Research Methodology on LanguageDevelopment from a ComplexSystems PerspectiveDIANE LARSEN–FREEMANEnglish Language Institute500 E. Washington St.University of MichiganAnn Arbor, MI 48104Email: dianelf@umich.edu

LYNNE CAMERONThe Open UniversityCentre for Language and CommunicationWalton HallMilton KeynesMK7 6AAUnited KingdomEmail: l.j.cameron@open.ac.uk

Changes to research methodology motivated by the adoption of a complexity theory per-spective on language development are considered. The dynamic, nonlinear, and open natureof complex systems, together with their tendency toward self-organization and interactionacross levels and timescales, requires changes in traditional views of the functions and rolesof theory, hypothesis, data, and analysis. Traditional views of causality are shifted to focus onco-adaptation and emergence. Context is not seen as a backdrop, but rather as a complexsystem itself, connected to other complex systems, and variability in system behavior takes onincreased importance. A set of general methodological principles is offered, and an overviewof specific methods is given, with particular attention to validity in simulation modeling.

IN THIS ARTICLE, WE WISH TO CONSIDERways of researching language development froma complex systems perspective.1 A complex sys-tem is one that emerges from the interactions ofits components. The components can be agentsor elements. An example of the former wouldbe a flock of birds, which emerges from the in-teractions of the individual birds that composeit. An example of the latter would be air cur-rents, moisture, and temperature interacting toyield a weather system. Complex systems are of-ten heterogeneous, being made up of both agentsand elements. The ecosystem of a forest wouldinclude, as component agents, animals, birds, in-sects, and people; component elements would in-clude trees, winds, rainfall, sunshine, air quality,soil, and rivers. Not only are there many agentsand elements in a complex system like an ecosys-tem, but they are of different kinds.

Some complex systems, such as the stock mar-ket, are dynamic and nonlinear. They are dy-

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namic, in that the worth of stocks changes overtime, sometimes continuously, both up and down.They are nonlinear, in that at other times, the sys-tems change suddenly and discontinuously. Thesesystems are open to outside influences; in the caseof the stock market, it is open to new investmentsor to changes in regulations. Following a precip-itous decline in the stock market, if new invest-ments are forthcoming, the system is said to self-organize, generating new, emergent modes of be-havior from the investments that are being made.2

Chaos/complexity theory has been used tostudy complex, dynamic, nonlinear, open sys-tems, including naturally occurring systems, suchas the weather and the rise and fall of animalpopulations. More recently, it has also been ap-plied to human behavior in, for example, thedisciplines of economics and epidemiology. Al-though predator–prey interactions influencinganimal populations and the spread of disease are,of course, different in many ways, they have incommon dynamical properties of change.

Many of the phenomena of interest to ap-plied linguists can be seen as complex systemsas well (Larsen-Freeman, 1997; Cameron, 2003).

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Applied linguistic complex systems are likely tocontain many subsystems, nested one within an-other. For example, if we see the speech com-munity as a complex system, then it will alsohave within it sociocultural groups that them-selves function as complex systems; individualswithin these subgroups can be seen as complex sys-tems, as can their individual brain systems. Thereare complex systems at all levels, from the sociallevel to the neurological levels. The complexityof a complex system arises from components andsubsystems being interdependent and interactingwith each other in a variety of different ways.

Because applied linguists deal with complex dy-namic systems, we think complexity theory offersa helpful way of thinking about applied linguisticmatters (Larsen-Freeman, 1997; Larsen-Freeman& Cameron, 2008; see also de Bot, Lowie, & Ver-spoor, 2007; Ellis & Larsen-Freeman, 2006). Weuse complexity theory as an umbrella term to in-clude not only complexity theory, but closely re-lated chaos theory, dynamic(al) systems theory,and complex systems theory. It also relates welland therefore embraces ecological approachesthat adopt an analogy between complex ecolog-ical systems and human language using/learningsystems (Kramsch, 2002; Leather & van Dam,2003; van Lier, 2004). Although complexity theoryhas originated in and benefited greatly from workin the natural sciences, there is certainly a mate-rial difference between applied linguistics and thenatural sciences with respect to objects of inquiry.However, the question we entertain in this articleis whether the difference is as clear when it comesto “methods of inquiry” (Gaddis, 2002, p. 113).3

To address this question, we will first discuss howcomplexity theory warrants changes from tradi-tional research that tests hypotheses in order toidentify causes for particular events. Then, we willoffer some general methodological principles forinvestigating language development from a com-plexity theory perspective. Last, we will make somesuggestions for how to take extant methods andapply the new principles to them so that they arerelevant for a new ontology. Central to all aspectsof these discussions is the dynamic nature of com-plex systems—change and variability become theheart of what is investigated.

CHANGES FROM TRADITIONAL RESEARCH

The Nature of Hypotheses

A first major area of difference between a com-plex systems and a traditional approach to re-search involves the nature of hypotheses and theo-ries that drive or frame research. Specifically, it has

to do with how we understand and attempt to ex-plain the phenomena that are observed—the na-ture of explanations and the level of explanations.Complexity theory works at the system level, andexplanation is in terms of the system’s behavior,not at the level of individual agents or elements(unless, of course, they are the system that is un-der investigation). Because many complex systemsare interconnected and coordinated, it is not al-ways possible to explain behavior, and changes inbehavior, by detailing their separate componentsand roles in what Clark (1997) called “a compo-nential explanation” (p. 104). To use an analogythat may be familiar to readers, when a sand pile isbeing steadily added to from above, it eventuallycollapses in a large avalanche, but we can neverknow which particular grain of sand will producethe avalanche (Bak, 1997). What we know is thatif sand keeps being added to the pile, eventuallyan avalanche will occur. We also know about pat-terns and distributions of avalanche sizes. Becausewe know these things, we can articulate an expla-nation at a higher level, that is, our explanationof sand pile avalanches is expressed in terms ofthe structure and stability of the sand pile, ratherthan in terms of the behavior of individual grainsof sand.

