learning science through technological design

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 38, NO. 7, PP. 768 790 (2001)

Learning Science through Technological Design

Wolff-Michael Roth

Applied Cognitive Science, MacLaurin Building A548, University of Victoria, Victoria,

British Columbia, Canada V8W 3N4

Received 9 December 1999; accepted 12 April 2001

Abstract: In the course of a decade of research on learning in technology-centered classrooms, my

research group has gained considerable understanding of why and how students learn science by designing

technology. In this article I briefly review two dimensions in which science and technology share

fundamental similarities: (a) the production and transformation of representations and (b) the action-

oriented language describing the two domains. Because it is fundamentally problematic to derive what

ought to happen in science classrooms from other dimensions, I provide three episodes to illustrate what

and how students know and learn science during technological design activities. Episodes and analyses

embody the two dimensions previously outlined. Because these episodes are representative of the database

established during an extensive research program, I suggest there is sufficient ground for using and

investigating science-through-technology curricula. 2001 John Wiley & Sons, Inc. J Res Sci Teach 38:768 790, 2001

Science educators have asked themselves for some time whether technology-centered

activities afford a learning environment that scaffolds students learning of science (e.g., Layton,

1994). The question of whether technology has a place in science education was probably

framed most provocatively in the title of an article by Carlsen (1998): Engineering design in the

classroom: Is it good science education or is it revolting? Carlsen answered his own question

with a qualified yes, an answer that required him to redefine science. Generally, some research

shows that technology-related activities provide a rich ground for learning science when they

focus on (a) designing and testing artifacts and (b) critical analysis and explaining performance

failures of artifacts (Roth, Tobin, & Ritchie, in press). Others, especially trained scientists,

suggest that technology is merely an application of science. Technological (design) activities

should therefore be used only after students have acquired sound scientific principles [see

Schon (1983) for examples and an incisive critique of this position].

The literature on the relationship between science and technology is rather heterogeneous

and includes contributions from many disciplines. A review of the literature shows that the

relationship between science and technology has been constructed in the following five ways

E-mail: [email protected]

2001 John Wiley & Sons, Inc.

(Fensham & Gardner, 1994). First, science is said to have ontological and historical priority over

technology. Second, technology was to have ontological and historical priority over science.

Third, science and technology are claimed to be independent domains of material and discursive

practice. Fourth, technology and science are supposed to engage in two-way interactions. And,

fifth, science and technology are claimed to be part of seamless webs that make any distinction

futile. Although particular historical events can be used to bolster one or the other of the first four

claims, none is sufficient to provide a consistent and universal account of the relationship

between the two domains. Because the distinction between science and technology appears to be

inherently fraught with conceptual and empirical difficulties (e.g., Pickering, 1995; Traweek,

1996), it makes more sense to attempt an integration of the two domains in analytical and

curricular terms.

How we conceive science education and whether we ought to organize it around

technological activities depends on how we see these two domains related. In this article I take

the position, consistent with the above-mentioned trends in the sociology of knowledge, that

science and technology are deeply related domains, part of a (semiotically) seamless web that

integrates any distinction (fifth position, above). I begin by conceptualizing the relationship of

science and technology on two levels. The first level concerns the production and transformation

of representations. The second level concerns a performative idiom as an analytic framework [a

performative idiom is a discourse that focuses on what scientists actually do rather than on the

unproven contents of their minds (Pickering, 1995)]. On both levels there are deep similarities

between science and technology.

Even with these similarities, it is difficult to make an argument for teaching science through

technology-based activities. Rather than argue, on the basis of these similarities, that we ought to

teach science through technology, I conducted a series of studies to show how and what children

learn about science when they do technology-centered activities (e.g., Roth, 1995b, 1996a,

1996b, 1996c, 1998a; Roth, McGinn, Woszczyna, & Boutonne, 1999). Here, I provide examples

from one of several research projects. Because technology-centered activities emphasize the

construction of accessible artifacts rather than more inaccessible (abstract) knowledge

representations, they provide students with many opportunities to develop representational

idioms related to technology and science. Illustrative examples underscore how these

opportunities were realized in a four-month technology-centered curriculum that I taught in a

split Grade 6 7 class as a means for students to learn about simple machines (the mandated

curriculum). I conclude this article by extending my discussion of the benefits that arise from

teaching science in technology-centered curricula.

Representations, Translations, and Performativity

There are at least two levels at which we can find deep similarities between science and

technology. First, science and technology engage in the construction and translation of

representations and artifacts. Second, scientific and technological activities can be described by

the same performative idiom, which highlights the processes (e.g., doing, talking, and

manipulating) rather than the products of each domain (e.g., knowledge representations and

objects in the world). In the course of my research I have elaborated a theoretical and

methodological framework for using both dimensions to study learning in science and in

technology-centered classrooms.

Some readers may want to argue that because there are different university departments of

science and engineering, the two domains must be different in principle. However, recent

research in the human and social sciences paints a different image. There are many historical and

ON TRANSLATING REPRESENTATIONS 769

current examples of the coevolution of scientific knowledge and technological development. For

example, the invention of the microscope by the Dutch spectacle makers Hans Lippershey and

Zacharias Jansen brought into motion frantic activity that intertwined optical principles,

astronomical and biological understanding, and further technological developments of the

telescope and microscope (Mason, 1974). Gains in the theoretical knowledge about the telescope

evolved together with gains in the understanding of its mechanical properties. Thus, Kepler

contributed to the further development of the telescope by designing new types and by

formulating the law of the inverse relationship between light intensity and square distance. An

increasing number of studies show that technology and scientific knowledge are increasingly

intertwined and mutually constitutive. This interlacing of science and technology is even more

prevalent in current (big) science, which depends on the appropriate technology (e.g., Galison,

1997; Pickering, 1995; Traweek, 1988). The natural objects described and explained by

scientists can be produced and observed because of considerable technological endeavor. The

phenomena exist only in and as representations, which are, in turn, created by complex chains of

scientific representations and instruments.

Some of the classical distinctions between science and technology are made according to

the apparent relation between nature and representation. Both domains accept the isomorphism

embodied in the relation {fundamental structure () mathematical form} as fundamental(Lynch, 1991). In this isomorphism science moves from left to right by taking as its goal the

coaxing from nature of the fundamental structure through representational abstraction.

Technology was said to move from right to left because it used mathematical forms and

constructed entities that became part of the world, man-made objects among natural objects

(e.g., Lee & Roth, 1999). Two recent developments suggest that this image of representations is

too simplistic.

