relate two objects. References that = use these terms refer to pairs of objects. The group used these terms to define= the form of relationship that was needed; by repeating, refining and explicating how these terms were to be used, the group converged on the structure of pa= ired configurations. The discourse broke down until the reference of the teacher’s question could be interpreted by all the students as being directed to the pair of rockets 1 and 2 instead of to a pair based on rocke= t 3 as a standard.

All the participants in the discourse understood that = the teacher’s rhetorical question was referencing a set of related rocket= s. It took several interactions to shift everyone’s understanding from a model of standard configurations to one of paired configurations. Because t= he reference was to a relationship rather than to a single object, the breakdo= wn in shared understanding could not be repaired by simply pointing, as Brent tried. It was necessary for Jamie and Stephen to take this further and explicitly name both of the objects, as well as the relationship (compare) itself.

Discourse and Understanding

The unfolding of the collaborative moment reveals= a subtle interplay between the group discourse and the understandings of the individual participants. This interplay becomes visible during a breakdown = in the discourse caused by a non-alignment of the individual interpretations. = The character of this interplay does not lend itself to description using traditional conceptualizations of meaning and minds. In particular, we are tempted to say that the students had various ideas in their heads, that they expressed these ideas in their utterances, and that they changed their idea= s in the course of the interaction. However, we have no evidence about ideas in their heads beyond the utterances (and other interaction behaviors) themsel= ves. Nor did the participants have any evidence about the mental states of their co-collaborators, other than the same utterances (including intonations and gestures) that we have as observers. The only meanings that we (or they) ha= ve access to are those embodied in the utterances of the discourse themselves.=

Nevertheless, the question arises as to how some of the participants could (according to our analysis above) understand the shared discourse in different ways, resulting in the breakdown as well as its grad= ual repair. It seems clear that there are two different levels of meaning making taking place: a group level on which meaning is built up through the discou= rse in which everyone participates, and an individual level on which each participant constructs his own evolving understanding of the references and other features of the discourse. In particular, the pauses in the collabora= tive interaction and the arguments in the group discourse seem to stimulate̵= 2;whether by applying some kind of social pressure or simply by opening up a creative space—reinterpretations by the individuals.

We already observed in the previous chapter that most = of the individual utterances had little meaning on their own if viewed in isolatio= n. The meaning was constructed at the level of (in the context of) the group discourse, through the references of words, phrases, gestures and glances to elements in the discourse, the social interaction, the associated artifacts= and the physical space. A word like sam= e derives its lexical meaning from its contrast to different, its use in c= ompare, etc. The word also builds up its socially shared meaning from repeated uses= of it and related terms. It is common in discourse for one speaker to repeat a term that someone else recently used, as a way of referencing the previous occurrence. In this way, the term takes on a role in the discourse that can= not be attributed to an individual as the expression of a mental idea. The word= is better analyzed as a resource for interaction that is shared by the group. While we may not know quite what a certain student intended when uttering a term, we can see how it was interactionally pic= ked up by others and how it came to play a role in the group discourse. The terms = used in the discourse gradually form a web of meaning, which specifies and deepe= ns the meaning of the various terms within this context. One can say that the students, as a group engaged in interaction, learn over time to understand these terms more deeply (as quasi-technical terms) and to use them more skillfully (as a fledgling team of scientists). One can say that the group discourse progressively refines the shared group meaning of the terms.

Indeed, in a group it is not clear in what sense we ca= n say what a word meant to its individual speaker as distinct from what it turned= out to mean in the group discourse. It is possible that the speaker had mentally rehearsed the word before speaking it. Then we might say that it had a mean= ing defined by that internal dialog—a very small-group discourse of one w= ith oneself, internalized in silent thought. We could also say that the word had gained a meaning for the speaker through his past personal encounters with = that word in a variety of social settings, including texts. One individually bui= lds, refines and abstracts personal webs of meaning (in some ways analogously to latent semantic analysis—see chapter 2) that approximate cultural lexicons.

The terms same= , different and compare are everyday words used to describe a relational refere= nce that might be discussed in terms of “holding variables constant”= ; in scientific jargon. At different points during the collaborative moment, each student shifted his understanding of this relational reference from a model= of standard configurations to one of paired configurations. This shift during = the collaborative moment was an important feature of the interplay between the group discourse and the individual understandings.

Through the reconfiguration of the use of the everyday= words within a quasi-scientific activity structure involving the computational artifact, the shared meaning of the rocket list underwent a Gestalt transformation from being seen as a shared configuration to being seen as a paired configuration. For this to take place at the group level, every group member had to learn to see or interpret the meaningful list in this new way= . To overcome the breakdown in the group discourse, the students eagerly taught = each other how to see in the new way. What the students had to learn was not an abstract rule about holding all but one variable constant. They already see= med to have a sense of this rule, but did not know how to apply it effectively = in practice in the given situation. Jamie, at least, was trying to apply the r= ule assuming a standard configuration of the rockets in the list. Rather, they = had to learn to see the list as already incorporating this rule—but throu= gh a paired rather than standard configuration.

Utterances like Brent’s pivotal pronouncement, “This one’s different,” refer to artifacts in the activity context. In chapter 12 we argued that different participants in the discour= se interpreted Brent’s reference differently, causing a breakdown in the shared understanding. The analysis in the current chapter shows that the deictic phrase, “this one,” does not simply refer to one indivi= dual rocket or one line on the list. It is a relational reference to a pair of rockets or descriptions that stand in a salient relationship to each other.= The ability to comprehend that relationship—and therefore the ability to = see the particular pair of rockets 1 and 2 as a pair (in a contextually meaning= ful sense)—is reliant upon a grasp of the overall list artifact as embody= ing its meaning through its paired configuration structure.

