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Introduction: Second Language Development as a Dynamic ProcessAuthor(s): Kees De BotReviewed work(s):Source: The Modern Language Journal, Vol. 92, No. 2 (Summer, 2008), pp. 166-178

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Introduction: Second LanguageDevelopment as a Dynamic ProcessKEES DE BOTUniversity of GroningenFaculty ofArtsDepartment ofAppliedLinguisticsP.O. Box 7169700AS GroningenThe NetherlandsEmail: [email protected]

In this contribution, some of the basic characteristics of complex adaptive systems, collectivelylabeled Dynamic Systems Theory (DST), are discussed. Such systems are self-organizing, dependent on initial conditions, sometimes chaotic, and they show emergent properties. Thefocus inDST is on development over time. Language is seen as a dynamic system, and languagedevelopment, both acquisition and attrition, as a dynamic process. A number of examples ofpossible applications of DST in the field of applied linguistics are mentioned. After a shortpresentation of each of the individual articles, some possible lines of research are discussed.

THIS SPECIAL ISSUE IS BASED ON THE Presentations at the Roundtable on Dynamic Aspects of Language Development sponsored byLanguage Learning, which was part of the 2006annual conference of the American and Canadian Associations ofApplied Linguistics (AAALand CAAL). This full-day roundtable took placeon June 20, the last day of the conference. It attracted a large and engaged audience, which isparticularly unusual on the closing day of a conference. The audience's interest in this topic mirrored an earlier experience at the 2006 Teachers of English to Speakers of Other Languages,Inc. (TESOL) convention in Orlando, Florida,

where an AAAL-sponsored symposium on unpredictability in language teaching, organized by Diane Larsen-Freeman, attracted an unexpectedlylarge crowd. It is not unusual for a small com

munity of researchers to get excited about a newapproach in their field, but here the interest appeared to have spread to a larger group thatsensed that something special was happening.Given the interest in these events, it seemed like

The Modern Language Journal, 92, ii, (2008)0026-7902/08/166-178 $1.50/0?2008 The Modern Language Journal

a good idea to find a venue for the papers tomake them publicly available. When The ModernLanguage Journal (MLJ) showed an interest inpublishing a special issue on this topic,1 all contributors expressed their support for such a publication that would, on the one hand, set a milestone in the introduction of new ideas on complexity and dynamic systems in the field of appliedlinguistics and, on the other hand, allow the largeraudience to get a state-of-the-art overview of theseideas.

In this introduction, I will present a short history of the development of theories on chaos,complexity, and dynamic systems, with a focus ontheir role in the social sciences. By looking at language as a dynamic system, and language development as a dynamic process, we can explore towhatextent and how ideas on complexity and dynamicscan be fruitful for our field. The main characteristics of dynamic systems will be presented brieflybecause several of the articles will present moreextensive elaborations of different aspects. Oneaspect, self-organized criticality, will be discussed infurther detail since ithas not figured prominentlyin the discussion on the application of DynamicSystems Theory (DST). Finally, a short introductionto each of the articles will be followed by a lookahead and some thoughts on how these ideas maybe developed further.

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KeesDeBot 167A SHORT HISTORY OF CHAOS THEORY,COMPLEXITY THEORY, AND DYNAMICSYSTEMS THEORY

As with most theories, it is rather difficult topinpoint the exact beginnings of this particularline of thinking. Some commentators (Schueler& Schueler, 1997) mention the publication ofLorenz's groundbreaking 1963 article on weathersystems as the firstmilestone in the developmentof Chaos Theory. Lorenz (1963) showed that, incomplex systems, small differences in initial conditions can lead to larger and unpredictable differences over time. However, according toWolfram(2002), sensitivity to initial conditions has beenshown to play a role in physics ever since the work

of Maxwell in the mid-19th century.The term chaos has a technical meaning herereferring to the fact that the outcomes of interactions of variables over time cannot be predictedusing conventional mathematics. Thus, chaos isunpredictability rather than lack of order. As aresult of sensitivity to initial conditions, the behavior of systems that exhibit chaos appears tobe random, even though the system is deterministic in the sense that it is well denned andcontains no random parameters. The two mainlines within Chaos Theory are that chaos canemerge out of the interaction of variables anddifferences in initial conditions, and that thereis universal order in seemingly chaotic patterns,like turbulence in liquids. Two of the leadingresearchers in the field can be seen as representatives of these two trends: Prigogine (1997)refers to "the end of certainty," while Holland(1998) refers to "structure from chaos." Mandelbrot (1982) added significantly oChaos Theorywith his discovery of fractal patterns?structuresthat repeat themselves on different levels of thesystem.

Complexity Theory looks at what happens "at theedge of chaos" (Lewin, 1999). Research on chaoshad shown that complex systems develop moreor less predictably for some time and then moreor less suddenly begin to show chaotic behavior.

Waldrop (1992) defines complexity as "a chaos ofbehaviors inwhich the components of the systemnever quite lock into place, yet never quite dissolveinto turbulence either" (p. 293).DST is part of the study of systems, inwhich systems are studied as a whole rather than with focus

on their parts. Systems Theory, which emerged inthe early 1950s, has been applied inmany fieldsranging from ontology to management and psychotherapy. One branch is the study of complexadaptive systems. Several institutes were set up in

the 1990s to study complex adaptive systems, withthe Santa Fe Institute playing a leading role andattracting top scientists like John Holland and Nobel Prize winner Murray Gell-Mann. DST startedout as a

purely mathematical approach for thedevelopment of complex systems over time, butit is now considered more a set of tools and approaches than a fixed and all-inclusive theory ofchange.

Dynamic systems are systems that change overtime. Van Gelder and Port (1995) use the following definition: "Roughly speaking, we take dynamical systems to be systems with numerical statesthat evolve over time according to some rule"(p. 5). Systems are sets of interacting variables.In DST, geometrical concepts play

animportantrole. Systems have a state phase, which is a position in a multidimensional space that definestheir preset state. Changes in systems are represented as trajectories in the state space. DST

employs computer models and simulations to describe changes of systems over time. Change typically is not continuous: Systems tend to settle inwhat are called "attractors," which can be dennedas "a set in the phase space that has a neighborhood in which every point stays nearby andapproaches the attractor

as time goesto infin

ity" (Meiss, 2008). Dynamic systems tend to shownonlinearity in development, which refers to adiscrepancy between input and effects. Althoughthe different theories have their own historiesand foci, in many publications the labels Chaos,Complexity, Complex Adaptive Systems, Nonlinear Systems, and DST often are used almost interchangeably to refer to a class of theories. Whatthey have in common is a focus on the development of complex systems over time. Here I willuse the term DST to refer to this whole set ofnotions.