First, analyses of laboratory work show that simple sign-referent relationships between

nature and mathematics (or other representational forms) do not exist. Rather, there are chains of

activities and translations that begin with screaming rats, defecating lizards, and burbling creeks

and end in some trace on some flat (two-dimensional) medium (e.g., Latour, 1993; Roth &

Bowen, 1999b). This chain of translation, which connects objects in the world (fundamental

structure) and ideas (mathematical structure), is represented in Figure 1. The figure embodies the

observation that any two representations are separated by an ontological gap (that is, by a gap

that separates different kinds of objects). The translation from one representation into another is

not inherently (logically) given but is a matter of convention (e.g., Bertin, 1983; Eco, 1984).

Crossing an ontological gap requires consensus within the community and is a matter of situated

practice (e.g., Suchman, 1995). Engineers generally move in the reverse direction by translating

some design idea into a technological artifact that becomes part of the material world (Fig. 1).

Again, translations between two consecutive representations are not inherently correct but

depend on agreements struck within the community, and the ontological gap is always crossed as

a matter of praxis (e.g., Bucciarelli, 1994).

Second, recent scholarship in science studies has shown that science does not just produce

representations by going from nature to abstract signs (from left to right in Fig. 1). Rather,

because preparation and detection of natural objects are tied so closely to technology, scientists

engage in both directions of the representational work. Preparation of phenomena, instruments,

and (material and discursive) practices are refined in a mutually constitutive manner until a stage

is attained in which they mutually stabilize each other (e.g., Gooding, 1990).

Engineers begin with some initial sketches and work out building plans that are translated

through a variety of representations until they have created three-dimensional models or

prototypes (i.e., from right to left in Fig. 1). They then perform, record, and analyze tests.

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All these activities generate new representations (i.e., from left to right in Fig. 1). Through

additional cycles of designing and testing, engineers evolve the prototype that subsequently goes

into production. This entire process, from the first vague idea to the working prototype,

constitutes the design phase of an artifact (Roth, 1998a). Thus, both science and technology

develop knowledge representations and artifacts. It is not surprising then that scientific

knowledge is often the by-product of technological activities and, conversely, technological

artifacts are the by-products of scientific activities (e.g., Hicks, 1992; Slaughter & Rhoades,

1996).

Science and technology are also similar in that both can be understood as modeling

activities. Inherent in technology and science are modeling activities that link existing culture

and future states of scientific and technological practice; this link, however, is one of historically

emerging contingency rather than one that is causal in nature. Modeling activities do not have a

determinate destination (e.g., Constant, 1989) because the goals of scientists and engineers arise

from a dialectic of resistance and accommodation of sociocultural, political, economic, and

material contingencies and therefore have an emergent quality.

Science and technology share fundamental similarities from an analytic perspective when

we use a performative idiom. A performative idiom makes salient the way activities unfold in

real time and highlights human agency. Invoking human agency foregrounds the temporal

structuring of practice, making it emerge from the dialectic of resistance and accommodation

(e.g., Ilenkov, 1982; Markard, 1984; Pickering, 1995). This view of cognition differs

considerably from the rather static image of cognition in other frameworks, in which it is built on

conceptions and conceptual frameworks or on declarative and procedural knowledge. In both

latter situations, knowing is conceived of as the application of mental structures to worldly states

(e.g., problems).

Figure 1. Traditionally, science and technology have been said to emphasize different representational

relationships between signs and world. Science moved from world to generate knowledge (in the form of

signs), whereas technology moved from ideas and plans to things in the world. Now, it is recognized that

both domains are based on cyclic trajectories in which world and sign are but two stages. Each element in

the center stands for a type of representation and the associated practices and is ontologically distinct from

its neighbors. The translations between neighboring elements are matters of convention rather than logic.


Grounded in semiotics, the performative idiom does not leave out the material. Rather, it

includes material constraints in terms of material agency. In praxis, human (psychological and

sociocultural) and material agencies are then intertwined in the dialectic of resistance and

accommodation. Here, then, the same mangling of social forces, material constraints in the

world, and disciplined human agency (such as gestures, and skills) occur in science and

technology (e.g., Gooding, 1990; Leontev, 1978; Pickering, 1995). In the analysis of scientific

and technological activity, human and material agencies are not entirely symmetric. There is an

asymmetry that arises from one additional feature of human agency that is not necessary for

understanding material agency. This feature is intentionality, which we know in the form of

specific plans and goals.

In the previous paragraphs, I showed that there are at least two levels on which science and

technology share a great similarity. These similarities have led researchers in science and

technology studies (including myself) to develop a common theoretical and methodological

framework for studying learning in both disciplines. These similarities, however, are not

sufficient reason to construct technology-based curricula as a means for teaching science. We

also need classroom research that documents and theorizes how science learning can emerge

from technology activities. At this time there exist few studies of this type. Over the past decade

my own research group has conducted several studies of this type in different contexts. In the

remainder of this article, I will illustrate and synthesize (in a new way) what we have learned

from these studies, beginning with providing a methodological background to this particular

study, from which the subsequent examples will be drawn.

Background

Over the past two decades I have designed, taught, and researched classroom environments

in which students engaged in technological design activities and in the process learned science.

My analyses have made it clear that particular features of learning environments are similar

between the open-inquiry science classrooms I investigated earlier (e.g., Roth, 1995a) and the

technology-centered courses I researched more recently (e.g., Roth, 1998a). These similarities

hinge on the presence of artifacts during the discourse situation. Thus, learning to talk about

technological design shares similarities with learning to talk in the presence of physical

phenomena by constructing semantic networks (concept maps), conducting open-ended

experiments, or modeling motion phenomena with computer software. In this sense the claims

presented here about learning science in technology-oriented courses could also be illustrated

with data from other contexts not concerned with the design of technological devices. In this

article all illustrative cases come from the same four-month unit on simple machines that I had

planned and taught in a Grade 6 7 class.

Simple-Machines Curriculum

This simple-machines curriculum was designed to put representations and performative

dimensions of learning into the foreground. Thus, I created opportunities for students to develop

discursive practices (i.e., representational dimensions) and material practices (i.e., performative

dimensions) in situations with which they could identify. In this class students therefore learned

to design and test artifacts; they learned to talk about the physics of simple machines in the

process. Thus, 60% of the time, students designed machines and presented their work to peers;

15% of the time, they conducted small-group investigations that I designed; and for the

remaining 25% of the time, I designed teacher-directed whole-class conversations. At the

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beginning of each design activity, students received a Request for Proposals originated by

Northern Explorations, a company that has done explorations in the high Arctic, for which it

needed manually driven devices as backup systems in case of power failure. To allow students to

develop their discursive competencies, I planned whole-class sessions during which some

presented their designs, on which their peers could critique and comment.

