5

Complexity theory

Diane Larsen-Freeman

Introduction

In a chapter discussing the recent major shift in the way language and language development have been viewed, child language researcher Evans (2007) wrote:

Since the late 1950s the dominant metaphor for language and cognition has been the digital computer and the belief that human intelligence is a process of computations on symbolic representations—rule-based manipulation of symbols. Language, from this perspective, is a symbolic system that is innate, residing in the human genetic code. As a result, the focus of much language research has been on the universal, stable, orderly, stage-like patterns in learners’ language and the discovery of these innate abstract linguistic structures.

The emphasis of child language researchers has shifted recently to highlighting the flexible, transient, dynamic aspects of the emergence of language abilities ... From this perspective, language is no longer a static, abstract, symbolic system, but language patterns that emerge over time as a property of the self-organization of a complex system. Language development is no longer seen as a process of acquiring abstract rules, but as the emergence of language abilities in real time, where changes over days, months, and years and moment to-moment changes in language “processing” are the same phenomena, differing only in their timescales ... [With] its emphasis on the fluid, transient, contextually sensitive nature of behavior, the goal of this approach is to identify the mechanisms and states of the child's emerging language abilities that engender developmental change at all levels of real-time continuous processing. (p. 128).

The shift from innatism to emergence, from a top-down process of computation to a bottom-up process of self-organization, from rules to patterns, from a static system to a dynamic one, from universal to contextually sensitive behavior, and from stability to transience all reflect a profound shift of perspective, one that is applicable to second language acquisition (SLA), as well as to first. Although there is no doubt a confluence of post-structural accounts that one could point to that propelled this shift in perspective,1 the new “science” of complexity theory (Gleick, 1987; Hall, 1993; Waldrop, 1992) has been a major contributor to this way of thinking.

Historical discussion2

One of the first to initiate the thinking that changed science was Warren Weaver (Érdi, 2007). Weaver is perhaps best known for his work with Claude Shannon on developing information theory. However, in an article that pre-dated his work with Shannon, Weaver (1948) distinguished between disorganized and organized complexity. Disorganized complexity, as the name implies, arises from random interactions of a large number of elements; gas molecules inside a container is an example. Organized complexity, on the other hand, also involves a large number of parts, but the parts work together to produce a coherent structure from their interaction, such as with individual birds coming together to form a flock. In Weaver's words “a sizable number of factors ... are integrated into an organic whole” (p. 539). The structure emerges and is not dictated to or embedded in any one part.

The idea of organized complexity is core to complexity theory (CT). Biologist von Bertalanffy (1950) applied this idea in his general systems theory. He sought to identify organizational principles that promote our understanding of the behavior of living systems and social groups. Of course living organisms and social groups, unlike my example involving a gas in a container, are open systems, which means that they are open to interacting with systems outside of themselves. They receive feedback from the environment and adapt as circumstances change.

As CT has been appropriated to deal with more human enterprises in the last 20 years or so, it has yielded insights into organizational development, economics, and epidemiology, to name but a few of its applications. Indeed, one of the strengths of CT is that it has been usefully applied to study different phenomena: traffic jams, stock markets, the growth of cancer tumors, the conservation and management of resources, and so on. A systems-level perspective also makes possible cross-disciplinary investigations, such as can be found in the work of Oxford University researchers Fricker, Efstathiou, and Reed-Tsochas (cited in Johnson 2007, p. 16), who analyzed the nutrient supply lines in a fungus in order to see whether lessons can be learned for supply-chain design in the retail trade.

Closer to our field, there has been a great deal of research in developmental psychology, based on principles from complexity theory and its close kin dynamic systems theory. Some of the pioneering work has been on investigating motor development in children (Thelen and Smith, 1994), modeling first language development (van Geert, 1991), and conceptualizing real-time language processing and the longer timescale of language development as integrated phenomena (Bates and Elman, 2000). In second language development, there is not a long history. Larsen-Freeman (1997) was the first to write about the value of seeing second language acquisition from a chaos/complexity theory perspective, following up in 2002a, 2007, and 2010 by showing how such a perspective can help to overcome the dualism that often besets our field. Larsen-Freeman (1997) and Larsen-Freeman and Cameron (2008a) have suggested that because CT features systems which are complex, dynamic, emergent, open, self-organizing, and adaptive, it holds great promise for inspiring innovative thinking concerning both first and second language development.