Different aspects of DST have been studied andapplied in a wide range of fields, such as economics, oceanography, meteorology, and, morerecently, cognitive science. In the next section, Iwill focus on the application of DST in the field ofcognition and then further narrow my discussionto the study of language development.

A DYNAMICAL APPROACH TO COGNITIONSeveral publications have focused on the application of DST notions in human cognition. Themost outspoken supporter of this is probably Timvan Gelder, who has defended a DST approach to

cognition in a number of influential publications.The first is the edited volume Mind as Motion:


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168 TheModern Language Journal 92 (2008)Explorations in theDynamics ofCognition (1995),which he edited with Robert Port. The otherpublication is van Gelder's keynote 1998 articlein Behavioral and Brain Sciences (BBS) entitled"The dynamical hypothesis in cognitive science,"which was published along with peer commentaries. Van Gelder does not eschew taking strongpositions in the debate. In his defense of the dynamical hypothesis, he claims that "Dynamics isarguably the most widely used and powerful explanatory framework in science" (1998, p. 622).Several of the BBS commentators take issue withthis statement and argue that, as yet, DST in cognitive science cannot claim to provide explanations;at best it can describe development, but not explain it (van Gelder, 1998). A characteristic of thecognitive system as a dynamical system that vanGelder mentions and most commentators seemto agree with is that cognition is embedded onthree levels: the nervous system, the body, and theenvironment. This view also has been expressedby other researchers, such as Beer (2000) and vanGeert (1998). The view of cognition as a dynamical system represents a move away from a strictlymodular approach inwhich cognition is viewed asa separate module confined to the brain workingin isolation.

The debate over whether DST can be seen asan alternative for existing paradigms, which is basically the position van Gelder is defending, continues to generate considerable controversy in thecognition community. Beer (2000) argues that traditional symbolic and connectionist approacheshave a lot in common with the dynamic approachand DST, which play a critical role in the consideration of existing notions: "... regardless ofthe eventual fate of the dynamical approach asan alternative or an adjunct to more traditionalapproaches, dynamical ideas are forcing a muchneeded critical evaluation of the notions of representation and computation in cognitive science"(p. 98).Along similar lines,Thelen and Bates (2003)support the view that connectionist and dynamicsystems approaches are more similar than theyare different and that a combination of the twois needed for an understanding of fundamentalprocesses and mechanisms of change. Van Orden (2002) says that "twentieth century cognitivepsychology was built on the assumption of linearity" (p. 1), and he argues for an approach thatchallenges this assumption. In his view, there aretwo approaches when trying to apply DST principles to cognitive processes like word recognitionor reading. In the first approach, subprocesses

can be looked at as nonlinear, but they can beisolated and studied separately. Traditional linear methods of linking behavior with underlyingmental processes can be applied in this approach.In the secondapproach,

van Orden (2002) argues, "nonlinear interactions may occur amongcognitive processes, between cognitive agents andtheir environments, and even among cognitiveagents themselves. If so, then empirical analyses will require nonlinear methods" (p. 2). VanOrden clearly favors the second approach, andin another article on self-organization of cognitive performance, van Orden, Holden, and Turvey (2003) propose a nonlinear dynamic systemsapproach as an alternative for mainstream cognitive

psychology.This led to a strong reaction byseveral researchers, including Wagenmakers, Far

rell, and Ratcliff (2005), who argue that the moretraditional approach is to be preferred as long asthe superiority of the alternative is not proven: "Ifthe new science of nonlinear dynamical systemstheory is truly superior to the current paradigm ofcognitive psychology, then its proponents shouldnot shy away from a head-on quantitative comparison" (p. 108).What emerges from the literature on this topicis that there is a

willingnessto consider DST as

an alternative. However, some of the proponentsof DST are overstating their claims, and there isnot yet enough substantial evidence to abandontraditional cognitive science in favor of a DSTbased approach.

LANGUAGE AS A DYNAMICAL SYSTEMAND LANGUAGE DEVELOPMENT AS ADYNAMICAL PROCESSWhether or not DST presents a full alternative

to existing cognitive theories, researchers in linguistics and language development have taken onthe theory as an interesting but basically complementary approach in the study of languageprocessing and language development. Cooper(1999) presentsaDST model for language changebased on attractors on different levels. Browmanand Goldstein (1990) apply DST to show howarticulatory movements and cognitive aspects ofphonology are related. Similarly, van Lieshout(2004) has applied DST in the studyof speechproduction. Rueckle (2002) describes how visualword recognition can be approached from a dynamic perspective.The most extensive and direct application ofDST to language processing can be found inthe work by Elman (1995, 2004); some of his


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KeesDeBot 169ideas that are markedly different from traditionalapproaches to language will be discussed here.Based on Elman's 1995 article, a number of characteristics of such traditional approaches are noncontroversial:

1. Processing is based on discrete and contextfree symbols, which means that the meaning ofsymbols is independent of their use.2. Grammatical rules are operators, while lexical elements are operands; in other words, rulesoperate on lexical items.3. Representations (words, rules) are static innature. Words in the lexicon are like words in adictionary that will remain the same over time,independent of use.4.

Buildingsentences is like

buildinga wall with

words, with the words as the bricks and the rulesas the mortar.

The most important reason Elman provides toexplain why we need a new theory on languageprocessing is that the traditional view of mentalprocessing is at variance with how we now thinkthe brain works: There are no static, discrete, passive, or context-free representations, and maybeeven the whole idea of representations iswrong.He proposes a view on language processing asa dynamic process in which the time dimension is crucial: Language elements are not staticbut change through use and are highly contextsensitive. Time is seen not as the moving of thehands of a clock but as representing its effectson processing, so time is inherently part of theprocessing rather than some external dimension.To show how language development might takeplace using a dynamic approach, Elman (1995)trained a simple recurrent network to predict subsequent words in a sentence using a small set of 29verbs and nouns with a corpus of 10,000 short sentences. The simulation showed that the networkdevelops an internal structure that reflects different meanings and approximations of word classes.In other words, the network can induce lexical categories from statistical regularities. In subsequentsimulations, Elman also showed that networks canlearn long-distance dependencies in complex sentences. This research suggests that a very simple iterative learning mechanism can lead to a dynamicstructure of language in which words have a distributed representation in a network that is adaptable and context-dependent. Van Gelder and Port(1995) summarize Elman's position: "Thus internal representations of words are not symbols butlocations in state space, the lexicon or dictionaryis the structure in this space, and processing rulesare not symbolic specifications but the dynamics

of the system which push the system state in certain directions rather than others" (p. 195). Thisperspective is rather different from that of traditional linguistics and psycholinguistics, and aswitch to this view will lead to a major shift in thefield.