Such a perspective is antithetical to the com-mon reductionist approach in science, which re-lies on the central principle that one can bestunderstand an object of inquiry by taking it apartand examining its pieces. From a complexity the-ory perspective, knowing about the parts individu-ally is insufficient because complexity theorists areinterested in understanding how the interactionof the parts gives rise to new patterns of behavior.In addition, reductionist explanations can neverbe exhaustive or complete because the behaviorof every part of the system cannot be fully known.Moreover, even if it were possible to know aboutthe behavior of the individual parts and their in-teractions, the individual parts do not make a con-sistent contribution to interactions over time. Fur-thermore, the systems can be very sensitive. Thislast point is often referred to as the butterfly effect ,the notion that even a small action, such as a but-terfly flapping its wings in one part of the world,can have a large influence on meteorological con-ditions somewhere else. The “unknowableness” incomplex systems, together with their nonlinearity,which leads to discontinuity and self-organizingchange, makes them unpredictable in the con-ventional sense of predictability.

Systems and behavior can, of course, be de-scribed retrospectively, after change has hap-pened, and this is the central work of a com-plexity theory approach. What we can observe

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in language development is what has alreadychanged—the trajectory of the system. This is atrace of the real system, from which we try to re-construct the elements, interactions, and changeprocesses of the system (Byrne, 2002). Such a pro-cess is retrodiction (or retrocasting), rather thanprediction (or forecasting); that is, it explains thenext state by the preceding one.

In conventional science, explanation producesprediction in the form of testable hypotheses. Incomplexity theory, after a system has changed orevolved, the process might be explicable throughan appeal to such notions as self-organization,but new predictions are not necessarily a conse-quence. Of course, we may have expectations ofhow a process will unfold, or even of its outcomes,based on prior experience, but essentially, adopt-ing a complexity theory perspective brings abouta separation of explanation and prediction.

Causality

Closely related, because a key type of scientificexplanation is that “cause x produces outcomey,” is the matter of causality. In the traditional re-ductionist scenario, the researcher searches fora critical “element whose removal from a causalchain would alter the outcome” (Gaddis, 2002, p.54) and that can thus be said to be the cause ofthe outcome. To suggest that an event may havehad many antecedents or causes is not consid-ered good research. Gaddis (2002) quoted a re-cent guide to social science research to illustratehow this traditional view of causality translates intomethodology: “A successful project is one that ex-plains a lot with a little. At best, the goal is to use asingle, explanatory variable to explain numerousobservations on dependent variables” (p. 55). Hethen explained that “reductionism implies, there-fore, that there are indeed independent variables,and that we can know what they are” (p. 55)—aconcept that entertaining language developmentas a complex system would encourage us, at least,to question because the unknowableness and in-terconnectedness of systems makes it much moredifficult, if not impossible, to isolate independentvariables that act in causative ways.

In fact, some would go even further. Byrne(2002) argued that social scientists’ adoption of“variable centred analysis,” in which some vari-ables are held to work as causative or determiningforces, is ill-advised. He urged: “death to the vari-able,” and then continued:

Let us understand clearly, once and for all, that vari-ables don’t exist. They are not real. What exists arecomplex systems, which systems are nested, intersect-

ing, which involve both the social and the natural,and which are subject to modification on the basis ofhuman action, both individual and social. (p. 31)

Although dealing a death blow to variables may bemore extreme than some would like, and indeedwe have preserved here the use of the term vari-able (though we redefine it as a collective variable—see “Methodological Principles” section), thereis no doubt that complexity theory types of ex-planation, which do not allow prediction in thetraditional sense, differ from what we are usedto. Instead of investigating single variables, westudy modes of system change that include self-organization and emergence. Emergent proper-ties or phenomena occur when change on onelevel of social grouping or on the timescale of asystem leads to a new mode on another level ortimescale. An applied linguistics example is whena new lexical item is first used in conversationsbetween individuals. As this behavior iterates, andothers adapt to it, the new lexical item later be-comes established in language use more generally.Eventually, it may become sufficiently convention-alized to warrant a dictionary entry. Cameron andDeignan (2006) cited the example of emotionalbaggage , a metaphorical phrase referring to long-term issues that are still active in a person’s mind.This phrase has emerged fairly recently in English,influenced by social changes and language uses.Its emergence could not have been predicted us-ing the usual definition of prediction; neverthe-less, the genealogy of such phrases can be studiedand their origin can sometimes be explained inretrospect.

We have termed one type of causality that is op-erable in complexity theory co-adaptation (Larsen-Freeman & Cameron, in press). Co-adaptation de-scribes a kind of mutual causality, in which changein one system leads to change in another sys-tem connected to it, and this mutual influenc-ing continues over time. For example, a nativespeaker may adjust pronunciation, speed, andlexicogrammar when speaking with a nonnativespeaker, and the nonnative speaker may adjustin response as the language she or he is hear-ing becomes easier to process. Co-adaptation, ofcourse, occurs in first language development, aswell, between an infant and an “other,” who, earlyon, is his or her caretaker. As the child and thecaretaker interact, the language resources of eachare dynamically altered, as each adapts to theother. In classrooms, teachers and students con-tinually co-adapt—establishing the patterns of fa-miliar routines and activities. From co-adaptationof teacher and student behaviors emerges a

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structure at another level, one that we might callthe lesson. Similarly, moving down one level, withinthe student as an individual, co-adaptation of mul-tiple subsystems of language leads to the emer-gence of new language resources with which tocommunicate.