Also finding the perspective helpful, de Bot et al. (2005, 2007) applied dynamic systems theory to second language acquisition, and Herdina and Jessner (2002) used it to discuss changes in multilingual proficiency on an individual level and to provide a more dynamic description of multilingualism. Research reports based on this perspective are featured in special issues of Applied Linguistics, co-edited by Ellis and Larsen-Freeman (2006), The Modern Language Journal, edited by de Bot (2008), and Language Learning, co-edited by Ellis and Larsen-Freeman (2009). Given the date of these publications, it is clear, as I wrote earlier, that there is not a long history to CT nor to its use in SLA, but interest is growing.

Core issues

The association of CT and related theories, chaos theory and dynamic systems theory, with the new sciences stems from their common rejection of Newtonian linear determinism. Rather than seeing the world through a reductionist lens, CT and its relatives adopt a more holistic perspective. What this means is that they adopt a systems perspective and look for (nonlinear) relations among variables that have previously been separately studied for their linear cause and effect relationship. The new sciences have a great deal else in common. They focus on complex systems, those whose complexity results from many interacting elements or agents. Complex systems demonstrate an initial state dependence, in which even the smallest of differences can have a huge, amplifying effect on the subsequent behavior of the system, a phenomenon known as “the butterfly effect.”

These systems are affected by “feedback.” As a result of the feedback, the systems adapt to new conditions. The system is typically “open,” which means it can be influenced by its environment. The system also exhibits emergent properties. It shows a mix of ordered and disordered behavior. Systems are said to operate at a number of different, but interconnected, levels, from a macro level, such as that of a whole ecosystem, all the way down to a micro level, such as subatomic particles. The system can thus be viewed at different levels of granularity, with each nested, one within another. The new sciences also focus on the dynamics of complex systems, making change, both gradual, and unpredictably sudden, a central focus of their investigation.

Perhaps its biggest contribution then is the shift of perspective it has ushered in. Not only is the perspective cross-disciplinary in scope, but it also makes possible a way to unify areas within language study. For instance, a CT perspective makes possible an integrated view across nested levels and across time scales from language processing in the brain, to language evolution and change, to language use, to language acquisition. To illustrate this, consider just one of these features of a complex system—its dynamism—and how it applies at different nested levels of scale.

At the level of language processing in the brain, cognitive scientist Spivey has developed a complex dynamic view of mind that he calls “continuity psychology” (Spivey, 2007). Spivey spurns cognitive psychologists’ computer models of the mind, in which one discrete stable non-overlapping representational state gives way to another. He argues instead that the mind is in continual flux and that mental processes are continuously dynamic. Rather than “the assumption of stable symbolic internal representations ...” (2007, p. 332), we should think of internal representation as a process.

This same dynamism can be seen to apply to language evolution and change. Complexity theory sees language evolution as a dynamic process, characterized by continuous change. In other words, language is a complex adaptive system (Ellis and Larsen-Freeman, 2009; Kretzschmar, 2009). Lee and Schumann (2005, p. 2) propose that linguistic structure emerges as a complex adaptive system from the verbal interaction of hominids attempting to communicate with each other. What the interaction does is to insure that the forms that ultimately become part of the grammar are those that fit the cognitive and motor capacities of the brain. The adaptive process inherent in the interaction modifies the grammatical structures to fit the brain rather than requiring the brain to evolve a genetically based mechanism designed to specify the form of the language.

Thus, language has the shape that it does because of the way that it is used, not because of an innate bio-program or internal mental organ. Of course, there may be domain-general evolutionary prerequisites to language that support its use and acquisition. For instance, these might include the ability to imitate, to detect patterns, to notice novelty, to form categories, or the social drive to interact, to establish joint attention with another, to understand the communicative intention of others, etc. (Larsen-Freeman and Cameron, 2008a). However, language itself is an epiphenomenon, emerging from the interaction of its speakers (Hopper, 1988), a claim that Bybee (2006) has supported using diachronic data.

As I wrote, dynamism applies to real-time language use as well. Complexity theory maintains that because language is perpetually dynamic, every instance of language use contributes to language change. Thus, speakers’ using a language at one time and at one level of scale (e.g., two speakers conversing) contributes to language change over time and at a higher level of scale, that is, the speech community. Of course, some emergent patterns in language become stable, for without stability, speakers of the same language would eventually be unable to understand one another. The stability is achieved as speakers adapt to each other. Resulting stable norms of the community, in turn, downwardly entrain emergent patterns, a process known as “reciprocal causality.” As Gleick (1987, p. 24) has written of other dynamic systems occurring in nature: “The act of playing the game has a way of changing the rules.” This does not assume, however, the existence of a homogeneous speech community. Language variation arises from language in use, from how people actually speak and write. Every group and every place, every situation, is different (Kretzschmar, 2009). For instance, phoneticians have long known that the same word is pronounced differently by the same person with every use (Milroy and Milroy, 1999).