FIRST LANGUAGE ACQUISITIONAS A DYNAMIC PROCESSLanguage development can be seen as one as

pect of general human development. In theirgroundbreaking book, A Dynamic Systems Approach to theDevelopment of Cognition and Action,Thelen and Smith (1994) argue that developments at different levels are governed by similarprocesses: "We approach the mystery of humandevelopment with the conviction that the acquisition of mental life is continuous with all biological growth of form and function" (p. XIII). Thisalso applies to language development, which isnot seen as something special in the cognitive system, but as a part of the larger system that developsin a similar fashion.

First language (LI) acquisition as a dynamicprocess has been studied in a variety of ways, butthe dominant approach has been a combinationof microgenetic studies and computer modeling.In microgenetic studies (see Verspoor, Lowie, 8cvan Dijk, this issue), fine-grained analyses of denseacquisitional data provide a rich set of information that reveals all the small steps that are takenin development. Child production data are often combined with analyses of caretaker talk toshow how amount and type of input are related todevelopment.

Modeling and simulations are fruitful ways ofenhancing our understanding of language development. The most important point is that we needto turn our intuitions and what we know aboutlanguage development into the strict language ofmathematics. For that, we need to be very explicit about what we think we know because itis nearly impossible to translate vague statementsinto equations. We may be convinced that motivation plays an important role in Second LanguageDevelopment (SLD), but it is far from easy to turnthat idea into a mathematical equation that statesexactly how and when that factor plays a role. Alegitimate question to ask iswhy we need modeling and simulations. The closest answer is that thisis the only way we can test our hypotheses on theinteraction of variables over time. Language development is seen as an iterative process inwhichnew input is added to the existing knowledge andthe expectations with respect to development are


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170 TheModern Language Journal 92 (2008)built in to the growth functions used for the modeling. There is no way we can set up experimentsby which to study development over time, takinginto account all variables that we assume to play arole. By comparing outcomes of simulations withreal developmental data, we can infer how the interactions of variables over time may have takenplace.For the description of language development asa dynamic process, the work by van Geert, who hasbeen leading the field for more than a decade, istaken here as a starting point. The basic elementsof his ideas on language development will be discussed in some detail here because many of theissues he raises are as relevant for second language(L2) development as they are for LI development,the area he has focused on so far. One of the

major contributions van Geert has made is to reformulate development in terms of "growth." Theadvantages of using this concept are that it ismathematically well defined and that in its simplestform it can be modeled using a logistic growthfunction, which is one of the most widely usedfunctions in the study of dynamic systems. Takingthe logistic growth function as a starting point,van Geert has developed more complex functionsthat take into account assumptions and findingsfrom research on language development. He usesthese formulas to estimate development over timeand then uses dense longitudinal data to test thefit of the model and the data.

Important characteristics of growth are thatthere needs to be something that can grow, whatvan Geert (1995) calls the "minimal structuralgrowth condition" (p. 314), and that growth is dependent on resources. In language developmentinput and output, as well as encouragement, motivation, attention, feedback, and time to learn, canbe viewed as resources. Resources typically are limited and interlinked in a dynamic system. Memorycapacity, input, time, and motivation are all limited, but they can be compensatory in the sensethat a lack of time can, to a certain extent, be compensated for with higher motivation or more effort. The interconnectedness of resources meansthat the resources interact over time: Motivation

may have an effect on external encouragementand the experience of success, which may lead towillingness to spend more time, and so on. Also,the level of development comes into play here:Specific resources will play a different role in different stages of development. In the early stagesof L2 development, for example, memory capacity

may be more important than analytic ability, whilein later stages the opposite may be true. The interlinked system of resources forms what is called

the cognitive ecosystem (van Geert, 1995). This isa highly individualized system of internal and external resources that defines the carrying capacity,the growth potential of a system at a given moment in time. The carrying capacity can be seenas a general notion of potential growth, but ismore relevant when applied to specific domains,such as lexical growth.Different developmental processes can takeplace in interaction. Van Geert (1995) refers tothese as connected growers. The connection between the growers may be parallel and simultaneous, but they are likely to have a differenttime path. An example of connected growers canbe found in a study by Robinson and Mervis(1998), who looked at vocabulary growth andthe use of plural markers. In order to combinethese two developmental curves, Robinson andMervis used the "precursor model" as proposedby van Geert (1995). In a precursor model, thereare two variables, a predecessor and a successor.Growth in the successor is initially suppressedby growth in the predecessor, a form of competition, until a threshold level is reached inthe predecessor. After this threshold is reached,growth in both variables shares any of the logicallypossible relations defined by competition andsupport.In addition to the modeling of the individualdevelopment of children, van Geert also has applied DST principles to social interaction betweenchildren and caretakers. This interaction is seen asan important part of the child's cognitive ecosystem: "A child's cognitive ecosystem, however, doesnot stop at the boundaries of the brain or thebody, but contains all aspects of the environment,as well, insofar as that environment is accessibleto and understood by the child" (1995, p. 332).