The design activities deeply engaged students and permitted them to identify with their

designs. In fact, when I handed out the third call for proposals, one student suggested, I dont

think that there exists a company Northern Explorations. You made it all up. Of course, such a

focus on activities and their purposes, which are experienced other than for the sake of learning,

is an important component of learning through participation (Lave, 1993).

Periodically, I prepared activities to focus the whole-class conversations on specific

scientific issues. For example, in one class I set up different pulley systems and projected

a drawing of each. Students were asked to make predictions about the forces in the different

parts of each system and provide justifications for their responses. As students provided different

responses, these were noted on the transparency and grouped. After about half the students had

provided predictions, the forces were measured in the actual system and noted in the

transparency drawing. The class was then called on again to provide revised explanations

about the outcome of the tests. These whole-class discussions therefore had several functions.

First, by selecting transparency and simple machine, I could introduce particular features to the

class discussion and thereby provoke new discursive developments at the class level (e.g., for

the development of the discourse about mechanical advantage, see McGinn, Roth, Boutonne,

& Woszczyna, 1995). Second, these sessions provided the class with opportunities to argue as at

a public (community) level and therefore to learn different ways of describing and perceiving

machines and designs. Third, students participated in the practice of constructing and talking

about two-dimensional representations of three-dimensional artifacts. Although I often int-

roduced some conventions as to the representational form (e.g., see graphical elements in Fig. 2),

it was important to me that students be given opportunities to construct their own graphical

representations. The research in this class provided evidence that constructing representations

and talking over and about them constitute an important aspect of learning, not only the

technological discourse but also the associated scientific discourse (e.g., Roth, 1996c).

Data Collection and Analysis

The data collection involved a team of four people spending considerable effort to

document knowing and learning in this classroom. Students were tested (using written

and practical formats) and interviewed before, during, and after the unit. Two cameras were

used throughout to record childrens activities; these recordings were enhanced by the

observations by two graduate students and by daily postlesson debriefing meetings. (These

were especially important because I was a teacher-researcher always caught up in the

contingencies of teaching, which evolved from working with students. This prevented me

from having a detached observer perspective.) As is usual in design experiments (Brown,

1992), any understandings that emerged from these debriefing sessions were used to adjust

the curriculum. All artifacts used for teaching (e.g., transparencies, instructions, and activities)

and those evolving from childrens activities (e.g., notebooks, glossaries, and devices) also

entered the database. Finally, our team analysis sessions were videotaped, thereby capturing

how categories emerged from the analysis. More detailed description of the particulars of

this design experiment including the rationale for each of the four activity types can be

found elsewhere, as well as detailed cognitive analyses of knowing and learning before, during,


and after the unit (McGinn et al., 1995; McGinn & Roth, 1998; Roth, 1996d, 1998b; Roth et al.,

1999; Welzel & Roth, 1998).

Student Characteristics

The study was conducted in a suburban school of a large city in western Canada. There

were 10 sixth-grade 6 (5 boys, 5 girls) and 16 seventh-grade students (7 boys, 9 girls); one of

the seventh-grade boys left midway through the unit. A considerable number of students

experienced problems in academic and social aspects of schooling; the homeroom teacher and

school guidance counselor, a 21-year veteran, found this the most difficult class he has worked

with in his career. Four of the students were classified as learning disabled (in one case paired

with attention deficit hyperactive disorder), and 1 boy had muscular dystrophy and associated

physical and cognitive difficulties. Two Grade 7 girls experienced difficulties because English

was their second language. There were also three Grade 7 students who had social difficulties

so pronounced that other students refused to work with them. Three students had personal

and family-related problems significant enough to affect their academic work.

Past research has frequently identified grade and gender differences in science achievement

(for a review see German, 1994). Such differences did not exist in the present classroom as

a result of the simple-machines unit. A 2 (boys, girls) x 2 (Grade 6, Grade 7) MANOVA

using students science marks on the final project, the written examination, and discursive compe-

tence during a debriefing session as dependent variables revealed no statistically detectable

Figure 2. During a discussion about why one teacher could pull 20 students using a pulley system, Sean

is in the process of arguing for an alternative design. Because he talks in the presence of his design, which

is visible to all, the drawing and his gestures constitute an alternative means of representations, making for

meaningful communication in the absence of a fully developed discursive competence.

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effects for gender (Wilkss l .87, p .43), grade (Wilkss l .88, p .49), or interactions(Wilkss l = .82, p .27). Five of nine students identified by the homeroom teacher ascognitively or socially disadvantaged achieved in (4 students) or near (1 student) the top quartile.

The following brief descriptions characterize students who benefited greatly from the unit.

Brenda was a Grade 7 girl whoaccording to her homeroom teacher and guidance

counselorwas gifted in many areas. At the same time, Brenda was also extremely disorga-

nized, so that her actual achievement level was low because of her inefficiencies and dis-

organization (The quintessential gifted child, because she is also the mad professor). She was

perhaps the most emotionally troubled child in the class and the most socially disadvantaged

child in that she did not have any friends in the school. Her peers refused to work with her, and

she found collaborators only after considerable teacher-mediated negotiations; nevertheless,

after much hesitation someone always agreed to work with her (though Brenda frequently

complained she had to do all the work, while her partners shared the grade). Interviews showed

that Brenda enjoyed the science lessons and displayed great interest and high levels of

participation. She contributed the multiplicative rule for balance beam and second-class lever

problems to the classroom discourse; from then on this rule was associated with her name

(Brendas law). In her overall achievement she placed in the top quartile.

In most subjects Jon was a very diligent and hard-working Grade 6 student, though he

worked slowly and usually took a long time to complete assignments. He did not catch on

quickly but remained persistent until he understood. Jon was a positive factor in the science

classroom; he was caring, compassionate, and had a strong moral sense. He showed great

interest, a lot of experience and competence in material practices, and developed great discursive

competence. Jon was willing to help others in their projects, to lend his tools, and to teach others

how to use them. He thus was an important figure in helping others to learn. Together with a

Grade 7 girl, Jon was the highest-achieving student in this unit.

