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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.

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