Van Geert refers to co-construction as a dynamical process of mutual information exchange. Hedescribes how two sets of equations, one for thegrowth in the child and the other for the finetuning of the caretakers, are linked over time, withthe child developing on the basis of the input fromthe caretaker and the caretaker adjusting to thelevel of development of the child. Van Geert doesnot claim that the type of modeling he proposescan explain the phenomena described:

There isnow reasonable evidence that in spite of theirunderlying complexity, developmental processes canbe viewed as instances of relatively simple growth models. It remains to be explained, of course, what it is inthe organization of the brain or of human culture thatmakes these developmental processes follow their particular growth trajectories, (p. 335)


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KeesDeBot 171SECOND LANGUAGE DEVELOPMENTAS A DYNAMIC PROCESS

One of the first applied linguists to see the potential of complex adaptive systems as a modelfor SLD2 was Diane Larsen-Freeman in her 1997article, "Chaos/complexity science and secondlanguage acquisition." In this article, she showsthat language has all the characteristics of dynamic complex systems: It isdynamic and changesover time both synchronically and diachronically;it is complex with different subsystems (syntactical, phonological, lexical, textual) that interact;it develops nonlinearly and sometimes is unpredictable and chaotic; it is sensitive to initial conditions, open, self-organizing, feedback-sensitive,and adaptive; and there are attractors in development. It follows that SLD also is a dynamic process.Larsen-Freeman points to the discrepancy amongthe static rules of grammar set by researchers (andtaken over in language courses). The complexity is visible in the many factors that shape thedevelopment of learners' interlanguages, such asamount and type of overlap between the LI andL2, amount and type of input and interaction, instructional context, motivation, age, aptitude, andso on. The nonlinearity of SLD is evident inwhatis generally referred to as "U-shaped behavior" inthe acquisition of the past tense of regular andirregular verbs. The interlanguage system is typically self-organizing in that on the basis of input,the learner develops a highly idiosyncratic systemthat reflects the unique characteristics of her developmental path.Larsen-Freeman (1997) warns against overoptimism with respect to the direct applicability ofDST inSLD, but she, similar towhat Beer (2000)did for current theories in cognition, shows thata DST perspective leads to some pertinent questions regarding SLD. One of the hard questionsconcerns the mechanisms of acquisition. LarsenFreeman points out that in contrast to the views onlanguage acquisition based on innateness, complexity can emerge from the repeated application of simple procedures to the point that thecomplexity in the output exceeds the complexityof the input, which solves one of the core issuesin language acquisition (for a different, but alsoDST-inspired view, see Mohanan, 1992).From an SLD perspective, a crucial issue iswhatconstitutes learning. As Larsen-Freeman (1997)points out, learning is not simple linear growthon the basis of input; there are backslides, stagnations, and jumps, and like the unpredictabilityof avalanches, it is not clear which instances ofinput or instruction lead to which instances oflearning. Learning is the interaction between in

put and the self-organizing system, which is bydefinition not open to inspection. Learning isalso growth through iterations as discussed by vanGeert (1995, this issue).In her 2002 article, Larsen-Freeman adds an

other important dimension by pointing out thatin a DST approach the social and the individualcognitive dimensions can be combined and theirinterrelatedness shown. This is a reaction to thearticle by Firth and Wagner (1998), who arguedthat the social dimension in second languageacquisition (SLA) has become too overshadowedby the cognitive dimension. Recently, LarsenFreeman (this issue) looked back at her owndevelopmental path with respect to the application of Chaos/Complexity Theory in SLD. Shenoted that after her 1997 article there was a longsilence until the publication of Herdina andjessner's book in 2002. Few researchers during thatperiod seemed to have followed Larsen-Freemanand, as she points out, theory building is also adynamic and therefore social process, which takestime and the availability of conversation partners.Furthermore, new ideas take time to settle, anda fundamental shift in perspective such as this isdifficult.

Asjust mentioned, the next milestone in the history of DST and SLD was the publication of Herdina and Jessner's book, A Dynamic Model ofMultilingualism: Perspectives ofChange inPsycholinguistics (2002). In this book, the basic notions of DSTand their application to SLD are brought togetherin a model for multilingualism in which variousfactors interact in the emergence of multilingualism. In the model, metalinguistic awareness playsan important role, although the mechanics of theimpact of metalinguistic awareness in dynamic

modeling remain poorly understood. In her 2006book and her contribution to this issue, Jessnerdiscusses various aspects of the model inmore detail; therefore, itwill not be discussed further here.The growing awareness of the potential of DSTfor SLD and multilingual processing is reflected inBilingualism: Language and Cognitions publishingof a keynote article with peer commentaries (in deBot, Verspoor, 8c Lowie, 2007, with commentariesby Ellis, Ionin, Lantolf, Larsen-Freeman, Liceras,Pienemann, and van Geert). A number of issuesemerged from the interaction among the authorsand the commentators, and most of them arediscussed in the contributions to this MLJ special issue: the relation between the cognitive andthe social in SLA (Larsen-Freeman 8c Cameron),the role of innate language features (PlazaPust), how variation should be handled (Verspooret al.), and formal and informal modeling (vanGeert).


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172 TheModern Language Journal 92 (2008)From all of these overviews and discussions,

there seems to be sufficient ground to examinethe various characteristics of dynamic systems andhow they can be applied to SLD. One issue thathas emerged as an important notion in the general literature on chaos, complexity, and dynamicsystems, but that so far has not attracted the attention of SLD researchers, is self-organized criticality(SOC). Several aspects of SLD seem to be exam

ples of such self-organized criticality, and therefore a more detailed explanation may be in orderhere.

SELF-ORGANIZED CRITICALITYThe idea that many systems tend to self

organize and become critical over time was developed by theDanish physicistPer Bak. Bak isbest known from the metaphor he used to explainSOC: the "sand pile" (1996). When grains of sandare dropped on a table, a cone-shaped pile willdevelop. When sand is added grain by grain, theslope of the pile will become steeper and steeperuntil it reaches a critical level. When such a levelis reached, the next grain of sand dropped on thepile will cause one or more avalanches; in otherwords, the system has reached a critical state. Systems in such critical states show specific behavior: they are highly unstable, and their behavioris unpredictable. Also, the relation between input (grains of sand) and outcomes (avalanches)is nonlinear: one grain can cause a large orsmall avalanche, and once avalanches start theymay cause more and larger avalanches. Modelsbased on these principles have been applied to awide variety of processes, such as forest fires, epidemics, earthquakes, and neural networks. Selforganizing neural networks that are in a state ofcriticality appear to be able to adapt quickly tonew situations. Bak's ideas on SOC have been veryinfluential in different fields of research, but heand his followers also met with fierce resistance totheir ideas (see e.g., Jensen, 1998). SOC is hard toprove because it is the result of many interactingvariables working over time.One of the characteristics of systems exhibiting SOC is that they show a specific pattern thatfollows so-called power laws. Simply, this meansthat there is a specific relation between the number of changes taking place and the size of thesechanges: How many large avalanches are therewith a constant addition of grains, and how manysmall ones? Log transformations of numbers andeffect sizes lead to a linear relation between frequency and size, the so-called Gutenberg-RichterLaw (Bak, 1996). Because power law effects are

characteristic of SOC states, some researchershave taken such effects as evidence of SOC. In various fields, SOC phenomena have been attested

by showing that patterns of development followthe power law. Likewise, van Orden et al. (2003)have looked at changes over time in simple reaction time experiments to show that they also fitwith the power law pattern and that they therefore can be seen as evidence of SOC in humancognition. In a critical evaluation of van Ordenet al. (2003), Wagenmakers, Farrell, and Ratcliff(2005) argued that the fact that the data showa power law pattern is no real proof for the existence of SOC in cognition since that kind of

pattern can emerge from various sources andcan be explained by more traditional theories oncognition. They state that the account of SOCgiven by van Orden et al. is underspecified, evenwith respect to the way in which an SOC approach does actually apply to human cognition:

We hazard to guess that the authors' view is that theslow driving of SOC systems (cf. adding grains of sandto the pile) corresponds to the gradual accrual of information and that when the threshold ispassed, thesystem responds (cf. avalanches in sand pile). Afterthe response ismade, the state of the system is relaxed, and the process of information accrual startsagain when a new stimulus ispresented, (p. 114)

Wagenmakers et al. conclude that the ideas putforward by van Orden et al. are interesting andchallenging, but that a specific model in whichSOC is applied to specific aspects of human cognition has yet to be developed.The idea of SOC is related to state changesand restructuring of systems. For language learning, various examples could be given: Krashen's(1983) "din in the head," Lightbown and Spada's(1999) "breakthrough," and Bahrick's (1984)"permastore" for language retention.Krashen (1983) refers to a phenomenon firstdescribed by Elizabeth Barber. She reports on avisit to Russia where she had to use the little Russian she had to communicate with her hosts. Shenoticed something unusual:

By the third day also, the linguist inme was noticinga rising din of Russian inmy head: words, sounds,intonations, phrases, all swimming about in the voicesof the people I talked with_My overall command ofRussian improved more in a single week than itwouldhave in amonth or two of intensive reading. (Barber,1980, p. 30)With his infallible talent to find a catchy label,Krashen (1983) called this the "Din in the head"

phenomenon, which takes place after a learner


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KeesDeBot 173has gone through a period of extensive input processing. For no obvious reason, sentences seem tobuild in the head as if the system has reacheda critical stage that turns receptive knowledgeinto productive knowledge. Unfortunately, no research providing evidence for this interesting ideais available. However, the idea is intriguing andat least suggests that input in a second languagedoes not lead to gradual changes in the system,but rather it builds up to a critical stage that leadsto a sudden and massive restructuring of the system. It suggests that the language system itselfwill develop or self-organize in such a way thatreceptive knowledge is automatically turned intoproductive knowledge.Another version of this restructuring is whatLightbown and Spada (1999) refer to as the"Breakthrough": the idea of a sudden jump inproficiency because all the disconnected information seems to fall in place. There is no real substantial research on this, but informal inquiriespoint to the fact that advanced students of a foreign language recall going through such a phase.Lightbown and Spada also indicate that the breakthrough is not irreversible: With nonuse, the system can fall apart again. Also, the feeling of havinga breakthrough is not related directly to languageproficiency; it is not the case that knowing 3,500words and being able to perform basic structureswill lead to this experience.

Similarly, the threshold hypothesis and the permastore hypothesis have been suggested to explainlong-term retention of language skills (Bahrick,1984; Neisser, 1984). The claim is that there is apoint in development at which the system is reorganized in such a way that knowledge becomesvery stable and almost immune rather than sensitive to loss, a major state phase change. What allthese changes have in common is that the statephase is not related to a specific parameter or factor, but results from the self-organization of thesystem.The idea that variation follows a power lawpattern may have interesting consequences forour thinking about variation. We tend to focuson large deviations and not on the small ones.One of the lines of research to be developedin the near future is whether target languageinput leads to a pattern of smaller and largerchanges that show a power law pattern suggestive of an SOC state for the language system indevelopment.

DST AND RESEARCH METHODOLOGYIn their introduction to Mind as Motion, van

Gelder and Port (1995) stress that

the dynamical approach is not some wholly new wayof doing research that is separate from all existing research paradigms in cognitive science and hopes todisplace them. Rather, to see that there isa dynamicalapproach is to see a way of redrawing one's conceptual map of cognitive science in accordance with thedeepest similarities between various forms of existingresearch, (p. IX)In practical terms, taking a DST perspective onthe study of language development at least leads toa shift of focus, as Larsen-Freeman and Cameron

point out in their contribution to this issue. It is ashift away from large-scale comparative studies ofsingle-factor effects and from the type of experimental reductionism that has dominated parts ofour field in the last decades. Two examples mayhelp to clarify this point. Macaro and Meng (2006)report on a study on the effect of code-switchingon learning words by Chinese learners of Englishas a Foreign Language. Interestingly, the Macaroand Meng presentation was part of a symposiumat the 2006 AAAL conference on the role of theLI in language teaching, and several of the presentations listed variables that have an impact onLI use:

1. Attitudes toward LI, L2, and code-switching2. Level of proficiency of learners and teachers3. Age of learners4. Type of learners5. Amount of code-switching and use of L1/L26. Teachers' beliefs7. Individual learning styles of learners8. Definition of classroom as interactive

settingMacaro and Meng focused on one aspect, code

switching, and they compared three conditions:code-switching (i.e., giving the translation of aword in the LI), giving a definition in the L2plus the translation in the LI, and giving a definition in the L2 only. In a carefully designedquasi-experimental study, no differences amongthe conditions were found, which was of coursedisappointing for the researchers, but not reallysurprising: In an FL classroom many variables playa role in the acquisition of vocabulary, and the useof the LI is likely to be secondary tomany otherfactors that play a role in the process. In a way,itwould have been

surprisingif such a

single factor had explained differences in learning success.This is not a critique of the Macaro and Mengstudy, which iswell designed and carried out carefully. The null effect found merely supports thefallacy of focusing on a single explaining factor ina setting in which there are clearly many potentially relevant factors.