Individual and Group Learning

The preceding analysis suggests that collaboratio= n may often take place with the following structure:

= a.      = A group is engaged in building shared meaning in its discourse.

= b.      Each participant develops an individual interpretation of the meaning of the discourse in parallel to the group interaction.

= c.      = Participation in the group interaction is affected by the individual interpretations; the individual contributions to the discourse reflect the distinctive interpretations, but simultaneously merge in the creation of the discourse’s group-level meaning.

= d.      Individual interpretations are visible (to other participants and to observers) in the interactions of the participants in the group as nuances in how their contributions are integrated into the discourse. The trajectory of an individual’s contributions can be seen as a personal narrative within= the history of the group interaction.

Such a structure would have important implications for= how individual learning can result from group collaboration. If group learning = and individual learning proceed in parallel as different interpretive facets of= a single, complexly interacting process, then we can look for both group and individual learning taking place in all collaborative settings, and not just those in which an individual division of labor is explicitly introduced. For instance, in the previous chapter’s moment of collaboration, the task= of isolating the nose cone effect was accomplished by the group as a whole. Individuals were not assigned sub-tasks or roles. However, an essential, th= ough unstated feature of the collaboration was that each individual had to understand the accomplishment of the group task. Each individual took responsibility for making sure that the others shared a common understandin= g. This responsibility can be seen to be at work in motivating the various contributions to the discourse. In fact, the intense collaboration in chapt= er 12 was precisely an attempt to re-establish shared understanding during a breakdown of it. As individuals started to understand the relational refere= nce that was the key to accomplishing the task, they focused on bringing the ot= her participants around to sharing that understanding. Only when all participan= ts acknowledged that their individual interpretations of the group meaning were aligned did the group proceed to look at the data sheet in accordance with = the relational reference to rockets 1 and 2 and solve the nose cone task.

The parallel working of group and individual learning = is often overlooked when investigating collaboration. Either (usually) one foc= uses on the individual learning and misses the group-level phenomena, failing to identify the process as collaborative, or one focuses on the group interact= ion and assumes that special interventions—role definitions, task divisio= ns, jig-sawing, interdependence, reflection, reporting—are necessary to stimulate individual effects. In our case study, however, we see that the participants have spontaneously organized their interaction to ensure that each individual understanding of= the meaning of the group discourse was aligned in agreement with each other. This was necessary for the discourse and the problem solving to proceed. Of course, such agreement is not absolute in any sense, but adheres to practic= al criteria having to do with permitting the collaboration to continue. The re= sult of this natural structuring of the collaborative process is that the individuals learn in parallel with= the group learning, to the extent needed for the practical purposes of the group activity. Our view of the discourse and the interaction generally made visible the learning at both levels.

The point is not that explicitly introducing individual roles into a group process is necessarily a bad idea; such pedagogical techniques have indeed proved useful in certain settings. Rather, the point= is that individual learning may automatically take place within collaborative interactions. This suggests a response to the argument that group learning = is irrelevant because the group will eventually break up and that we therefore need to focus on individual learning. On the contrary, it may be that group learning often supplies an essential basis for individual learning, providi= ng not only the cultural background, the motivational support and the interactional occasion, but also an effective mechanism for ensuring indivi= dual learning.

In this chapter we have seen an example of how a proce= ss of collaboration required the participants to ensure agreement among their individual understandings. Within the scope of one complex process, the gro= up meaning of the rocket list shifted from a standard configuration to a paired configuration, and each participant learned to make and interpret appropria= te relational references and to see, interpret and discuss the referenced mean= ing accordingly. We will further explore issues of making learning visible, gro= up meaning making and individual interpretation in part III of this book.

1:20:30	Teacher	So how would you find out which is better four fins= or three fins. (1.0)
	Chuck	By launching (&nbs= p; ) with two different things on it–
	Teacher	–Which one—which two.
	Chuck	one with fou::r (.) n one with three: like (0.6) rocket four an rocket o= ne. (0.8) Err no—(.) Ro:cke:ts= , (.) fou:r, n rocket three. Cuz they both have the same engine. (0.8) An they both have the same nosecones.

1:26:46	Brent	I would say that éthree is bett= er than four
	Jamie	&nbs= p; &= nbsp; ëthree is better than four ( &nbs= p; )=3D
	Chuck	Yeah, three is better than four so=3D
	Teacher	=3DSo éyour rocketù
	Chuck	ë(we want) û three fins n a rounded noseécone
	Teacher	&nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; ëYour rocket three goes up higher ‘n rocket four=3D
	students	Yeah ((multiple voices))
	Teacher	So that means that three fins i= s better ‘n four.

1:21:53	Teacher	And (0.1) you don’t have anything like that t= here?
1:21:54		(2.0)=
1:21:56	Steven	I don’t think so
1:21:57	Jamie	Not with the same engine
1:21:58	Steven	┌ No
	Jamie	└ Not with the same
1:21:59	Teacher	With the same engine … but with a different (= 0.1) … nose cone?=3D
1:22:01	Chuck	┌ =3Dthe same=3D
	Jamie	└ =3DYeah,
1:22:02	Chuck	These are both (0.8) the same thing
1:22:03	= ;	(1.0)=
1:22:04	Teacher	Aw┌ right
1:22:05	Brent	= └ This one&#= 8217;s different
1:22:06	Jamie	Yeah, but it has same no…
1:22:07	= ;	(1.0)=

1:22:07		(1.0)
1:22:08	Chuck	Pointy nose cone=3D
1:22:09	Steven	=3DOh, yeah=3D
1:22:10	Chuck	=3DBut it’s not the same engine
1:22:11	Jamie	Yeah, it is, =3D
1:22:12	Brent	=3DYes it is,
1:22:13	Jamie	┌ Compare two n one
	Brent	└ Number two