Van Geert and Steenbeek (in press) describeda particular type of co-adaptation when they ap-pealed to the notion of superposition, in which aphenomenon is characterized by two (apparently)incompatible properties at the same time. Theirexample is the construct of intelligence, whichis, they argued, “at the same time (almost) com-pletely determined by the environment and (al-most) completely determined by genes” (p. 5).This apparent paradox is resolved when it is seenthat “genes and environment are locked in a com-plex chain of steps over time and that they can-not be conceived of as variables that make mutu-ally independent contributions to development”(p. 5). Van Geert and Steenbeek (in press; seealso van Geert, this issue) used the idea of mutualcausality in modeling first language development.They saw this development as

a web of interacting components that entertain sup-portive, competitive and conditional relationships.The relationships are reciprocal but not necessarilysymmetrical. For instance, it is likely that an earlierlinguistic strategy bears a supportive relationship toa later, more complex linguistic strategy. The latter,however, may have a competitive relationship with itspredecessor . . . . By modeling such webs of reciprocalaction, it is possible to understand the emergenceof stages, temporary regressions, inverse U-shapedgrowth and so forth. (p. 9)

Following a suggestion from Gaddis (2002), itmay be helpful to think of causation as contin-gent, rather than categorical. In other words, weshould think in terms of “particular generaliza-tions” (p. 62), not universal generalizations. Wemight acknowledge tendencies or patterns, but re-sist claiming applicability for our findings beyondspecific times and places. For example, if askedwhether a particular teaching technique is effec-tive, a teacher’s reply, “It all depends,” is particu-larly apt to illustrate this point, because the successof a given technique depends on many things. Itdepends on the characteristics and goals of theparticular individuals who compose the class. Itdepends on the school and community in whichthe class is situated. It depends on the day of theweek that the technique is used, even on the timeof the day, and so forth. If we think in terms ofreality as a web, then “everything is connected insome way to everything else” (Gaddis, 2002, p. 64).The independence of any individual variable then

becomes questionable, as does the idea of a singlecause giving rise to a complex event. Rather, it islikely that there are multiple and interconnectedcauses underlying any shift or outcome. “We mayrank their relative significance, but we’d think itirresponsible to seek to isolate—or ‘tease out’—single causes for complex events” (Gaddis, 2002,p. 65). Of course, because the future is unknow-able, it does not follow that there is no continuityfrom the past. “Some continuities will be suffi-ciently robust that contingencies will not deflectthem” (p. 56).

In summary, a complexity theory perspective,by deconstructing the very notion of causality, un-does the conventional expectation that a goodtheory is one that describes, explains, and pre-dicts. Instead of static laws and rules that socialscientists and applied linguists, in following re-search in the natural sciences, have traditionallysought to uncover, we are faced with tenden-cies, patterns, and contingencies. Instead of sin-gle causal variables, we have interconnecting andself-organizing systems that co-adapt and that maydisplay sudden discontinuities and the emergenceof new modes and behaviors. A good applicationof complexity theory describes the system, its con-stituents, their contingencies, and also their inter-actions. Teasing out the relationships and describ-ing their dynamics are key tasks of the researcherworking from a complex systems perspective.

Data and Evidence

A complexity theory view of language use andlanguage development has implications for re-search methodology beyond the nature of hy-potheses, causality, and predictions. What data dowe collect and what kind of measurements areto be made, in a perspective where everything isconnected and continually changing? Adoptinga complexity theory perspective shifts our viewof what seems to need empirical investigation, inparticular the role of context and environment. Itchanges what we need to collect as data to under-stand a complex system, in particular our attitudeto variation. It changes what we notice in the be-havior of systems: Flux and variability signal possi-ble processes of self-organization and emergence;sudden phase shifts signal important changes andcan direct attention to the conditions that lead upto them. In this section of this article, we considerthe implications for research of three key com-plexity aspects: stability and variability, context,and interacting levels and scales.

Stability and Variability. In complexity theory,phenomena of interest are visualized by evoking

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spatial metaphors. For instance, the state spaceof a complex system is a multidimensional land-scape that represents all possible states of the sys-tem. As a complex system makes its way throughstate space, it is attracted to or prefers a particularregion of that space. The trajectory of the systemover its state space thus represents the actual suc-cessive states of the system. Even when a complexsystem is in a stable mode (called an attractor), itis still continually changing as a result of changein its constituent elements or agents andchange in how they interact, and in response tochange in other systems to which it is connected.In other words, stability is not stasis. A complexsystem will show degrees of variability around sta-bilities, and the interplay of stability and vari-ability offers potentially useful information aboutchange in the system. From this perspective, vari-ability in data is not noise to be discarded whenaveraging across events or individuals, or the re-sult of measurement error (van Geert & van Dijk,2002), but is part of the behavior of the system,to be expected around stabilities, and particularlyat times of transition from one phase or mode ofbehavior to another. Changes in variability can beindicators of development. If we smooth away vari-ability, by averaging, for example, we lose the veryinformation that may shed light on emergence(Larsen-Freeman, 2006a). If, instead, we pay at-tention to the nature of changes in stability andvariability, we may find new ways of understand-ing language learning or development processes.As Fischer and Bidell (1998) suggested when theydiscussed cognitive development:

The static notion of stage structure, which dominatedtheories of cognitive development from its inceptionas a field of study through the early 1980s, has provenincapable of accounting for the massive and grow-ing evidence of both variation and consistency: wide-ranging variability within and across individuals in theage of acquisition of logical concepts across domainsand contexts, systematic sequences in the order ofacquisition of many of these concepts and their com-ponents, and high synchrony in development of someconcepts under some conditions . . . . Why have therebeen so few efforts to account for systematic variabilityin developmental patterns? (p. 470)

We might ask the same question about patterns oflanguage development.