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174 TheModern Language Journal 92 (2008)The second example, a study on English lan

guage proficiency in adolescents in seven European countries (see Bonnet, 2004, for a full description of the study), isproblematic from a DSTperspective but for different reasons. The problem with this study seemed to be that the focus wastoo much on the group rather than on individuallearners. In the study, in which the present authorwas one of the researchers, more than 12,000 students were tested on their language proficiencywith different tests. In addition, an extensive questionnaire on language contact through media, socioeconomic status, attitudes, and school characteristics was administered.

The outcomes were disappointing from a research perspective for various reasons. One is that"country" came out as a very important explanatory variable, while itwas not possible to link othervariables of the very large set used to explain whatcountry actually meant. The other was that only avery limited amount of variance (17-25%) couldbe explained. So in contrast toMacaro and Meng(2006), there were many variables in this study,but the impact of most of these variables couldnot be shown.

It is very likely that individual learners' developmental tracks are influenced by factors likecontact with the target language, attitudes, andsocioeconomic factors, but the patterns of howthese factors interact over time are likely to bedifferent for individual learners. This finding supports the claim of Larsen-Freeman and Cameron(this issue) andVerspoor et al. (this issue) thatweshould focus more on individual patterns of development and therefore on intra-individual andinter-individual variation. One of the intriguingdimensions of the SOC research discussed earlieris that specific patterns of variation may be inherent in complex systems and that large changes arepart of these patterns; as such, large changes donot need a specific explanation, or at any rate notmore than small changes.As Bak (1996) puts it, referring to the example of the extinction of species, "specific narratives may explain each large catastrophe, but theregularity, not to be confused with periodicity, suggests that the same mechanisms work on all scales,from the extinctions taking place every day, tothe largest one, the Cambrian explosion, causingthe extinction of up to 95 percent of all species"(p. 18). In a way, this clashes with one of the ma

jor changes in perspective that Larsen-Freemanand Cameron (this issue) and Verspoor et al. (thisissue) suggest: a focus on microgenetic studiesin which the role of context and environmentis taken into account and in which narratives

are used to show how development emerges overtime and how small and large variations shapethe process. Therefore, Bak argues, there is noreason to worry about large variations becausethey do not need a specific explanation?thisis how systems work universally. Larsen-Freemanand Cameron, however, as well as van Geert (thisissue), and Verspoor et al. argue for detailed analyses of what can account for the variation overtime with a specific focus on phases with largevariation.

As pointed out by various authors (Jordan,2004; Wagenmakers et al., 2005) a new paradigmcan only prove itself by showing its superioritythrough empirical and, according to some, quantitative research. On the basis of monolingualresearch (Holden, 2002; Rueckle, 2002), experiments can be set up to show the relevance ofDST for core aspects of applied linguistics, suchas bilingual processing, but there is a certain riskin jumping too quickly to strict experimental settings: "Concentration on experimental design atthe formative stage of model building brings obvious detail to the fore. That makes it difficult toapply intuition, metaphor and all the other subtle understandings that go into insightful modelbuilding" (Holland, 1998, p. 237). It could be argued that while we are making leaps forward inour understanding of the relevance for languagedevelopment, we may not have reached a stage inwhich meaningful experiments can be set up toshow the relevance of a DST approach in competition with or in addition to current models andaccounts.

THE RELEVANCE OF A DST APPROACHTO OTHER SUBFIELDS IN APPLIEDLINGUISTICSIn this introduction, the focus has been on SLD

mainly, but it could be argued that the DST modelcan be applied to various other aspects. Languagepolicy development is a prime example of a dynamic process. In two issues of the MLJ, variousaspects of language policy have been discussedextensively: heritage languages (Winter, 2005,vol. 89, edited by Heidi Byrnes) and U.S. foreignlanguage policy (Summer, 2007, vol. 91, editedby Robert Blake and Claire Kramsch). As the articles in these issues show, political systems displayall the characteristics of dynamic systems, with

many variables interacting over time, sensitivityto initial conditions, nonlinearity, and the emergence of complexity from the implication of seemingly simple rules and procedures (e.g., No ChildLeft Behind policy). Analysis of the development


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KeesDeBot 175of language policies using the DST frameworkmay be elucidating and present a picture of thedevelopmental process that ismore accurate thana linear approach to policy analysis as presentedin Cooper's (1989) framework for the analysis oflanguage planning activities.Another area in which DST may be applied isdiscourse analysis. Cameron and Stelma (2004)applied ideas from DST to the use of metaphors,and their analyses showed that many other aspectsof discourse could be fruitfully studied from thisperspective.As Burns and Knox (2005) have argued, language classrooms show all the characteristics ofdynamic systems, and for the analysis of processesof interaction in the classroom, DST may providea new framework inwhich learning at the individual and group levels can be connected. Accordingly, language instruction can be studied alongthe lines set out for LI development proposed byvan Geert. Instruction is part of the resources thatdefine potential growth, and although it is impossible to include all possible variables that playa role in instruction in a model, the complexitycan be reduced to a smaller number of variablesrelevant for learning.The field of multilingual processing has grownimmensely in the last decades and has considerably enhanced our understanding of the multilingual mind. Various neuro-imaging techniqueshave been applied with varying success to showthe relation between processing and neural substrates (see de Bot, 2008, for a critical review). A

DST perspective raises new and maybe somewhatunsettling questions. As discussed in detail by vanGelder and Port (1995) and Elman (1995, 2004),such a perspective challenges the established viewof processing as operations on stable representations. This is a large issue that goes well beyondthe scope of our field, but it is likely to have animpact in the near future. There will be a needfor new methodologies to study language as a dynamic system that is not based on static representation but in the notion that language is alwayson the move and that language use is languagechange on different time scales.In cognitive science, some steps have beentaken to develop such new paradigms. Holden(2002) argues for a move from means analysis to

variation analysis: "A means analysis assumes theexistence of a characteristic pronunciation timethat is shrouded by unsystematic, additive sourcesof noise. By contrast, a variability analysis is concerned with identifying systematic changes in variability; it assumes that the pattern of changes invariability is informative, that itmay reflect the in

trinsic dynamics of the system" (p. 57). The statistics used in these approaches are very advanced,but the idea of looking at variation as a sourceof information is central to a dynamic perspective, not only in developmental processes on timescales spanning years, but also on short-term variation in standard language processing techniqueslike word recognition and naming. So there isclearly a need to develop at least a grasp of thestatistics involved in this line of development.