The same dynamism also characterizes second language acquisition. Both the evolving language system of a speech community and the developing interlanguage system of individual language learners change through use. Language is an autopoietic system, not an entropic one.

As Evans (2007) writes:

Developmental outcomes can be explained through the spontaneous emergence of more complex forms of behavior due to the cooperation of the multiple heterogeneous parts of the system that produce coherent complex patterned behavior. This process is known as self-organization. It occurs without pre-specification from internal rules or genetic code. Rather, development is truly self-organizing because it occurs through the recursive interactions of the components of the system. This process depends both on the organism itself and on the constraints put on the organism by the environment ... (p. 132)

Thus, from a CT perspective, an analogous process to real-time language change, self-organization in a dynamic system, occurs in first and second language development. During a particular communicative interaction, speakers soft-assemble their language resources. “Soft-assembly” refers to processes involving the articulation of multiple components of a system, where “each action is a response to the variable features of the particular task” (Thelen and Smith, 1994, p. 64). In other words, the assembly is said to be “soft” because the elements being assembled, as well as the specific ways in which they are configured, are adaptive; they can change at any point during the task. The soft-assembled patterns that arise from interaction are the products of dynamic adaptation to a specific context (Tucker and Hirsch-Pasek, 1993). The adaptation to a context includes the process of co-adaptation in which each individual in an interaction imitatively adapts to the language of another.

In communicative interactions, learners draw on what they know—the initial condition of their language systems. Given the pressures of responding in real time, they cobble together constructions (Goldberg, 2006; Tomasello, 2003)—form-meaning-use composites3: Words, phrases, idioms, metaphors, noncanonical collocations, grammar structures—a much more complex and diverse set of language-using patterns than the “core grammar” of formal approaches (Larsen-Freeman and Cameron, 2008, p. 99). By having an opportunity to repeatedly soft assemble, to revisit a similar semiotic space again and again, the language resources of learners are built up in an iterative fashion. Over time, those that occur frequently become emergent stabilities in a complex system. “Sequences of elements come to be automatized as neuromotor routines” in individuals. (Beckner et al., 2009, p. 11).

Through this building up process, certain structures achieve stability. However,

[w]hile achieving behavioral stability is critical in development, so is the need for flexibility and dissolution of old forms. With the emergence of novel, more complex forms, stable patterns must become unstable for change to occur. This instability itself allows the components of the system to reorganize in novel ways. From a [dynamic systems theory] perspective, variability is not simply “noise” in the system but instead provides valuable insights into the nature of language development and may in fact be the actual mechanism of change in development (Gershkoff-Stowe and Thelen, 2004, p. 13). (Evans 2007, p. 132)

The instability arises when two established patterns compete. This is signaled by a period of fluctuation between the competing patterns, followed by a phase shift in the system when a certain critical threshold is crossed, and some wider reorganization is triggered. The sudden discontinuity of the phase shift illustrates the non-linearity of complex systems, arising from the interaction of variables, whose modulating, mediating, attenuating, and amplifying effects on each other in positive feedback relationships (Ellis and Larsen-Freeman, 2006), cause a phase transition to be reached, which results in a change of state.

Moving between stability and instability, language can be seen as a “statistical ensemble” of interacting elements (Cooper, 1999, p. ix), and, similarly, a learner's language resources as “a network of dynamic language-using patterns” (Larsen-Freeman and Cameron, 2008). Through encounters with others, a process of co-adaptation takes place, in which each interlocutor's language resources are shaped and reshaped throughout the interaction (Larsen-Freeman and Cameron, 2008). Not only is “positive evidence” available in the interaction, so also is negative evidence. As Spivey (2007, p. 202) notes, learners can learn from the conspicuous absence of positive evidence. Its absence allows learners to decrement the probability of a relationship in the target language that they would have otherwise expected. Or, as Spivey puts it, “Negative evidence from the environment is not needed in such a situation because the predictive learner generates his or her own negative evidence.”