Variability and its relations with stability can bemeasured in two ways. First, the degree of variabil-ity around the stable mean serves as “an index ofthe strength of the behavioral attractor” (Thelen& Smith, 1994, pp. 86–87). If variability increases,with concurrent loss of stability, the system maybe about to enter a transition to a new mode. An-

other measure uses the outcome of perturbing,or pushing, the system away from its stable behav-ior. The more stable the system is, the more likelyit is to return to the stable mode. A less stablesystem is more likely to shift into a different be-havior. Around times of transition, the system willbe more easily perturbed when pushed out of itspath (Thelen & Smith, 1994).

Lack of stability in knowledge or performancemay suggest something interesting happening inthe language or language development system. In-vestigation of variability occurs in dynamic mod-eling (see van Geert, this issue) and can indicatepotentially fruitful points in longitudinal data forin-depth investigation.

The Changed Nature of Context . In a complexityperspective, context includes the physical, social,cognitive, and cultural, and is not separable fromthe system. Context cannot, for example, be seenas a frame surrounding the system that is neededto interpret its behavior (Goffman, 1974). Theconnection between system and context is shownby making contextual factors parameters or di-mensions of the system. Complex systems are of-ten sensitive to changes in context and adapt dy-namically to them in a process of “soft assembly”(Thelen & Smith, 1994, p. 60). For example, thegalloping motion of the complex system formedby a horse and its rider will be soft assembledas the horse adapts to changes in the positionof the rider, the firmness of the ground surface,wind speed and direction, and its own fitness andhealth. Similarly, the children observed learningto reach and grasp by Thelen (Thelen & Smith,1994) adapted their movement dynamically to thelocal conditions of each task, such as the slopeof the surface or the distance at which an ob-ject was placed. Furthermore, these local adapta-tions to contextual conditions are the foundationfor emergent change, that is, development, on alonger timescale. From repeated adaptive experi-ences in the “here-and-now” of context, attractorsemerge in the system that represent a more globalorder, that is, at a higher level of social organiza-tion or longer timescale.

In our applied linguistics context, any use oflanguage can be seen as the soft assembly of lan-guage resources in response to some language-using activity. Use of language need not be verbalproduction but would include any activity, insideor outside the classroom, that involves mental ac-tivity around language: understanding, speaking,recall of language, meaningful practicing, and soon. Language learning or development emergeswith these adaptive experiences of language use.

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The context of a language learning or language-using activity includes the intrinsic dynamics ofthe learner, that is, what individuals bring to theactivity, for example, their cognitive context (e.g.,working memory); the cultural context (e.g., whatroles the teacher and the students play in this cul-ture); the social context, including relationshipswith other learners and the teacher; the physicalenvironment; the pedagogical context, that is, thetask or materials, and the sociopolitical environ-ment; and so on. Many of these contextual con-ditions also will be complex, dynamic, adaptivesystems. The students in action will soft assembletheir language and other resources in responseto these contextual conditions, and the teacherand other students (to the extent that they can)will adapt in response to the students’ actions.We thus cannot separate the learner or the learn-ing from context in order to measure or explainthem. Rather we must collect data about and de-scribe all the continually changing system(s) in-volved. In holding learner and context as insep-arable, a complexity theory perspective makes asimilar argument to sociocultural (e.g., Lantolf,1994) and ecological approaches (e.g., van Lier,2004), but perhaps emphasizes a different facet,seeing learner and a complex context as interact-ing, co-adaptive dynamic systems.

The complexity theory perspective also puts aslightly different slant on the claim that learning,as change, is at once individual and social. Eachindividual is unique because he or she has devel-oped his or her physical, affective, and cognitiveself from a different starting point and throughdiffering experience and history. Each individualthus acts as a unique learning context, bringinga different set of systems to a learning event, re-sponding differently to it, and therefore, learningdifferently as a result of participating in it. In aver-aging across individuals, we lose detailed informa-tion about how those systems change in responseto changes in context. When an individual partici-pates in a group, the group as a system both affectsand is affected by the individual. So, to understandlanguage learning processes, we need to collectdata about individuals (as well as about groups),and about individuals as members of groups aswell as working alone. When researching groups,we need to see them as interconnecting systemsof individuals. As van Geert and Steenbeek (inpress) said:

Although it is statistically possible to separate context-and person-aspects, such separation requires the as-sumption of independence of persons and contexts.This assumption is untenable under a dynamic in-terpretation of performance. On a short time scale,

context affordances4 and person abilities result fromthe real-time interaction between the two and are,therefore, inherently dependent on one another. Ona longer time scale, persons tend to actively selectand manipulate the contexts in which they function,whereas contexts on their turn help shape the per-son’s characteristics and abilities.

Nested Levels and Timescales. One other specialconsideration must be made in studying languageand its development from a complex systems per-spective, and that is the matter of nested levelsand timescales. To start with nested levels, froma complexity theory, systems exist at different lev-els of granularity; that is, they are nested from amacrolevel, such as that of a whole ecosystem, allthe way down to a microlevel, such as subatomicparticles. Such scale hierarchies are well knownin biology (Salthe, 1993). The various systems op-erate at different levels but are interconnected.When attempting to explain the behavior of thesystem, each of these levels may contribute. In thisexample, cited by Sealey and Carter (2004), thespread of tuberculosis is explained through invok-ing four nested, interacting levels:

In accounting for who gets TB and in what contexts,Byrne argues, we must first acknowledge a biologicalaetiology (people must be exposed to the bacillus)and a genetic component (some people will have anatural resistance to the bacillus). However, whetherparticular individuals contract the disease or not willbe socially contingent, since it will depend on theinteraction between these features and other levelsof the social world. Byrne identifies four such levels—the individual, the household, the community and thenation-state—existing in a nested hierarchy. (p. 198)

In addition to nested levels, the complex sys-tems researched by applied linguists operate on arange of timescales, from the milliseconds of neu-ral processing through the minutes of a classroomactivity to change on an evolutionary timescale.For a particular study, certain levels and scaleswill be focal, but they will be affected by whathappens on other levels and scales. As Lemke(2002) pointed out, “certain events widely sep-arated in linear time may be more relevant tomeaningful behavior now than other events whichare closer in linear time” (p. 80). Because activ-ity on one level and scale influences what hap-pens on other levels and scales, with phenomenasometimes emerging at a particular level or scaleas a result of activity at a lower level or in anearlier period, it is important when we are con-ducting research within a complex systems ap-proach that we seek to find relationships withinand across different levels and timescales. When

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we are able to do so, the results will be all the morepowerful.