THE CONTRIBUTIONS INTHIS ISSUEThe contributors to this special issue comefrom different parts of the world and from awide range of theoretical and paradigmatic back

grounds. What they share is an interest in the application of DST principles in the study of language development in the broadest sense. Thecontributions can be arranged in two groups, onefocusing largely on methodological issues (vanGeert; Larsen-Freeman 8c Cameron; Verspooret al.) and the other focusing more on theoretical issues (Ellis, Plaza-Pust, Jessner).Paul van Geert takes several episodes fromLewis Carroll's Through the Looking Glass to explain some of the basic thinking behind DST,which in his view has not developed the momentum itdeserves. In particular, for our understanding of change and growth in systems, there is norival theory at the moment. Van Geert explainsthe steps to be taken for the construction of a dynamic system for the L2. His focus ison amodel ofgrowth or development. While acknowledging theinterconnectedness of systems, van Geert, somewhat in contrast with what Larsen-Freeman andCameron propose, argues that we need simplification and some form of reductionism in order toarrive at manageable models of development overtime. L2 proficiency is one of the constructs thatstill can be used, although it is a simplification ofa whole range of issues. The aim of the modelsis to find the "evolution rules" that might explainthe dynamics. Development takes place on various time scales, and these scales tend to interact.Therefore, according to van Geert, it is useful tolook at variation on all those scales and see howvariation at one level has an impact on variationon other levels. In the last section of his contribution, he provides some details about a model forLI acquisition that is related to empirical data.Diane Larsen-Freeman and Lynne Cameronfocus on the specific requirements of a changefrom a traditional approach to research methodology in applied linguistics to one inspired by aDST perspective. Their main points are that the


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176 TheModern Language Journal 92 (2008)notion of causality has to be redefined and that coadaptation may be a better label. They point outthat the natural variation in systems also changesour perspective of causality and explanation. Inaddition, more attention is needed to the situatedness of the behaviors or skills we are interested in, since these skills or behaviors cannot beinterpreted independent of the context of use.Larsen-Freeman and Cameron provide a list of

methodological principles that challenge manyof the largely accepted ways of thinking about research in the social sciences generally and in applied linguistics inparticular.They end by listinga number of approaches that may help us form abetter picture of SLD as a dynamic process. Formative experiments, dense longitudinal data collection, and different ways of studying variation asdiscussed inVerspoor et al. are mentioned, alongwith computer modeling.

Marjolijn Verspoor, Wander Lowie, and Marijnvan Dijk compare earlier research on variationin SLD with a new approach to variation basedon DST that takes variation as a source of information rather than as noise. The argument isthat variation informs us about the dynamics ofthe developmental process and that differences inranges of variation are indicators of steps of development. These authors argue that variation is thenatural outcome of interaction of variables in development and that therefore there may be "freevariation" in SLD, a hotly debated issue among sociolinguists interested in language development.Using a case study of the development of writing skills as an example, Verspoor et al. show howdifferent new methods can be used to describepatterns of variation.Nick Ellis presents a rich picture of the emergence of SLD in adult learners from a dynamiccycle of language use, language change, languageperception, and language learning. According toEllis's cycle, usage leads to change, change affectsperception, perception affects learning, learningaffects usage, and so on. In his contribution, helinks individual change and variation with similar processes on the societal level, reintroducingthe old idea of a connection between synchronicand diachronic language change and languagedevelopment.In her contribution, Carolina Plaza-Pust arguesfor a link between a DST approach and Universal Grammar (UG). She uses the metaphor ofthe turbulent mirror to describe the order andchaos that characterize systems. As she indicates,"linguists have not been very keen in enteringturbulent mirror worlds and their unpredictablelandscapes" (p. 250). Plaza-Pust argues for amedi

ation function of UG between stability and changewith universal principles or constraints as stabilizing factors and functional categories as potentialagents in change. This leads to a more open perspective on UG as a part of the language systemthat is not completely encapsulated but interactswith other aspects of language and the social environment inwhich it is used.

Ulrike Jessner, one of the "early adopters" ofDST in the fieldofmultilingualism and SLD, discusses the Dynamic Model ofMultilingualism thatwas first presented inHerdina and Jessner (2002).In her contribution, Jessner argues for an important role for metalinguistic awareness in the development of multiple languages, even though,as she admits, the implementation and formalization of metalinguistic awareness in DST terms isstill underdeveloped. She supports her argumentswith data from a recent study on third languagelearners in Tyrol who show interesting patterns ofinteraction between and within language systems.The articles in this special issue provide a richoverview of the role DST and related modelsand lines of thinkingdo play and will play inthe field of applied linguistics. Research will develop along three interrelated lines: analysis oflanguage development on the basis of dense datacollection, experimental work focusing on variation and interactions of variables, and modeling oflanguage use and language development. Development and variation will be studied on differenttime scales, from the growth and decline of language proficiency over the life span, to variationin developmental processes ranging from weeksto years, to variation on the level of the millisecond in experimental tasks. Applied linguistics as afield basically is concerned with the developmentof systems, be they individual learners, classes, ethnic groups, or policy makers. The DST perspectiveallows us to look at those systems in a structuredway, with many tools and instruments developedin other fields waiting to be employed in ours.

ACKNOWLEDGMENTSThe author is indebted to Ludmila Isurin, Wander

Lowie, Marjolijn Verspoor, and twoML] reviewers fortheir comments on earlier versions of this contribution.

NOTES1We are grateful toHeidi Byrnes for her mediatingrole in the process.


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KeesDeBot 1772The term Second Language Development is used instead of the more traditional term Second Language

Acquisition to capture both growth and decline?thatis, acquisition and attrition?which are both aspects ofdevelopment.

REFERENCESBahrick, H. (1984). Fifty years of second language attrition: Implications for programmatic research.Modern Language Journal, 68, 105-118.Bak, P. (1996). How nature works: The science of self

organized criticality.New York: Copernicus.Barber, E. (1980). Language acquisition and appliedlinguistics. ADFL Bulletin, 12, 26-32.Beer, R. (2000). Dynamical approaches to cognitive science. Trends inCognitive Sciences, 4, 91-99.Bonnet, G. (Ed.). (2004). The assessment ofpupils skillsinEnglish in eightEuropean countries 2002. Paris:European Network of policy makers for the evaluation of education systems.