Thus, it is not necessary to posit a central rule-governed mental grammar that applies in a top-down manner. The knowledge underlying fluent, systematic, apparently rule-governed use of language is the learner's entire collection of memories of previously experienced utterances, both the learner's own and what the learner has attended to in the learner's interlocutors’ speech during co-adaptations. This socially situated view accords an active view of the learner—someone who learns from positive evidence, while generating her own negative evidence from her active noticing and exploration of the boundaries of the system.

As has been known for some time (Larsen-Freeman, 1976), frequency of occurrence has an important role in explaining the regularities that do exist in learner language (Ellis, 2002; Chapter 12, this volume). Of course, the language acquisition process is not mere imitation of frequently occurring forms. The failings of operant conditioning in language acquisition are well known. Therefore, it is not only frequency; development of a particular construction also depends on the degree to which the salience of a particular construction captures learner attention. Because learners must notice forms, and sometimes the forms are not very salient, factors relating to learner attention, such as automaticity, transfer, and blocking (Ellis, 2006), play a role in the development and use of any linguistic construction. Also important are a construction's cue contingency, the reliability with which learners can ascribe meaning or function to the construction in the language that flows about them, and its social value, and the role of particular constructions in organizing discourse (Celce-Murcia and Larsen-Freeman, 1999; Larsen-Freeman, 2002b, 2003). Another factor is the affective attachment learners have to certain patterns over others (Todeva, 2009). Learners thus exercise agency in the constructions they choose to use. With the ascription of meaning/function/value to forms, learners can begin to categorize them and generalize their meaning, often doing so around prototypes.

It is also true that learners do not merely reproduce what is said to them, or else, as Chomsky (1959) argued long ago, linguistic creativity would not take place. However, unlike the Chomskyan claim that a rule-governed process is required for novel forms to arise, CT offers morphogenesis through recombination and analogy (Larsen-Freeman, 1997, 2003). Indeed, connectionists’ simulations show that generalizations can be formed from increasing experience of usage, which develop over time (Christiansen and Chater, 2001; Elman et al., 1996), and that new forms, which are not present in the input data, can arise through overgeneralization, just as they do in natural language acquisition (Rumelhart and McClelland, 1986).

These observations are consistent with a view of the social, discursive world as systematic— patterned and often predictable, but where the systems in play are open and dynamic, with human meanings and human agency not only reproducing familiar patterns, but also generating novelty and surprise. (Sealey, 2009, p. 216)

Ultimately, “It is the multiple integrations of many component processes in many different tasks that leads to a system that is flexible, inventive, and exquisitely adaptive” (Smith and Breazeal, 2007, p. 67).

Of course, learners do not immediately begin using new forms in a target-like manner. Learners design their own systems on the basis of the affordances in the language they are exposed to, so input does not lead directly to output; instead, L2 learners are known to adopt a frequently occurring or perceptually salient form, especially if it is prototypical, or similar to a form in their own language. Once a particular form has emerged, it stays around for a time. It does not suddenly disappear from a learner's repertoire. A hallmark of complex systems is their variable behavior at one point in time. Over time, increased variability is a sign that a sudden non-linear jump is about to take place (van Geert, 2003). The phase shift signals a restructuring of the learners’ interlanguage. In fact, variation is essential for development to take place, just as it is for evolution in nature.

A very important caveat to all this, as always in SLA, is the powerful influence of what learners know of other languages. In a multilingual situation, there are multilingual norms instead of monolingual norms; furthermore, “the presence of one or more language systems influences the development not only of the second language, but also the development of the overall multi-lingual system” (Jessner, 2008, p. 274). In order to avoid the monolingual bias (Ortega, 2010), no longer can we assume language learners to be native speakers of a single national language, interacting with native speakers of another national language, and moving inexorably in a line from L1 to L2. Multilingualism is the norm.

Nor should we expect the processes of L1 and subsequent language development to be the same. Indeed, it is likely that SLA will need to be accomplished not only through implicit, but also through explicit, learning, at least for most older learners. In addition, languages are developed in local contexts of use. Because, from a CT perspective, open systems interact with the systems in their context of use, we should also not expect the details of SLA to be identical in all contexts.

As for the well-attested individual difference issue, individual difference factors are also seen to be dynamic (Dörnyei, 2009a; Ushioda and Dörnyei, Chapter 24, this volume), so that, for example, motivation is not static, but rather ebbs and flows and interacts with other factors. Moreover, there are so many individual differences, which are constantly changing and interacting, that it is difficult to separate the acquisition process from the one doing the acquiring (Kramsch, 2002). From a CT perspective, each individual is unique because he or she has developed his or her physical, affective, and cognitive self from a different starting point and through differing experience and history. Each individual thus acts as a unique learning context, bringing a different set of systems to a learning event, responding differently to it, and therefore, learning differently as a result of participating in it.