Amy was one of the learning-disabled Grade 6 students. The homeroom teacher/guidance

counselor described her as having problems with expressive language and language processing.

She had had a lot of learning assistance in the past but still did not do well on tests. She did not

understand instructions well and needed a lot of reinforcement to understand concepts. Amy

enjoyed the science lessons, often made comments during the discussions, and was eager to learn

tool-related practices (sawing, drilling, and hammering). At first she hardly participated in

whole-class conversation; later, with mounting confidence and a front-row seat, she contributed

considerably. She always volunteered for cleanup. Amy drew great benefit from this unit. Based

on the criterion measures (material practice, discourse, and written test), she placed first in the

second quartile of achievement.

What Technological Activities Afford

This section has several of my examples from a technology curriculum in which students

learned important scientific concepts. However, because these activities took place in the context

of scheduled science lessons, I also designed activities that brought scientific representations

(e.g., language, diagrams, and mathematics) as resources to describe the machines that children

designed. Limited space here does not allow me to make an existence proof for my claim that

technology activities provide an ideal context for learning science; instead, I have to rely on a

few illustrative examples and references to published studies. [A book is available by my

colleagues and me on the various ways in which science discourse can emerge and is constraint

from emerging from technology-based activities and on the strategies teachers might employ to

encourage scientific discourse (Roth, Tobin, & Ritchie, in press)].


The subsections illustrate the benefits of using technology-based (design) activities. The

Making Ideas Inspectable and Arguable subsection shows how design diagrams support

students communication by making ideas concrete, providing an indexical ground to gestures,

and thus allowing complex communication even in the absence of a fully developed verbal

discourse. The Thinking in the World subsection illustrates how artifacts allow students to

unload some of the cognitive effort into their environment, how students step back and evaluate

their (concretized) ideas, and how artifacts give rise to even more ideas. Finally, the Toward

Designing Communities subsection illustrates how presentation and critique of design artifacts

turn into sustained student-centered whole-class conversations that support the emergence of

shared technological and scientific language.

Making Ideas Inspectable and Arguable

Introduction. This section illustrates two important aspects of technology-centered

activities for learning science. First, when students begin designing technological artifacts,

they have to communicate their ideas to peers. Because of the material basis of technology,

design drawings are part of the discourse. These drawings make students accountable for their

ideas that have, as inscriptions, become materially embodied representations. As such, they are

inspectable and arguable. Second, the material basis of these representations (compared to the

more ephemeral ones of spoken utterances) brings an additional dimension to that of topic.

Inscriptions can become the backdrop to conversation that elaborates deictic utterances (it, they,

there) and deictic (pointing) and iconic gestures. As such, inscriptions became part of the

conversation as indexical ground. In this case, it makes more sense to speak of a distributed

communicative act that consists of words, inscriptions, and gestures. These features are shown in

the following illustrations.

Episode 1. This episode is taken from a whole-class discussion designed to account for the

outcome of a tug of war that 20 Grade 6 and 7 students, both girls and boys, lost against a single

opponent (me). This tug of war occurred several weeks after I explored pulley systems with

students during whole-class discussions as described above and after students completed

designing two of their own machines, some of which used pulleys. Prior to the lesson I set up

a block and tackle using a banister just outside the class as a support. During the lesson I placed

myself such that there was a mechanical advantage of 5 (discounting friction) in my favor.

Initially, I asked students to account for why they lost the competition, for which we used the

same type of elements and drawings previously used throughout the lessons (these therefore

constituted recurrent or stable forms of representational practice). Then, students shifted

the discussion by proposing alternative pulley designs that would have changed the outcome.

Sean proposed one of these alternative designs. At first he attempted to describe the design

from his seat. But neither his peers nor I understood what he meant, so he moved to the

chalkboard and began to draw a pulley system. It is at this moment that the present episode began

(Fig. 2).1

Unlike Seans earlier verbal presentation from the back of the classroom (which was

difficult and even incomprehensible to his peers and teacher alike), his description in the form of

a drawing was far less equivocal. Now everyone in the class seemed to understand which

elements Sean wanted included (pulleys, ropes, and a banister) and how the different elements

related with respect to each other (Fig. 2). (In our design efforts, we often used one fixed or

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moveable pulley as a shorthand notion for an entire system.) Because Seans ideas now existed

as a durable inscription, it could be inspected, critiqued, and argued about. That is, Sean did not

just provide some idea and rest with it [as often happens in traditional classrooms (e.g., Lemke,

1990)]. Rather, the drawing committed him and made him accountable for his ideas. In that

situation a critique was immediately instantiated. Alain has observed that in the final drawing the

teacher does not have to pull at all. This observation reiterates a concern Sharon had voiced

earlier: the pulley was attached in such a way that the class pulled on the banister rather than

competing against the teacher.

Analysis. At the heart of the ongoing debate was what should be the exact placement of the

different elements in the pulley system (i.e., support/banister, rope, pulley) and who (class,

teacher) was pulling at different places in the system. Deictic gestures (pointing) therefore

played the important role of identifying elements and their location in the system; iconic gestures

animated the drawing and showed the direction in which each party had to pull. Here then,

deictic gestures isolated and individuated specific elements. Drawing an element did double duty

in (a) making the element salient and (b) indicating its placement in the system. Verbal and

gestural action contributed to bringing each element (and that it already existed) to the

foreground. Thus, Sean drew the presently existing elements (Fig. 2) and suggested that I could

have that (Line 01). In the situation it was not clear to me what he meant, so I requested

specification (Line 02). Seans left hand rose to the top of the pulley represented in the diagram

and then continued to move along the rope attaching the pulley to the horizontal line (the

banister). In this discussion everyone referred to the banister because that is where I had fixed

the block and tackle in the earlier tug of war.

Here, Sean did not just describe a pull but enacted an iconic gesture that stood for the pulling

force. Force therefore was not only represented in the word Sean uttered but also in the gesture

requiring muscles to contract (or expand) and the associated motor neurons (neuronal networks)

to become activated. Force therefore appeared as a verbal and sensorimotor representation.

This is an important aspect of Seans activity given recent neurological findings. First, the same

neuronal circuits responsible for action are also involved in perception (Decety zes, 1999); and

second, language uses the same neuronal circuits that are responsible for motion and motion

perception (Bates, in press). Here is where performative and representational dimensions of

technology overlap.