Browman, C, 8cGoldstein, L. (1990). Gestural specification using dynamically defined articulatory structures.Journal ofPhonetics, 18, 299-320.Burns, A, 8cKnox, J. (2005). Classrooms as complex systems:An emergent research agenda. Paper presentedatAILA World Congress, Madison, WI.Cameron, L., 8c Stelma, J. (2004). Metaphor clusters indiscourse. Journal ofApplied Linguistics, 1, 7-36.Carroll, L. (1895). Through the looking glass. London:Macmillan.Cooper, D. (1999). Linguistic attractors: The cognitive dynamics of language acquisition and change. Amster

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Cambridge: Cambridge University Press.de Bot, K. (2008). The imaging of what in the multilingual mind? Second Language Research, 24{A),111-133.

de Bot, K., Verspoor, M., & Lowie, W. (2007). A DynamicSystems Theory approach to second language acquisition. Bilingualism: Language and Cognition,10, 7-21.

Ellis, N. (2008). The dynamics of second language emergence: Cycles of language use, language change,and language acquisition. Modern Language Journal, 92, 232-249.

Elman, J. (1995). Language as a dynamical system. InR. Port 8c T. van Gelder (Eds.), Mind as motion:Explorations of the dynamics of cognition (pp. 195225). Cambridge, MA: The MIT Press.

Elman, J. (2004). An alternative view of the mental lexicon. Trends in Cognitive Sciences, 8, 301-306.Firth, A, 8cWagner, J. (1998). SLA property: No trespassing Modern Language Journal, 82, 91-94.Herdina, P., 8c Jessner, U. (2002). A dynamic model ofmultilingualism. Perspectives of change in psycholinguistics. Clevedon, UK: Multilingual Matters.

Holden, J. (2002). Fractal characteristics of responsetime variability. Ecological Psychology, 14, 53-86.Holland, J. (1998). Emergence: From chaos toorder. Reading,MA: Perseus Books.

Jensen, H. (1998). Self-organized criticality. Cambridge:Cambridge University Press.Jessner, U. (2006). Linguistic awareness inmultilinguals:English as a third language. Edinburgh, UK: Edinburgh University Press.

Jessner, U. (2008). The role ofmetalinguistic knowledgein L2 and L3 development: A dynamic systemstheory perspective. Modern Language Journal, 92,270-283.

Jordan, G. (2004). Theory construction in second languageacquisition. Amsterdam/Philadelphia: John Benjamins.Krashen, S. (1983). The din in the head, input, andthe language acquisition device. Foreign LanguageAnnals, 16, 41-44.

Larsen-Freeman, D. (1997). Chaos/complexity scienceand second language acquisition. Applied Linguistics, 18, 141-165.Larsen-Freeman, D. (2002). Language acquisition and

language use from a chaos/complexity theory perspective. InC. Kramsch (Ed.), Language acquisitionand language socialization (pp. 33-46). London:Continuum.

Larsen-Freeman, D., 8c Cameron, L. (2008). Researchmethodology on language development from acomplex theory perspective. Modern LanguageJournal, 92, 200-213.Lewin, R. (1999). Complexity: Life at the edge of chaos.Chicago: The University of Chicago Press.

Lightbown, P., 8c Spada, N. (1999). How languages arelearned. Oxford: Oxford University Press.Lorenz, E. (1963). Deterministic non-periodic flow.Journal ofAtmospheric Sciences, 20, 130-141.Macaro, E., & Meng, Q. (2006). The effect f teacheruse ofLI on Chinese EFL learners' vocabulary acquisition.Paper presented at the 2006 AAAL conference,Montreal.

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178 TheModern Language Journal 92 (2008)Robinson, B. 8cMervis, C. (1998). Disentangling early

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Thelen, E., & Smith, L. B. (1994). A dynamic systemsapproach to thedevelopment of cognition and action.Cambridge, MA: MIT Press.van Geert, P. (1995). Growth dynamics indevelopment.In R. Port 8cT. van Gelder (Eds.), Mind as motion:Explorations in the dynamics of cognition (pp. 313337). Cambridge, MA: Bradford Book.van Geert, P. (1998). A dynamic systemsmodel of basicdevelopmental mechanisms: Piaget, Vygotsky andbeyond. Psychological Review, 5, 634-677.van Geert, P. (2008). The Dynamic Systems approach inthe study of LI and L2 acquisition: An introduction.Modern Language Journal, 92, 179-199.van Gelder, T. (1998). The dynamical hypothesis in cognitive science. Behavioral and Brain Sciences, 21,615-628.

van Gelder, T. & Port, R. (1995). It's about time: Anoverview of the dynamical approach to cognition.In R. Port & T. van Gelder (Eds.), Mind as motion:Explorations in thedynamics of cognition (pp. 1-45).Cambridge, MA: MIT Press.van Lieshout, P. (2004). Dynamical systems theory andits application in speech. In B. Maassen, R. Kent,H. Peters, P. van Lieshout, & W. Hulstijn (Eds.),Speech motor control in normal and disordered speech(pp. 51-82). Oxford: Oxford University Press.van Orden, G. (2002). Nonlinear dynamics and psycholinguistics. Ecological Psychology, 14, 1-4.van Orden, G., Holden, J., & Turvey, M. (2003).Self-organisation of cognitive performance. Journal of Experimental Psychology: General, 132, 331350.

Verspoor, M., Lowie, W., & van Dijk, M. (2008). VariabilityinL2 development from a dynamic systems perspective. Modern Language Journal, 92, 214-231.

Wagenmakers, E., Farrell, S., & Ratcliff, R. (2005). Human cognition and a pile of sand: A discussionon serial correlations and self-organized criticality. ournal of xperimental Psychology: General, 134,108-116.

Waldrop, M. (1992). Complexity: The emerging science atthe edge of order and chaos. New York: Simon 8cSchuster.Wolfram, S. (2002). A new kind of science. Champaign,IL: Wolfram Media.

Survey of Doctoral Degrees Soon To Be Available OnlineThe annual survey of doctoral degrees granted in foreign languages, literatures, cultures, and linguistics,and in foreign language education in the United States, which usually appears in the fall issue of theMLJ, has been published by the journal as a service to its readers since 1926. For the last 30 years,Dr. David P. Benseler has been compiling and editing this extensive listing. However, Dr. Benseler hasdecided to hand over this feature starting this year, and the listing from now on will be compiled bythe new editorial office and will be made available on our new Web site at http://mlj.miis.edu/. Wewould like to extend our sincerest appreciation to Dr. Benseler for his long service to the MLJ and theprofession.

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