From this perspective, as heretical as it may seem to others, there is no end and there is no state to language or to its development (Larsen-Freeman, 2005). In fact, we would be better off using the term “second language development” rather than “second language acquisition” in that learners have “the capacity to create their own patterns with meanings and uses (morphogenesis) and to expand the meaning potential of a given language, not just to internalize a ready-made system” (Larsen-Freeman and Cameron, 2008, p. 116). Language acquisition is not a matter of conformity to uniformity. Thus, developmental change seems “not so much the stage-like progression of new accomplishments as the waxing and waning of patterns, some stable and adaptive and others fleeting and seen only under special conditions” (Thelen and Bates, 2003, p. 380). In conclusion:

Embodied learners soft assemble their language resources interacting with a changing environment. As they do so, their language resources change. Learning is not the taking in of linguistic forms by learners, but the constant adaptation and enactment of language-using patterns in the service of meaning-making in response to the affordances that emerge in a dynamic communicative situation. (Larsen-Freeman and Cameron, 2008, p. 158)

Data elicitation and common measures

Characteristics

Complexity theory/second language acquisition researchers are primarily interested in learner performance data. Such data can be obtained from any language-using activity, inside or outside the classroom, which involves mental activity around language: understanding, speaking, recall of language, meaningful practicing, and so on. Language learning or development emerges with these adaptive experiences of language use.

In order to demonstrate endurance, and not only emergence of a form, longitudinal data would be desirable. In particular, dense corpora, with frequent samplings of learner language, are valuable in order to identify the “motors of change” (Thelen and Corbetta, 2002). Data are considered from an emic phraseological perspective (e.g., using “idea units” as the unit of analysis Ellis and Barkhuizen, 2005), seeking as much as possible to view learner performance from the learner's point of view, with comparison to the target language usually avoided.4

Furthermore, “Models which assume that speaker characteristics are ‘independent variables’, with linguistic features as ‘dependent variables,’ imply a linear model of causality. Such models do not allow for the interaction between the variables, and they do not model well the dynamic, systems-based realities” with which CT researchers are concerned (Sealey, 2009, p. 222).

Where to draw the ecological circuit (Atkinson et al., 2007) for a particular study and how to include enough detail for a rich, holistic account are challenges to doing research within this framework. This is because from a complexity perspective, context includes the physical, social, cognitive, and cultural, and is not separable from the system. That is, context cannot be seen as a frame surrounding the system that is needed to interpret its behavior (Goffman, 1974). The connection between system and context is shown by making contextual factors parameters of the system. We thus cannot separate the learner or the learning from context in order to measure or explain SLA. Rather we must collect data about and describe all the continually changing system(s) that are relevant to our research question, and be especially cautious about generalizing.

Another difference from traditional data is that since we are especially interested in change over time, CT changes what we look at in the behavior of systems: Flux and variability leading to stability signal self-organization and emergence; sudden phase shifts signal important instability in the system and can direct our attention to the conditions that lead up to them. Of course, the study of variability is not new in SLA. However, CT encourages us not to view variability as the result of some extrinsic factor, but rather to adjust our perspective so that we see the variability as necessary for learning to occur (Thelen and Smith, 1994). A complex system will show degrees of variability around stabilities, and the interplay of stability and variability offers potentially useful information about change in the system. From this perspective, variability in data is not noise to be discarded when averaging across events or individuals, or the result of measurement error (van Geert and van Dijk, 2002), but is part of the behavior of the system, to be expected around stabilities, and particularly at times of transition from one phase or mode of behavior to another. Changes in variability can be indicators of development. If we smooth away variable data by averaging, we lose the very information that may shed light on emergence (Larsen-Freeman, 2006). If, instead, we pay attention to the nature of changes in stability and variability, we may find new ways of understanding language learning processes.

Complex systems operate on a range of timescales, from the milliseconds of neural processing through the minutes of a classroom activity to change on an evolutionary timescale. They also operate on a number of nested levels. For a particular study, certain levels and scales will be focal, but they will be affected by what happens on other levels and scales. As Lemke (2002) pointed out, “certain events widely separated in linear time may be more relevant to meaningful behavior now than other events which are closer in linear time” (p. 80). Because activity on one level and scale influences, indeed is a part of what happens on other levels and scales (Kramsch and Whiteside, 2008; Kramsch, 2008), phenomena emerge at a particular level or scale as a result of activity at a lower level or from an earlier period. It is desirable, therefore, when researchers are conducting research within a complex systems approach that they seek to find relationships within and across different levels and timescales. When we are able to do so, the results will be all the more powerful.