Elements of the pulley system and their placement with respect to each other were only one

part of the communication that resulted. Because these elements existed as representation in the

world, visible to all, Sean no longer needed to use concept words; deictic terms (here, there, it)

and gestures were sufficient to make salient the relevant element. Furthermore, Sean could

illustrate what participants were to do and where they were to pull. Here he enacted what everyone

could understand as pulling and where in the system such pulling would occur, even without using

a corresponding concept word for entity or action (Fig. 2). In this way communication became

distributed across the setting. In Seans production, speech, gestures, and visual representations in

the background were coordinated. Seans utterances (however limited at that stage in the unit)

together with his gestures and the drawing provided a narrative that made sense. This of course is

an important feature because of the enormous amount of mental effort involved when people have

to construct complex sentences and verbal arguments in domains with which they are not familiar

and therefore lack vocabulary and verbal fluency (e.g., Anderson, 1985). Distributing his

presentation across the representational modalities (i.e., speech, gesture, and drawing) afforded

complex communication that would not be possible otherwise.


Thinking in the World

Introduction. Cogitating with or without scribbling, making sketches, or doing detailed

drawings are important activities during design. However, these activities are limited in that the

dynamic of the constitutive elements and their relations is not specified. That is, an individual

may look at a series of pulleys or cogwheels and suggest that the last one in a series should move

clockwise. Neither the image the person envisions nor the drawing can provide feedback as to

whether this movement would occur in the corresponding physical device. I proposed earlier that

designing should actually refer to the entire set of activities that lead from initial, vague ideas

[which may exist verbally (we are making an Eiffel Tower) or visually] to the construction of

initial prototypes that are tested and to the final working model (Roth, 1996a, 1998a). In this case

the later stages of the process, which involve building and testing prototype models, constitute an

epistemic shift to actively situating parts of cognition into the environment (this shift, of course,

involves both the performative and representational dimensions of human activity, which are

central to my theoretical and methodological framework). Prototyping constitutes an important

stage in the process of designing, for it affords thinking in the world by means of entities

and their relationships, which are represented in real objects and gestures. Design artifacts

allow an externalization of ideas; externalization makes ideas concrete and accessible.

Design artifacts therefore constitute starting points for critical reflection and a rich ground for

even more ideas.

Episode 2. The episode in this section arose during a design activity that asked students to

submit their ideas (i.e., plans, prototypes, and scientific explanations) for a device that was

manually driven and could move heavy loads in a horizontal direction.

Jon and Dave expressed their first idea vaguely as something that is like a ski lift. Dave

made a sketch that although it did not specify the exact dimensions, provided them with a two-

dimensional representation over and about which they could negotiate further issues and that

already provided a basis for communication. It also showed the devices topology, that is, the

shape and relations between the parts of the devices, where and how many pulleys were to be

used, and where the load should be placed. By this stage in the course, they knew that one

important criterion for a machine is mechanical advantage, a quantity determined as the relation

of load to effort. (For the developmental trajectory from the mundane notions of advantage and

disadvantage to the scientific notion of mechanical advantage including the mathematical means

of finding and expressing it, see McGinn et al., 1995.) Their design of the present device was

oriented toward achieving a ratio that was as high as possible.

During this lesson they did not have all the materials to proceed to a first prototype. So Jon

and Dave decided to run a test. This test was designed as a check to see if their machine did

what machines should do: provide a mechanical advantage (What we should do is a 25-gram

weight and then just get a piece of string and right now just see right now if it is a mechanical

advantage.). In this test they wanted see how the different parts of their system interacted and

how the design affected the relationship between effort and the weight of the object. They had

previously used a scale to measure the load, which turned out to be 100 grams (the units on the

scale). Now they began to test the device (Fig. 3).

01 Jon: Just pull it like that. No, wait. You gotta move it down [attaches scale; pulls

on scale (Fig. 3)]. Theres a knot in it.

02 Dave: 350 or so.

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03 Jon: Wait, just try it again. You ran out of the . . . . OK, when you try to pull, howmuch is it? Wait. OK, now stop. OK, its 300, Dave.

04 Dave: Its 300.

In their conversation Jon and Dave made salient that the 300-gram reading was much more

than the 100-gram reading with the object alone. They knew that in their final design the

situation should be different in a number of ways as shown by their comments: We shouldnt

use shoelaces, Well theres going to be pulleys, and It cant be dragging on the ground.

This test provided Jon and Dave not only with a sense of the crucial points in their design but

also of further design ideas about other aspects of the prototype. That is, they represented their

observations during the test so as to allow them to frame new problems and solutions. Jon pushed

on the suspension (Popsicle sticks) intended to hold the pulleys, which bent slightly under the

force of his push. A few moments later he suggested, I got an idea. Maybe we should put like

double. Ill get the glue gun. Ill glue; you hold. Here, as he interacted with the model, Jon

realized that what he had originally planned as a suspension might not hold up under the kind of

loads that intended to move with his system. As he interacted with the model, he noticed the bend

and then suggested how to strengthen the piece by doubling up, that is, layering several Popsicle

sticks.

Analysis. We can look at this episode as an instance in which part of the cognitive effort was

moved into the physical world. This involved a radical change in the form of representation, with

Figure 3. Jon and Dave test the model of their design. They know that using shoelaces instead of round

string and using Popsicle sticks instead of pulleys will decrease their mechanical advantage. But already at

this point, they are concerned with the mechanical advantage their system will give them.


considerable consequences for the observed situated cognition. Each time an idea as concretized

and embodied in a material way, students enact an epistemic move. By making their ideas

concrete, they decrease the demands on mental resources (e.g., Kirsh, 1995). Using real

materials to set up a model of the prototype they were to build, Jon and Dave thought through the

design in the world. Just a tad different from a writing pad, using objects allowed them to explore

the dynamic aspects inherent in their design even if it were incomplete. Some materials used

stood in for those they would ultimately employ. In this sense, the materials were

representations, things standing in for other things. In this the episode was an example not

only of how to do things with things (Streek, 1996) but of things to think with, a process we

called thinkering (Roth et al., in press). Watson (1968) did a similar thing by moving around

cardboard and metal cutouts representing the four chemical bases, which ultimately allowed him

to determine the structure of DNA. By using cutouts, he moved a part of his task into the physical

environment (if we consider the cutouts on the table and Watson as one cognitive system, all we

really see is cognitive activity being shifted around within one and the same system).