Summary

To summarize thus far: In complexity theory,we search for ways to access the relational na-ture of dynamic phenomena, a search that is notthe same as the pursuit of an exhaustive taxon-omy of factors that might account for behavior ofany given phenomenon. Furthermore, we attemptto distinguish between contingent and necessaryoutcomes. Thus, the nature of description andexplanation changes, cause and effect no longeroperate in the usual way, and reductionism doesnot produce satisfying explanations that are re-spectful of the interconnectedness of the manynested levels and timescales that exist.

METHODOLOGICAL PRINCIPLESFOR RESEARCHING LANGUAGEAND LANGUAGE DEVELOPMENT

From this complexity theory perspective, cer-tain methodological principles follow. In the com-plexity approach that we adopt, it is important

1. To be ecologically valid, including context aspart of the system(s) under investigation;

2. To honor the complexity by avoiding reduc-tionism, and to avoid premature idealization byincluding any and all factors that might influencea system;

3. To think in terms of dynamic processes andchanging relationships among variables, by con-sidering self-organization, feedback, and emer-gence as central;

4. To take a complexity view of reciprocalcausality, rather than invoking simple, proximatecause–effect links;

5. To overcome dualistic thinking, such as ac-quisition versus use or performance versus com-petence, and to think in terms of co-adaptation,soft assembly, and so forth;

6. To rethink units of analysis, identifying col-lective variables (those variables that character-ize the interaction among multiple elementsin a system, or among multiple systems, overtime);

7. To avoid conflating levels and timescales, yetseek linkages across levels and timescales, and in-clude thinking heterochronically; and

8. To consider variability as central, and inves-tigate both stability and variability in order to un-derstand the developing system.

MODIFIED RESEARCH METHODOLOGIES

We now move to consider practical implica-tions of the complexity theory perspective for theempirical investigation of language development,such as measuring the effectiveness of pedagogicinterventions or tracking stabilities and variationin learner language. When enacted, some of themethodological principles cited previously will nodoubt lead to innovations of which we are cur-rently unaware. Some methods, however, are al-ready in existence with designs that make themuseful for investigating complex systems. Othermethods will need some modification.

Ethnography

In many ways, qualitative research methods,such as ethnography, would appear to serve theunderstanding of language as a complex dynamicsystem well, in that they “attempt to honor the pro-found wholeness and situatedness of social scenesand individuals-in-the-world” (Atkinson, 2002, p.539), by studying real people in their humancontexts and interactions, rather than aggregat-ing and averaging across individuals as happensin experimental and quantitative studies. Atkin-son cited as examples of applicable ethnographicmethods the works of Holliday (1996), Davis andLazaraton (1995), and Ramanathan and Atkinson(1999).

Agar (2004) went further, arguing that ethnog-raphy is itself a complex adaptive system, thatevolves and adapts as the researcher uses it:

[It] will lead you to ways of learning and documentingthat you had no idea existed when you first started thestudy. You will learn how to ask the right question ofthe right people in the right way using knowledge youdidn’t know existed. You will see that certain kindsof data belong together in ways that you would neverhave imagined until you’d worked on the study forawhile . . . methods “evolve” as local information abouthow to do a study accumulates. Ethnography does this.Traditional research prohibits it. (p. 19)

It is important to note that ethnographers seekemergent patterns in what they study. Agar sug-gested that ethnography is a fractal-generatingprocess. What ethnographers are looking for areprocesses that apply iteratively and recursively atdifferent levels to create patterns, variations thatemerge from adaptation to contingencies andenvironment.

One possible modification of ethnographicmethod, from a complexity theory perspective,however, is the assumption that, when applied

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effectively, ethnography can produce objectivity.From our perspective, no matter how a researchertries, total objectivity—a view of matters apartfrom who he or she is—can never be achieved.A complex system is dependent on its initialconditions, and these conditions include the re-searcher. Accounts of the “same” phenomenonwill differ when produced by different ethnogra-phers (Agar, 2004). This finding, of course, is nota problem, just a fact.

Formative and Design Experiments/Action Research

Conventional experiments are problematicfrom a complexity theory perspective because oftheir ecological invalidity. Furthermore, they canonly, at best, lead to claims about proximate, lin-ear causes, while not allowing for multiple orreciprocally interacting variables, which changeover time. Although we would not wish to discountexperimental claims, we need to problematizethem in light of the fact that any cause and effectlink that is found might actually occlude fun-damental nonlinearity (Larsen-Freeman, 1997).Who can say, for example, on the basis of apretest/posttest design that a particular experi-mental treatment works or does not work? If theresults are not significant, the effects of the treat-ment may not yet be manifest; if the results aresignificant, they may have followed from an ex-perience prior to the pretest. A further limita-tion of conventional experiments occurs whenresearchers attempt to control context and sit-uation, rather than investigating adaptation tothe unique particularities of context: “They try toensure that an intervention is implemented uni-formly despite different circumstances; and theyfocus on post intervention outcomes instead ofwhat happens while the intervention is imple-mented” (Reinking & Watkins, 2000, p. 384).

Qualitative and ethnographic studies, whichcarefully document instructional practices, arethe means traditionally looked to in order to off-set these limitations. However, these studies oftenfail to tease out factors that affect success or fail-ure in educational interventions, and then fail toexplore how interventions might be adapted inresponse to those factors to be more effectivelyimplemented (Reinking & Watkins, 2000).