Two new sources of SLA data, which are associated with CT, involve the use of computers. First, it is possible to use computer models to generate data—these are then checked for how closely they pattern with what would be expected in natural data (Ellis with Larsen-Freeman (2009). For example, Meara (2004, 2006) used dynamic modeling to describe vocabulary development and loss. Second, computer-searchable linguistic corpora have been used to chart the change in the use of a particular pattern over time in SLA research (Ellis and Ferreira-Junior, 2009; Ellis with Larsen-Freeman, 2009). While computer and corpus-based research has certain drawbacks, for example, the stripping away of context, they have the advantage of providing a way to model systems and condense time periods in the case of computer models and provide abundant exemplars in the case of corpora.

To summarize this section, complexity theory researchers search for ways to study the relational nature of dynamic phenomena, a search that is not the same as the pursuit of an exhaustive taxonomy of factors that might account for behavior of any given phenomenon. To do this, researchers must collect data that include the richness of the context, that do not strip away the variability, and that include data collected from different levels and timescales. All this is to avoid the reductionism that does not produce satisfying explanations, which are respectful of the holistic interconnectedness of complex dynamic systems.

Empirical verification

Port and van Gelder offer three methods of studying complex, dynamic systems: quantitative modeling, qualitative modeling, and dynamical description. The first is not appropriate for studying human behavior because it requires researchers to measure everything that could possibly influence a system, something that is not possible with humans. However, dynamical description and qualitative modeling have been used in our field, and I will give examples of each.

An example of a dynamical description is a classroom observation conducted by Cameron (Larsen-Freeman and Cameron, 2008) to study collaborative activity in an EFL classroom in Norway. I have chosen it to illustrate the notion of collective variables, an operational construct in the study of complex systems. Collective variables are “actions and responses that index the cooperativity of a multidimensional system” (Thelen and Smith, 1994, p. 99). They describe dynamic patterns, of varying and changing stabilities. The participants in the study were 11-year-old children in a rural classroom in northern Norway. The lesson Cameron observed began with the teacher asking the students to talk about polar animals in English, using content and language that they had encountered in previous lessons. To prompt them to speak, the teacher asked each student to select a particular animal and then to talk about it to the rest of the class.

The ecological circuit that Cameron drew centered on action on a task and so had the three components: teacher, students, and task. Relations among these components produced emergent “talk on task” that served as a learning opportunity or affordance for a particular individual. The trace of the talk, in the form of recording and transcription, represented the trajectory of the system over its state space landscape, that is, all possible outcomes of the task in that classroom. Each interactional episode with an individual learner showed the teacher's talk adapting to the learner's talk through interaction on the task. The data showed how the system started from the teacher's expectation that there would be extended talk, but quickly a not particularly helpful, but rather stable, attractor of limited questions and answers emerged.

In observing a series of such interactions between the teacher and other students, Cameron found that, with one exception, what started as an open invitation to students to speak about a polar animal transformed almost every time into a sequence of questions from the teacher followed by short answers from a student, sometimes added to by further comments from the teacher. In other words, it was the teacher who did much of the talking.

Applying a complex systems description to the unfolding lesson, the teacher-student interaction can be seen as co-adaptive, with each response constructing a feedback loop between participants. The move from an open description task to a series of questions and answers can be seen as a move to a stable attractor in state space landscape of talk on task, since most of the interactions between teacher and individual student ended up in this way. To describe the system in action, moving from the unstable interactional mode to the more stable, limited question and answer mode, Cameron needed to find a suitable collective variable for the system, that is, one that brings together teacher and learner talk on task into one collective variable (Thelen and Smith, 1994, p. 251). A collective variable for this interactional system was derived by comparing the actual language used by learner and with the expected language as set up by the teacher's utterances, something Cameron called the interaction differential.

This collective variable not only usefully described the shift from instability to stability, but it also showed how the trajectory was affected when a more advanced learner transformed the task to suit his own predilection. Rather than discussing a polar animal, he spoke about his pet tropical bird. By changing the task, the learner was able to use more complex language, and the teacher responded with fewer elicitations and more responsive language during his own turns. The result was that the interaction differential took on a wider range of values in this interaction, and did not follow the pattern of a large differential that was rapidly closed down.