Thinking in the world also affords a person the ability to literally stand back and detach

himself or herself from the idea (what thinking in the world affords can equally be considered as

a constraint that operates such that a person enacts only one activity: the desired one). Thus,

students can reflect on these ideas and define and analyze their current stage better than when

they manipulate mental images. This gives rise to further discoveries that might not otherwise be

available to students. For example, Jon had thought that Popsicle sticks were sufficient (ideal) to

support the pulleys that were to carry the string. However, during the above episode he noticed

that the Popsicle sticks were bending as he pulled on the string. He framed this as a structural

weakness, which he proposed they should remedy. Jon and Dave then began to layer the Popsicle

sticks into laminates. There were also pieces of dried glue that were lying on the table. All of a

sudden Jon uttered, I got an idea; we can melt the glue. He went on to place a bit of the

hardened glue on another Popsicle stick and heated it with the glue gun. As it melted, he added

more glue from the gun and then layered another Popsicle stick. Here the situation afforded him

an invention. He found out a material property of the glue: it could be softened and used again. In

this way students continuously expanded their life world, they constructed new objects and

practices, and with these new objects and practices they expanded the range of action

possibilitiesa sure sign that learning and development had gone on (e.g., Holzkamp, 1991;

Lave, 1997).

This episode illustrates another point made earlier. That is, what looks (sounds) like an

incomprehensible utterance when in isolation may in fact be a sensible thing to say in context,

for instance, that in which Jon and Dave found themselves: Just pull it like that. No, wait. You

gotta move it down. There have already been repeated suggestions that communication should

not be thought of as words alone; we need to account for the entire situation, including material

configuration, history of the conversation, gestures, and aspects of the life world taken as shared

by participants. Thus, when we consider Jons utterance only as part of a communicative act, the

totality of which also includes his gestures and the material setting shared by him and his partner,

the communicative act of the system is sufficiently complete such that Dave could know what

Jon was talking about. Thus, technological design contexts provide students with many

communicative opportunities even if they have access to a limited linguistic repertoire. On the

other hand, during the initial phases of learning in a particular content domain, the context

provided by materials, tools, equipment, and the (deictic and iconic) gestures allows students to

communicate with others in a meaningful manner.

Designing technological artifacts therefore allows students to move part of their cognitive

effort into the world in two ways. First, designing itself occurs partially in the world as ideas are

780 ROTH

concretized into material elements and their relation and thinking is done in concord with these

materials. Second, cognition related to communication partially rests in the environment because

entities that are visually available go without saying and serve as background to and constrain

meaning of gestures [an extensive analysis of these phenomena is provided elsewhere (Roth &

Lawless, in press)]. In contrast to the present lessons, many science teachers provide students

only with language as a resource (books, lectures) to express themselves. Therefore, it is not

surprising to me when researchers report that students inevitably think about producing desirable

outcomes before they are able to do more analytic forms of thinking associated with science

(Schauble, Klopfer, & Raghavan, 1991). Even Watson (1968) played around with cardboard and

metal shapes before shifting his talk to chemical bases and the pairwise bonds they form.

Choosing, as I do, students-in-setting as the unit of analysis (e.g., Roth, 2001b) prevents

researchers from employing the unfortunate, problematic, and wanting distinction between

concrete and abstract as they relate to cognition.

Toward Designing Communities

Introduction. Technological design activities inherently make available activity structures

recommended by constructivist educators. For example, when students are called on to develop

their design ideas, the lessons automatically start at developmentally appropriate points for each

student. In traditional science lessons, it is never quite clear where students are at the moment;

thus, a teacher would never quite know whether students like Jon and Dave would be ready now

for a concept like mechanical advantage or levers. However, asking students to produce artifacts

of their own design, as was done in this study, inherently begins at the point they actually are at

that moment. Furthermore, because this form of design asks for the students own ideas,

motivation is inherently intrinsic, as it was in Jon and Daves activities. They wanted to feature

their ideas and thereby contributed in the first instance to the cultural production and only in the

second instance to the cultural reproduction of science. Finally, because there are potentially

many artifacts with different underlying scientific principles, students are exposed to and are

challenged to engage with a variety of ideas and scientific principles. [An important aspect of the

teachers work is to help students make salient those structures that are relevant to science. This

is the crucial point for making the science technology link succeed (Roth, Tobin, & Ritchie, in

press)]. This also provides students with grounds to develop a critical stance to others and to their

own work.

Episode 3. In this situation it was Alain, Brenda, and Julies turn to present their design

for the second Request for Proposals. Their design was a machine that could be used to

manually move heavy loads over a considerable distance. The three students set up the model

they had developed over the past couple of weeks and began their presentation. Having

been enculturated to schooling as a matter of sitting and listening, after the first month

the students still found it difficult to articulate themselves in the unit. This was even true

for Brenda, one of the top-achieving students in this unit (Turn 01). However, in the presence

of the artifact, the three managed to show how their device worked. This immediately

provided opportunities for comments, criticisms, and suggestions for design development.

As they still were present, Randy and Alain already likened the design to a clothesline

(Turns 02, 03).


01 Brenda: OK, there is one pulley down the side, and its like a chairlift.

[Demonstrates movement of object with machine]

02 Alain: Please pull it and it takes.

03 Randy: Looks like a clothesline.

04 Alain: Yeah, like a clothesline.

05 David: Cool, how it works.

06 Julie: Goes back and forth like that

07 Lea: How come you didnt use a crank for moving it there?

08 Alain: How could you put a crank here?

09 Julie: Because it has to go back and forth.

10 Alain: Because you cant just make it go one [moves left hand right (Fig. 4)] way

because then you have to reload [returns left hand to left side (Fig. 4)] it

again, it has to be going back and forth.

11 David: You could put a crank right here [points to crank], just like this, loop the

string around twice and then just turn it because then it will go.

12 Sean: Its also. . .you lose some mechanical advantage when you have to pull it inyour hand, and its good cause the pulleys. . .help, but also, on this work,right here you can [manipulates pulley]. . .

Lea was the first to raise a question that could also be heard as a critique. The designer-

presenters had not thought of a crank for moving the clothesline (Turn 07). Alain (Turns 08,

10) and Julie (Turn 09) each responded in turn, elaborating the previous speaker. They

questioned how it was possible to use a crank if you wanted the line to haul loads in both

directions. Alains gesture (Fig. 4) made the back and forth between the two extremities of the

design quite explicit. In their way of seeing and presenting the issue, it seemed impossible to

have a crank and move loads in two directions. (Julie and Alains responses read together make it

Figure 4. Alain responds to a critique during the presentation of his machine. When asked about why

there is no crank on one of the pulleys, he suggests this would make the machine asymmetric so that, from

his perspective, it could not move loads back and forth.