A different type of experiment, called a forma-tive experiment (Jacob, 1992, as cited in Reinking& Watkins, 2000), focuses on the dynamics of im-plementation, using the ideas of soft assembly andco-adaptation, and might thus be capable of over-coming these limitations. Using Newman’s (1990)

words, Reinking and Watkins defined it as follows:“In a formative experiment, the researcher sets apedagogical goal and finds out what it takes interms of materials, organization, or changes inthe intervention in order to reach the goal” (New-man, 1990, as cited in Reinking & Watkins, 2000,p. 388). This (neo-)Vygotskyan idea appears to becompatible with a complex systems perspective.Formative experimenters attempt to investigatethe potential of a system rather than its state; theyaccept that change in one system can producechange in other connected systems; they attemptto describe the interconnected web of factors in-fluencing change; and they investigate processesof co-adaptation in response to changed peda-gogic goals.

Another research method that has some charac-teristics that are compatible with complexity the-ory is what has been called design-based research ora design experiment . Barab (2006) explained that,in complex learning environments, it is difficultto test the causal impact of particular variableswith experimental designs. Design-based research“deals with complexity by iteratively changing thelearning environment over time—collecting evi-dence of the effect of these variations and feedingit recursively into future design” (p. 155). Lobato(2003) discussed how design experiments differfrom traditional experiments in that the focus ofinvestigation is shifted from the products or out-comes of learning to learning processes. Teachersare encouraged to respond flexibly to what is tak-ing place in the classroom, as they might ordinar-ily do, not to follow some experimental treatmentprotocol. In this way, a design experiment shifts“from a reductionist cognitive view of learning toone that is also social in nature” (Lobato, 2003,p. 19).

Better known, perhaps, is action research. Al-though often motivated by sociopolitical reasons(Kemmis, 2001), action research is also con-cerned with possibility rather than prediction,and with the study of systems. Its researchers,who may be practitioners rather than outsideexperimenters, deliberately introduce “noise”into the system to see what transpires. Theychoose a problem in their teaching which theystudy and to which they apply the Lewinian cy-cle of diagnosing/action planning/action tak-ing/evaluating/specifying learning (Baskerville& Wood-Harper, 1996). Action research takesplace in the system environment, and investiga-tion of the system’s response to a perturbationcontributes to a deeper understanding of the sys-tem dynamics.

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Longitudinal, Case-Study, Time-Series Approaches

Another methodology that might be useful,when modified for complex system purposes, isa longitudinal, case-study, time-series approach,which enables connections to be made across lev-els and timescales. In contrast, often interlan-guage studies tend to be cross-sectional, deny-ing us the idiographic description of individualgrowth and variability.

It is not sufficient simply to lengthen theamount of time that behavior is sampled. Thereis a need to identify appropriate timescales onwhich data are collected—does the change showitself over a period of days, or months, or doesit take a lifetime? (Ortega & Iberri-Shea, 2005).There is also a need to select appropriate sam-pling intervals, which will depend on the rate ofchange. Willett (1994) suggested that a researcher

must assemble an observed growth record for eachperson in the dataset. If the attribute of interest ischanging steadily and smoothly over a long period oftime, perhaps three or four widely spaced measure-ments on each person will be sufficient to capture theshape and direction of the change. But, if the trajec-tory of individual change is more complex, then manymore closely spaced measurements may be required.(p. 674)

In addition, to be true to a complexity ap-proach, any longitudinal study must be set up tocapture variability at various levels and timescales,from the general shape of the development pro-cess over a long period of time to the short-termvariability that takes place between data collec-tion intervals, to the within-session variability thatinevitably arises. Van Geert and van Dijk (2002)argued that a study should attend to all timescalesgiven that variability may be different on eachscale: For example, “a developmental variablemay be slowly oscillating while gradually growing,while another variable may increase discontinu-ously with sharp day-to-day fluctuations” (p. 346).

Capturing variability can take advantage ofpowerful computational tools now available. VanGeert and van Dijk (2002) showed how we canuse computerized databases, graphing, and statis-tics to track complex patterns of variation in sec-ond language learners over time. Cameron andStelma (2004) showed how cumulative frequencygraphs and other types of visual data displays canassist analysis of the dynamics of discourse. Tech-niques, statistical and otherwise, used in analy-sis need to be suitable for genuinely longitudi-nal data rather than cross-sectional comparisons.We need to adopt and develop more appropriate

ways of analysis to allow for the nonlinearity ofthe process, such as multivariate time-series mod-eling, growth curve analysis, latent factor model-ing, and the like (Ellis, personal communication,2006).

Methods of analysis of variability in dynam-ics systems, compiled by van Geert and vanDijk (2002), include “moving min-max” (p. 340)graphs, which, by plotting moving minima, max-ima, and averages, show the data using the band-width of observed scores; graphs of score ranges—change in the range width might reflect variouskinds of developmental phenomena; and stan-dard deviations and coefficients of variation (seeVerspoor, Lowie, & van Dijk, this issue).

Microdevelopment

One approach to the study of change in be-havior over a relatively short timescale is microde-velopment. It has become increasingly clear thatin order to study “motors of change” (Thelen &Corbetta, 2002, p. 59), we need not only longitu-dinal corpora, but also dense corpora that involvehighly intensive sampling over short periods oftime. Thelen and Corbetta suggested that the cor-pora that such an approach yields will not onlyallow us to fix the when of developmental mile-stones, but, what is important, the how of develop-ment by making development more transparent.

Thelen and Corbetta (2002) asserted that in tra-ditional research, change is often inferred froman endpoint measurement. One assumption ofresearchers using a microdevelopment approachis that there are moments in the evolution of be-havior where we can directly observe change hap-pening. Furthermore, given that change works atmultiple timescales, these small-scale changes canilluminate change at a longer timescale. A mi-crodevelopment approach also allows us to plotmultiple developmental routes to the same end-point. This plotting allows us to capture importantdevelopmental differences among learners, bothchildren and adults. From a dynamic systems per-spective, variability needs to feature prominentlyin any account of development (Thelen & Cor-betta, 2002).