Another dynamical description done recently illustrates the important process of adaptive imitation, where learners used an amalgam of old and new patterns to suit their communicative needs. Macqueen (2009) adopted a CT perspective in her investigation of the development of four ESL learners’ writing. A qualitative methodology (lexical trail analysis) was used to capture a dynamic and historical view of the lexicogrammatical patterning in the learners’ writing. Recurring patterns were traced, and the adaptations that learners made were noted. The newly adapted language-using patterns subsequently become part of the learners’ language resources, available for further use and modification. Macqueen's results demonstrate learners’ ability to imitate and to adapt, and thus transform their language resources. “Adaptive imitation is the means of gaining the power to conform and the power to create. This power is what enables reciprocal causality in language patterning where ... the communication patterns of individual people contribute to the prevailing norms of their discourse communities ... ” (p. 266).

A study that illustrates qualitative modeling is one conducted by Ellis and Larsen-Freeman (2009). The focus of this study was on the acquisition of English verb-argument constructions (VACs) by EFL learners. As I mentioned earlier, first language acquisition researchers Tomasello (2003) and Goldberg (2006) had found support for the usage-based acquisition of constructions. They demonstrated that learners appear to induce categories from exemplars centered around verbs prototypical of a particular VAC.

What Ellis and Larsen-Freeman did was two-fold. First, they reviewed a corpus-based study conducted earlier by Ellis and Ferreira-Junior (2009), which analyzed the speech of seven second language learners of English and the language spoken to them as compiled in the European Science Foundation (ESF) corpus. They found that, just as was the case with L1 acquisition, L2 learners appear to encounter an overwhelming number of tokens of a given verb in a particular VAC. In turn, not surprisingly, when the learners began to produce VACs, the first verb to emerge for a VAC was the one with the highest frequency. Thus, the use of such exemplars by learners’ interlocutors presumably facilitates comprehension of the learners in the micro-discursive moment, and perhaps their subsequent emergence and ultimate acquisition of VACs.

Ellis and Larsen-Freeman went on to use computer simulations to see if they would pattern VAC input data in a similar manner to the learners. Although decontexualized, computer simulation supports the investigation of the dynamic interactions of these factors in language learning, processing, and use. In fact, the simulations showed how simple general learning mechanisms, exposed to the co-adapted language usage typical of native speakers as they speak with non-native speakers, produced the same order of emergence as non-native speakers and used the same cues. In other words, the factors that were measured in the corpus study were corroborated in the computer simulations. Learning takes place through the continual revisiting of the same space over and over again.

Applications

From a CT perspective, teaching involves managing the dynamics of learning, exploiting the complex adaptive nature of action and language use while also working to see that co-adaptation works for the benefit of learning. It is not about bringing about conformity to uniformity through transmission. Teachers do not control their students’ learning. Teaching does not cause learning; learners make their own paths. This does not mean that teaching does not influence learning, far from it; teaching and teacher-learner interaction construct and constrain the learning affordances of the classroom. What a teacher can do is manage and serve her or his students’ learning in a way that is consonant with their learning processes. Thus, any approach consonant with CT would not be curriculum-centered nor learner-centered, but it would be learning-centered—where the learning guides the teaching and not vice versa.

Another implication for instruction, drawing on CT, is the acknowledgment that language is a dynamic system. Treating language more dynamically is an answer in part to the “inert knowledge problem,” which arises when students are taught static rules of form using psychologically inauthentic activities. What students learn from traditional grammar drills is not available for use outside of the lesson. I have coined the term “grammaring” to suggest that grammar be treated in a more dynamic manner (Larsen-Freeman, 1995). Grammaring involves using grammar structures accurately, meaningfully, and appropriately (Larsen-Freeman, 2003). Students learn to do this when they are engaged in practice activities that are psychologically authentic, with the conditions of learning aligned with the conditions of use, when they are provided with appropriately tuned feedback, and when the activities are deliberately iterative, not repetitive (see Segalowitz and Trofimovich, Chapter 11 in this volume). In other words, from a CT perspective, language learning is seen as a process of meaningfully revisiting the same territory again and again, although each visit begins at a different starting point. In this way, language teaching is not about getting students to add knowledge to an unchanging system. It is about changing the system (Feldman, 2006).