782 ROTH

plausible that they already had talked about these issues.) Here was where David came to help

(Turn 11), proposing his idea for including a crank while conforming to the specification that the

machine should work reversibly. David actually got up and demonstrated where and how he

would wrap the drawstring around the pulley to make the crank work in both directions. Finally,

Sean suggested that the three presenting students would lose mechanical advantage if they were

to pull directly on the rope rather than using the crank (Turn 12). Remarkably, his critique was

not uttered in contest or animosity but, as the completion of his turn suggests, when he praised

the design, as a contribution to the critique for epistemic (knowledge) reasons.

Analysis. This excerpt exhibits a typical feature of the class conversation about students

artifacts. The conversation included scientific concepts [crank (as instance of wheel and axle

system), mechanical advantage, and wrapping string twice to create friction] and was sustained

by students themselves, without teacher intervention. Even though the school system had labeled

a high proportion of these students as learning disabled, there was always sustained interest in

maintaining the conversations, so that they often had to be interrupted to provide all students

with opportunities to present their design. As it was, the interest was so sustained that the public

presentation and testing of the design took much longer than I had originally planned before the

unit started. Students who sustained an interest in talking about design also developed

competence in talking design. That is, such conversations provide an ideal context for bringing

about and participating in a communal discourse. This discourse, by design, arose from students

own discourses and incorporated, in part because of my infusion of concepts and representations,

new elements that are typical for scientific conversations. Such infusion was possible only

because of the family resemblance between science and everyday discourse, the differences

arising from the particularity of topic and words employed in talking about them. [Elsewhere we

provide detailed descriptions of the dynamics of student-led and teacher-led whole-class

discussions and how discourse patterns change with group size and physical configuration of

speakers and artifacts (Roth et al., 1999).]

Thus, these features of the curriculum provided students with many opportunities to use

their language, to talk about their interests relating to machines, and to suggest features they

noted and found relevant. Even more so than during conversations about inscriptions, the

prototypes could be tested and operated, providing additional occasions that could be talked

about and critiqued. The presence of the device provided opportunities for deictic and iconic

gestures to emerge and opportunities for designing as public performance (e.g., Davids

embodied design move).

In this episode as presented, some readers may notice the absence of follow-up questions

that deepen scientific concerns and concepts. That these were not addressed here was a situated

decision I made as a teacher not to interrupt student discussions as long as these were sufficiently

sustained by student interest. Because I wanted to leave them with a sense of being empowered

and did not want to curb their interest, I made a note of important issues but did not bring them up

until after the discussion had ended.

Discussion

In the previous section I provided illustrations from one technology-centered classroom

in which students learned about simple machines, energy, and forces in increasingly scientific

ways. That curriculum is consistent with my theoretical and methodological framework

because it focused on representations and representational transformations and on the


performative dimensions of learning. The episodes are representative of technology-centered

classrooms that lead to science learning in that they embody some of the central features of all

my studies.

First, artifacts and their representations provide students with concrete topics of talk. They

also provide students with a background against which gestures can be meaningfully used and as

an additional form of communicative representation. Depending on the type of representations

(discourse, inscriptions) and how accessible these are to students, teachers can constrain the

evolution of discursive patterns to become increasingly scientific (e.g., Roth, Tobin, & Ritchie,

in press). Second, because students externalize their ideas in concrete form, they open

themselves up for critique and negotiation with others. The concrete form of design artifacts also

allows students to distance themselves from their own ideas, which literally lie in front of them

in concrete form (sketch, building plan, or material artifact). This distance facilitates students in

critically reflecting on their own ideas. Designing artifacts actually moves thinking partially into

the world and thereby frees up mental resources in developing increasingly complex ideas.

Third, when students present, discuss, argue, and critique their designs in a public forum (e.g.,

whole-class discussion), further opportunities are provided for developing a discourse. Because

this activity structure makes students own products the focus of the lessons, it is likely that

interest in the topic will be sustained and conversation maintained. Participation in practice,

however, is known to be constitutive of learning the practice and constructing the identity of a

practitioner (e.g., Lave, 1993).

In the following subsections I extend my argument by suggesting when and why technology

activities are such ideal contexts for learning science. In making this argument, I am resting my

case not just on these illustrations and on my understanding from this classroom; rather, my

understanding is consistent with evidence from an extended database established during a

decade of research and on studies published in a variety of domains. Here I present a novel way

for theorizing those research findings.

Gestures, Embodied Representations, and Emergence of Language

Having conversations in the presence of design artifacts (drawings, objects) provides

opportunities to use gestures as a core aspect in communicative effort. Gestures are an important

means of representing material entities and relations, for they are also occurring in the world and

are capable of obtaining an iconic relationship with the referent. Words, numbers, and diagrams,

on the other hand, have a more arbitrary relationship to the things they stand for (i.e., the

referents). In a series of linguistic studies I showed the close relationship between students

manipulation of objects (i.e., ergotic and epistemic movements) and their gestures (i.e., iconic

movements) (Roth, 1999, 2000, in press-a; Roth & Lawless, in press; Roth & Welzel, 2001).

These iconic gestures then provide the resources for linguistic expressions to develop. For

example, a student may initially show how she pushed (or saw being pushed) an object before

she was able to articulate forces in ways consistent with Newtonian physics. That is, because

gestures have both topological (show dynamic of motion and relation) and typological character

(can stand for a single entity), they facilitate transitions between embodied and abstract forms of

representation and knowing. These gestures often appear prior to the viable language students

eventually develop to talk about phenomena. This feature is also shown in Figure 4, where

Alains gesture representing back and forth actually preceded the corresponding verbal

instantiation by about 1 s. Later, when students are more familiar with the phenomena, talk and

corresponding gesture always fall within 100 ms of each other. Often, gestures becomeancillary and are dropped altogether.

784 ROTH

Jon and Dave physically employed forces in their designs (possible because of the epistemic

nature of moving design activity into the world), felt the resistance provided by the current setup,

and saw the bending of the Popsicle sticks. These are representations that students understand

because they are part of the same world as the objects and events they have designed. All these

are forms of understanding that are traditionally characterized as embodied knowing.

Representational transformations and performative dimensions that are so central to scientific

and technological activities fall together in this instance.