Computer Modeling

As articles in this issue demonstrate, computersimulations or models offer an important ap-proach to researching complex dynamic systems.Although still in its infancy, modeling in ap-plied linguistics shows great promise. This ap-proach builds a computer model of the real-world

Diane Larsen-Freeman and Lynne Cameron 209

complex system under investigation and takes itthrough multiple iterations, replicating changeover time. The computer model is an analogy (ormetaphor) of the real-world system, inevitably in-volving some reduction of complexity and someapproximation. However, it is designed and ad-justed so that the outcomes over time reflect whatis known of the real-world system. Taking themodel through successive iterations, which modelevolution over time, or changing parameters andobserving how outcomes change, which modelschanging conditions, allows the researcher to ex-plore the workings of the model system and ex-trapolate back to the real-world system. In a fur-ther step, the processes of development seen inthe model are examined and may be hypothesizedas representing change in the actual system.

Turner (1997) contrasted the modeling processwith conventional approaches to research:

Instead of creating a hypothesis, testing it on the ex-perimental and observational facts until a counterex-ample shows its flaws, and then trying another, wecan create an accurate facsimile of reality by succes-sive tweakings of the variables and the connectionsamong them, run the model in a computer as long aswe like, check that its behavior continues to resemblethat of the reality, and then read off what those pa-rameters are. This procedure reverses the top-downtheory-to-phenomena approach of classical science,and thus can provide an admirable complement to it.(pp. xxv–xxvi)

The activity of building a model is an importantpart of the research process because it requiresexplicit statements of theory and the most accu-rate empirical knowledge about the real systemsand processes being modeled. Model building canthus be a very useful and formative activity. How-ever, any model is only as good as the assumptionsbuilt into it. Inevitably, the model differs fromthe actual system, being idealized or simplifiedin some respects, approximated in others. Thislimitation raises new issues for applied linguisticsaround the validity and robustness of computermodels of language development.

Articles in this issue demonstrate the poten-tial of the two main types of models currentlyin use: neural network (or connectionist) mod-els and agent-based models. Neural network mod-els can replicate the learning of an individualbrain and the emergence (or learning) of cate-gories through self-organization. From very sim-ple rules and initial conditions, the models canproduce outcomes that closely resemble humanlearning and development in areas includingvocabulary learning (Meara, 2006), past tenselearning (Rumelhart & McClelland, 1986), and

the emergence of syntax from lexical learning(Elman, 1995). A major limitation of neural net-work models is their representation of the in-dividual learner as isolated and as only cogni-tive, rather than as also an affective and socialbeing.

Computer software such as “Swarm” (Minar,Burkhart, Langton, & Askenazi, 1996) enablesresearchers to construct detailed, robust, agent-based models that involve a population of inde-pendent agents who interact in discrete eventsin a specific open-ended environment. Simula-tions consist of groups of interacting agents ina sequence of events that reflect the passage oftime. Swarm simulations allow a researcher toinvestigate the global consequences of these lo-cal interactions and are beginning to advanceour understanding of the evolution of languagein social groups (Ke & Holland, 2006), creole-genesis (Sattersfield, 2001), self-organizing vocab-ularies (Steels, 1996), and the acquisition of lan-guage from complex, situated input (Marocco,Cangelosi, & Nolfi, 2003).

The validity of a simulation model is checked bycomparing the outcomes produced by the modelwith the outcomes of the real-world human sys-tem. If the model reflects the real-world behavior,it is said to be valid. Gilbert and Troitzsch (2005)set out some of the issues around model validity.These issues include the uncertainty introducedby the stochastic nature of processes in both real-world and model systems; the path-dependence ofsimulations, that is, the sensitivity of a model toits initial conditions; the possibility that the sim-plification involved in model construction leadsto its being incomplete in some important way;and the possibility that the real-world data usedto build the model were themselves incorrect orbased on incorrect assumptions. This last issuemay be particularly important for our field be-cause empirical data about language learning thatwe may need to build into the model may havebeen collected and analyzed under theoretical as-sumptions that differ greatly from those of thecomplex systems perspective. Cohen and Stewart(1994) made this point quite vividly in the contextof biological models:

The hardest [errors] of all to spot are the implicit as-sumptions in the worldview that suggested the model.For example, suppose you’re setting up a modelof biological development based upon the idea ofDNA as a message. You would naturally tend to fo-cus upon such quantities as the amount of informa-tion in a creature’s DNA string and the amount ofinformation needed to describe the animal’s physicalform. If you then model development as a process of

210 The Modern Language Journal 92 (2008)

information transfer—lots of messages buzzing to andfro—you will implicitly have built a model in which in-formation cannot be created. You will then be able to“prove” that humans can’t develop a brain becausethe amount of information needed to list every con-nection in the human brain is a lot more than thetotal amount of information in human DNA.

But we do have brains . . . . Impeccable mathematicscan produce nonsense if it is based on nonsensicalassumptions . . . . Don’t be impressed by mathematicsjust because you can’t understand it. (p. 186)

Choices are made at each step in the building ofa simulation model, from choosing and describ-ing the real-world system to be modeled, throughprogramming the rules for interaction among theagents in the model, to adjusting the parametersof the model and interpreting outcomes. Eachchoice can affect the model’s validity and needs tobe scrutinized and justified. Theoretical assump-tions built into the model should be clearly statedin published papers so that readers can evaluatethis aspect of validity.