Also implied is the idea of a more “organic” syllabus, which would evolve with learners’ readiness to learn the particular form. Instead of a pre-determined sequence of language forms of any sort, learners would engage in tasks or activities that are designed to encourage the use of particular forms (task-essential use). From learners’ use, teachers would offer feedback and diagnose the learners’ readiness to learn a particular form. Notice that this approach calls for some pre-specification of the items to be learned, partly to fill in the gap and partly because without a teacher's monitoring language that arises in the classroom, certain language forms may never be used by learners who skillfully avoid them. Avoidance is, of course, a sign that learners are experiencing difficulty with particular language forms, and these, too, need attention—even though they are only detectable by their absence. Of course, what is being suggested is not easy to accomplish in a large class of students; nevertheless, it needs to be attempted because teaching students something they already know is not teaching.

Future directions

Complexity theory as applied to SLA is in its infancy; therefore, it is not difficult to imagine a robust research agenda for some time to come. Here are but four questions that would benefit from more exploration from a CT perspective:

(1)   Are there patterns in individual differences? As is well known, there is a great deal of individual variation in SLA. However, to what extent are there patterns in the variation? There is reason to believe that even though each individual charts his/her own path uniquely, the variety among the paths is not infinite. While entertaining CT would suggest that there are few generalizations that would hold across learners, at best banal ones, for example, “motivation is important,” there may well be configurations that capture generalizations among groups of learners or certain combinations of individual differences that act as integrated wholes (Dörnyei, 2009b). For example, Larsen-Freeman (2006) found that certain of the research participants were more analytically oriented and others more expressively oriented (also, see Meisel et al.’s multidimensional model (1981)).

(2)   Can we see the motors of change if our corpora are dense enough? Not unlike any other SLA research effort, a CT approach would benefit from thick longitudinal descriptions, with many learners of many different languages in many contexts. Especially helpful would be dense corpora, which involve highly intensive sampling over short periods of time. Thelen and Corbetta (2002) suggest that the data which such an approach yields will not only allow us to fix the “when” of developmental milestones, but, importantly, the “how” of development by making development more transparent.

An assumption of researchers using a CT approach is that there are moments in the evolution of behavior where we can directly observe change happening. Furthermore, since change works at multiple time scales, these small-scale changes can illuminate change at a longer time scale. Microdevelopment, Thelen and Corbetta suggest, would allow us to dynamically describe important developmental differences among learners, both children and adults.

(3)   What are the potential and limitations of computer modeling? As we have seen, van Gelder and Port (1995) make a distinction between two types of modeling for dynamic systems. Quantitative modeling cannot be undertaken in the human sciences, for in order to do so, numerical values would have to be assigned to all factors. Qualitative modeling, on the other hand, does lend itself to investigating SLA. Though it still involves quantification, qualitative modeling offers a way of exploring the dynamics of complex systems. Researchers build a computer model of the real world complex system under investigation and take it through multiple iterations, replicating change over time. The model is designed and adjusted so that the outcomes over time reflect what is known of the real world system. Further iterations or changes in parameters then allow the researcher to explore how the model system responds to changes in conditions.

Developing a computer model requires explicit statements of theory and the most accurate empirical knowledge about the real systems and processes being modeled. As a result, the model is only as good as the assumptions built into it. Inevitably, the model differs from the actual system, being idealized or simplified in some respects, approximated in others. Its potential and its limitations remain to be investigated.

(4)   To what extent is implicit learning responsible for SLA? This is, of course, a question that has been circulating in the field since its inception. No longer can we be content with addressing this question in the absolute sense. There is a need “to create more fine-grained analyses that characterize precisely the ways in which basic implicit generalization mechanisms interact with higher level explicit control processes” (MacWhinney 1997, p. 280).

These are but four questions. With the change of perspective that CT offers, many more questions could easily be formulated and studied. And, I hope they are.

Notes

1   For example, this shift also, at least partly, overlaps with the assumptions of usage-based grammar, emergent grammar, cognitive linguistics, construction grammar, corpus linguistics, conversational analysis, computational linguistics, emergentism, and probabilistic linguistics.

2   For a more complete history see Larsen-Freeman and Cameron, 2008; van Geert, 2003; van Gelder and Port, 1995).

3   Construction grammarians and many others speak of form-meaning connections, but I have long maintained that the pragmatics governing the use of a particular structure is also part of knowing it. With this knowledge, speakers not only know how to form a structure and what it means, they also know when to use it, that is, on what particular occasion a particular form is appropriate.

4   I say, following Bley-Vroman (1983) “usually avoided,” because sometimes, as in the study of instructed SLA, the directionality of the evolution of the interlanguage toward the target language merits consideration, even if the path is not a linear one.

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