This increasing abstraction of knowledge from the concrete situation can also be observed at

the level of writing. When students are allowed to use diagrams, they make use of them to

communicate (Roth, in press-a). As they become familiar with the topic of study, students evolve

from using iconic representations of entities (e.g., drawing of hands, charges, rubbing of

materials) to employing more abstract sign forms (circuit diagrams, words). This is no different

in design environments (Roth, 1998a). Thus, the gestures used by Grades 4 and 5 students to

represent the forces in the architectural designs they had evolved showed up as correct force

arrows in subsequent glossary entries (Roth, 2000). Technological design therefore allows

students to flexibly use representations and representational translations. Initially, these

representations have more material character, whereas with experience the same entities may be

represented in what are called more formal representations. At this stage students handle formal

representations in the same way they had handled the material representations earlier. From the

accounts in this article it should be clear that it makes little sense to place a representation (e.g.,

discourse, image, drawing, or diagram) along a continuum from concrete to abstract.

Rather, concrete and abstract are different kinds of relations people develop in respect to the

same representations (e.g., Wilenski, 1991).

Distributed Representations Versus Mental Models

In the previously mentioned linguistic studies of language development in school science

laboratories, I showed how students are enabled to communicate much more complex ideas

when their environments provide resources for physical representations around them and for

using gestures (e.g., Roth, in press-d). Students also learn to use and produce two-dimensional

representations in relation to their three-dimensional referents and to translate these

representations into other representations. For example, Sean and his classmates learned to

talk about pulley systems (e.g., block and tackles) by using abstract diagrammatic

representations of them. As we showed in the context of a three-year study of scientists

graphing at work and in controlled conditions, the relationship between signs and their referents

arises from experience (Roth, in press-b; Roth & Bowen, 1999a). Even scientists have

difficulties interpreting graphs when they are not familiar with the situations they represent (Roth

& Bowen, 2000).

Conceivably, students could tinker with materials until their devices proximately did what

they wanted them to do. There is evidence this form of technology lesson would not lead to the

emergence of scientific discourse (e.g., Roth, Tobin, & Ritchie, in press). That is, if students are

just operating on materials and not forced by the situation to also represent them, scientific

discourse (including talk about force, velocity, acceleration, and addition of vector quantities) is

not likely to occur. However, when students have to articulate and explain their devices and to

defend their design decision in front of their peers, they have to represent their understanding in

some form accessible to the audience. Articulating involves both making salient some aspect of

the world (the boundaries that divide it from other things, and the boundaries that subdivide it

into different but interacting parts) and using specific words to name the aspect (e.g., Dreyfus,


1991). There is philosophical (Merleau-Ponty, 1945), neurocomputational (Churchland &

Sejnowski, 1992), and neurophysiological evidence (Varela, 1995) that without moving about

and physically interacting with the world, articulation of the former type is impossible.

At the same time, being able to perceive entities and to talk about them goes hand in hand.

Isolating something as entity from a heretofore indistinct ground and making it a figure

that stands against the remaining ground requires some form of activity (sometimes movement

to change perception; imagined movement may suffice). Technology-based activities are

prime candidates for engaging students in the world and thereby making figure-ground

distinctions.

Thinking with (and talking in the presence of) physical models and inscriptions adds a

cognitive advantage that has been little discussed in the science education literature on mental

modeling (e.g., Gentner & Stevens, 1984). Mental models (loosely defined as anything we image

and imagine while cogitating on our own) are not subject to the same kind of constraints as

objects in the world. That is, whereas the relationship between parts of some design is arbitrary

in a mental model, material agency constrains the relationship between design elements. Watson

(1968) first used cardboard representations of the different chemical bases that were thought to

be part of DNA. However, when they locked in place, he did not trust the fit (which he could

not even bring about through mental manipulation of chemical structure) and had new

representations made from metal. In this sense, mental models are even more flexible and

uncertain than the models one can make from cardboard.

In other words, designing with material models has an advantage because they constrain

considerably how elements set into a relationship (i.e., by means of some connection, physical

forces, friction, etc.) can behave. It is interesting that engineers also design, prototype, and test

designs that, when these have become artifacts in the world, do not hold up to specification. One

of the best-known examples is the Tacoma Narrows Bridge, which collapsed within days of

completion. That is, although the engineers had perfect mathematical and drawn models of the

situation, the bridge when actually built behaved differently. Furthermore, even though

engineers, builders, and city planners along the Pacific Northwest have known for decades about

the dangers to buildings from earthquakes, it took repeated disasters to change building codes

sufficiently to make structures more earthquake proof.

Design is inherently open, contributing to the continuous maintenance of whatever interest

is possible. Each design decision arises as a contingent from the constraints of the moment and

from the dialectic of resistance and accommodation. However, because of the emergent

character of the next decision, it is not possible to foresee what comes after, as the possibilities

escalate exponentially. [Even experienced engineers working on multibillion megaprojects such

as the French Aramis project (Latour, 1993) have not foreseen to any extent where their design

would be in a few weeks or months.] Thus, learning to model physical systems in the world

provides considerable cognitive advantage to students as problem solvers because of the

constraints on the viability of communication, idea development, and descriptive and theoretical

discourse.

Teaching Science and Technology

In concluding this article, I want to return to the question that constitutes its central concern:

What do technology-related activities bring to the learning situations that do not exist in teaching

science through textbook activities? To me, the most important aspect of the complex answer to

this question is: In technology activities focused on design, students are deeply involved in

creating and transforming representations in the directions of science and technology, arenas

786 ROTH

traditionally denoted as separate. They are also deeply involved in activity and therefore in the

performative aspects of knowledge. In artifacts individual elements and their relations can be

described and explained in terms of a scientific idiom. This, however, is not the only possible

idiom. Other idioms may be concerned solely with the functioning of the artifact, its artistic

value, and so forth. This appears to be the crucial point for teaching science through technology-

related activities. Because technological activities provide grounds for the development of

discourses that bear family resemblance with scientific discourse, there is legitimate reason to

employ such activities in science education. Technological activities are therefore prime

contenders for an integrated approach to teaching, for they could be the hub in which students

engage in a variety of discourses that bear a resemblance to those traditionally associated with

the arts, technological design, mathematics, science, language arts, and so forth.

Notes

1The following transcription conventions have been used.

*: up arrow indicates at which part in the utterance the gestural position represented above it occurred;(0.6): time in seconds between gestures and words;

DRAWS [rope]: verbs in capital letters represent actions and an argument in brackets is the object of

the action;

: equal sign indicates a shorter pause than normal between two utterances.

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