The further step, of inferring back from themodel to the real world about the processes ofdevelopment, raises issues beyond what we mightcall outcome validity, as described previously. Simi-lar outcomes may be produced by computer mod-els and human systems through very differentprocesses. For example, neural network modelshave an internal structure very different fromthat of a human learning system, and similarityof outcomes would not justify claiming similarityof internal processes. Process validity in simulationmodeling is a more difficult construct than out-come validity. Inspecting the processes of simula-tion models may lead to areas worth investigatingback in the real-world system, but claims of simi-larity should be treated with caution. We need totake care in how we label and talk about processesand parts of simulation models in order to avoidunwarranted or premature theoretical inferences:For example, van Geert’s (this issue) choice of theterm generators to describe processes establishedthrough model building prompts resonances witha specific theory of language development thatmight lead researchers’ thinking in particular di-rections, whereas a more neutral term might beless constraining.

Simulation modeling of complex dynamicsystems is clearly going to be very important forapplied linguistics. Validity issues need careful at-tention and, because the methodology and tech-nology are still unfamiliar and difficult for manyresearchers, the onus of validation will inevitablyfall on the modelers themselves.

Brain Imaging

Technological advances in brain imaging, in-cluding improvements in the temporal and spa-tial resolution of electro-encephalographic andfunctional magnetic resonance images are allow-ing detailed descriptions of the dynamics of brainactivity, promoting a shift of emphasis from knowl-edge as static representation stored in particularlocations to knowledge as processing involving thedynamic mutual influence of interrelated typesof information as they activate and inhibit eachother over time (Ellis, personal communication,2006). Brain imaging may contribute a useful toolto researching microdevelopment, although cur-rently it is an expensive resource, often difficultfor researchers to access.

Combinations of Methodologies

Combinations or blends of methodologieswould seem to be particularly appropriate to thestudy of complex systems, allowing different lev-els and timescales to be investigated. We outlinethree possibilities.

Discourse Analysis and Corpus Linguistics. Largecorpora of language use give us access to stabilizedpatterns and variability around them. Althoughwe acknowledge that a corpus is a static collec-tion of attested language and cannot show thedynamics of language as it unfolds in use or itsfuture potential (Larsen-Freeman, 2006b), a cor-pus can serve to some extent as representative ofthe language resources of members of the speechcommunity where it was collected. We can thencombine corpus linguistics with close analysis ofactual discourse, to trace the genesis and dynam-ics of language patterns, such as the convention-alization and signaling of metaphors (Cameron &Deignan, 2003, 2006).

Second Language Acquisition and Corpus Lin-guistics. The field of second language acquisition(SLA) needs to make more use of computer-searchable longitudinal corpora for addressingtheoretical issues. Rutherford and Thomas (2001)and Myles (2005) advocated the use of Child Lan-guage Data Exchange System (CHILDES) toolsfor SLA research. Mellow (2006) illustrated theimpact of large new computerized corpora suchas CHILDES and TalkBank (MacWhinney, Bird,Cieri, & Martell, 2004) on theories of second lan-guage learning. A corpus of adult English as asecond language (ESL) learners in a classroom

Diane Larsen-Freeman and Lynne Cameron 211

setting is also a powerful aid in helping us to un-derstand adult language learning better (Reder,Harris, & Setzler, 2003).

Second Language Acquisition and ConversationAnalysis. Conversation analysis (CA) attends tothe dynamics of talk on the microlevel timescale ofseconds and minutes. In a recent special issue ofThe Modern Language Journal (Markee & Kasper,2004), it was argued that joining a CA perspec-tive on interaction with a long-term view of lan-guage development holds great promise (Larsen-Freeman, 2004; Kelly Hall, 2004). CA offers a richdescription of “the most basic site of organized ac-tivity where learning can take place” (Mondada &Pekarek Doehler, 2004, p. 502). If these analyseswere to be done with a sufficient density so thatretrospective microdevelopmental analyses couldbe conducted, it would offer another means ofconnecting synchronic dynamism to its over-timecounterpart.

CONCLUSION

Clearly, each of the approaches just discussedhas advantages and drawbacks. CA offers an in-depth view of conversational interaction, but itignores any insights that a conscious introspec-tion would permit. Corpus linguistics offers richusage data, but the data are attested; they do notdemonstrate the potential of the system. Otherapproaches, such as brain imaging and neural net-work modeling, illustrate or simulate the dynamicpatterns of brain activity, but do so by isolating thelearner’s brain from society and from its normalecology of function. Computer models might bemore encompassing in this regard, in allowing fora social interactive dimension, but they, too, in-volve ecologically reduced ways of representingreality.

We began this article by asking whether themethods of inquiry of the natural sciences wouldwork for applied linguists whose theoretical com-mitment is to understanding complex, dynamicsystems. We have pointed out that different as-sumptions (e.g., about causality) underlie tradi-tional research methods used in both the naturaland the social sciences and have discussed thosemethods that are perhaps the most suitable for acomplexity theory perspective.

What we can aspire to at this point is to en-tertain the principles we have enumerated earlierin this article while blending and adapting meth-ods, a trend that is increasingly adopted across thesocial sciences. It should not be surprising that re-searchers are entertaining the possibility of using

multiple blended methods. It is, after all, a prag-matic solution to the demands of a theoreticalperspective that seeks to understand the dynam-ics of change in complex systems.

NOTES

1 We are grateful for discussions we have had onthese issues with colleagues, especially Nick Ellis and KeJinYun. Also, portions of this article appear as a chapterin Larsen-Freeman and Cameron’s (2008) book.

2 It should be noted that self-organization is not somekind of automatic self-improvement, but is neutral as towhether its outcome is better or worse than the previousstate.

3 Gaddis is an historian, not an applied linguist, buthe is insightful about the nature of research in a waythat we think is helpful to applied linguists. We thankGad Lim for bringing this book to our attention.

4 An affordance is an opportunity for use or inter-action that some object or state of affairs presents toa certain kind of agent. “For example, to a human achair affords sitting, but to a woodpecker it may affordsomething quite different” (Clark, 1997, p. 172).

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