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Diane Larsen-Freeman
Introduction
Despite its being a relatively new area of inquiry, the study of English as a lingua franca (ELF) has spurred those of us in the language professions to rethink some fundamental concepts: two of which are the nature of language and the ideology of native-speaker privilege. Offering assistance in rethinking these is Complexity Theory (CT). Complexity Theory itself has only relatively recently been taken up in the physical sciences, but it has since been widely applied to the social sciences as well. It is a metatheory of and for our times. I begin by introducing CT as a metatheory; then, I discuss how the study of ELF supports and is served by viewing language as a complex adaptive system (CAS). I turn next to the inherent challenge to native-speaker privilege in this view. Before concluding, I briefly discuss design features for an ELF research agenda informed by CT.
As with all theories, tenets in CT have antecedents, stretching at least as far back as the Greek philosophers. However, the particular constellation of principles that we have come to know as CT today has emerged from the radically transformed scientific thinking that began in the previous century with the advent of quantum mechanics, the adoption of a non-reductionist approach, and the embrace of systems thinking.
CT is a metatheory in the way that Overton (2007: 154) defines the term:
A metatheory is a coherent set of interlocking principles that both describes and prescribes what is meaningful and meaningless, acceptable and unacceptable, central and peripheral, as theory—the means of conceptual exploration—and as method—the means of observational exploration—the context in which theoretical and methodological concepts are constructed. Theories and methods refer directly to the empirical world, while metatheories refer to the theories and methods themselves.
In other words, with a metatheory there is room for, indeed still the need for, more specialized theories that refer directly to the empirical world. For instance, any attempt to account for second language development would minimally need a theory of language and a theory of learning/development. With CT as the metatheory, a candidate for the former might be characterized as usage-based, where language is continually transformed through use (Beckner et al., 2009), and the latter as emergentism (Ellis and Larsen-Freeman, 2006). The point is that when it comes to ELF, CT provides meta-level guidance, and more focused “object” theories are still needed. As long as the theoretical concepts and principles of the object theories are consonant with those of CT, they would sit comfortably within the scope of CT. I turn next to consider what concepts and tenets are featured in CT as a metatheory.
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Complexity theory
Perhaps the most powerful insight from CT lies in its non-reductionist concept of emergence. In a complex system, novelty emerges out of the interaction of its parts. This position is somewhat different from the meaning of the aphorism that the whole is greater than the sum of its parts. Emergence stresses that something new arises from the interaction of the components of a system. Instead of assuming that every phenomenon can be explained by breaking it down into simpler components, a more holistic perspective is called for. CT defines the problem domain as investigating how patterns continually emerge from components interacting within the changing ecology in which they operate (van Lier, 2000: 246). It is centrally a theory of change, in which the parts of a complex system self-organize—there is no inherent preformationism. As patterns emerge upwards through self-organization, they are downwardly entrained due to both the historic trajectory of the system and the conditions present in the environment (Thompson and Varela, 2001). This cyclical dynamic has been referred to as “reciprocal causality.” The way the science writer, James Gleick, has worded it, “the act of playing the game has a way of changing the rules” (1987: 24).
Notice that emergence is situated within an ecology or context. Many multicomponential systems are “merely” complicated. What makes a system complex is both the interconnectedness of its components and the fact that they are context dependent (Juarrero, 2000: 26). A complex system changes both through internal reorganization and through the system’s adaptation to a changing context. Furthermore, because of the interconnectedness of its components, change in any one part of the system impacts the others. Complex systems also operate at different levels of scale—from micro to macro and levels in between. CT is a relational theory, so researchers do not just focus on one level of a complex system, but rather look for the connections among them (Larsen-Freeman and Tedick, 2016).
Complexity arises from the nonlinear nature of the interactions among the components of a dynamic system. Change does not occur at regular intervals; sometimes it is gradual, other times sudden. While knowing the parameters of a linear system makes it possible to predict its future trajectory (Byrne and Callaghan, 2014), this is not true in a nonlinear system. In such a system, a small change in one parameter can have unanticipated consequences at a later point in time. The result is not proportionate to the cause.
Complex dynamic systems are open: they take in and expend energy, matter, or information, depending on the type of system, all the while they are self-organizing. When systems self-organize, they settle into preferred states, which are called attractors. The potential for future development lies in the variability around the relatively fixed stability of an attractor. A good way to think of an attractor state is to imagine an eddy in a stream (Thelen, 2005). The water droplets that comprise it are always different, constantly flowing through it. However, the whorl remains a more or less continuous emergent pattern or attractor in the flux. Its existence and rate of flow is due to the physical contours of the streambed and the temporal conditions, e.g., the fact that its waters come from the spring melt of the snow that fell the preceding winter. If either of these change, the eddy would disappear or be otherwise transformed.
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As I have written, CT is a metatheory of and for our times. Its influence has extended beyond its point of origin. It offers a systems-based, non-reductionist way of thinking. It seeks patterns in the flux of performance, while maintaining stability through reciprocal causality. It insists on the importance of interconnectedness and of perpetual dynamism within a context. It recognizes the nonlinearity of change. It offers a metalanguage that encodes these notions and connects a variety of phenomena. Indeed, because of its defining characteristics—continuing variation, its situatedness, and its novelty, ELF is one of these phenomena. The study of ELF has contributed to our rethinking the nature of language and thus encouraging a view of language, consonant with CT, that of language as a complex adaptive system (Seidlhofer, 2011; Mauranen, 2012; Hülmbauer, 2013; Baird et al., 2014).
Nature of language: ELF as a CAS
One of the issues in accounting for ELF is to overcome a way of thinking about language that has been inherited from linguistics, i.e., a static, atomistic view. Linguists adopt this view in order to describe language synchronically as an idealized system. While such an approach may yield descriptive adequacy, this pursuit provides no vocabulary or concepts for the discussion of dynamic processes (Larsen-Freeman and Cameron, 2008).
The problem for ELF researchers is that the predominance of this view makes it is easy to commit the fallacy of analyzing and reifying language in use (Herdina and Larsen-Freeman, forthcoming). As Baird et al. (2014: 177) warn,
In facing the challenges that accompany systematic and useful engagement with the roles and proliferation of English, it should be clear that any treatment of language that neglects the dynamic and contextual nature of communication is likely to misrepresent both the data gathered and the explanations for what is observed.
The problem is compounded by experience with language instructional materials, where materials authors have to corral, segment, and sequence an otherwise protean subject (Larsen-Freeman and Freeman, 2008). Presumably, when individuals seek to communicate with others, they do not think in terms of an inventory of constructions. Rather, as speakers communicate with others, they employ all the semiotic resources at their disposal, including nonverbal ones and contextual cues. Of course, communication is not an individual act. Several individuals come together in a languaging episode (Maturana and Varela, 1987), enacting a CAS, and in so doing something new emerges.
Speakers “soft-assemble” (Thelen and Smith, 1994) their language resources in the moment to deal with the exigencies at hand. The patterns are softly assembled, which means that the patterns can be flexibly adapted by speakers, depending on their intentions, their interlocutors, and the context of use. By so doing, the language resources they are using are transformed. Patterns emerge “upwards” in the sense that language-using patterns arise from individuals using the language interactively, co-adapting to one another’s resources. However, there is reciprocal causality, in that the language-using patterns themselves “downwardly” entrain emergent patterns in a given communal language (Larsen-Freeman and Cameron, 2008). Importantly, because most ELF speakers are multilingual, the historical contingency that shapes the way that they use English is affected by the other languages they know. It follows then that ELF speakers who speak English as a third language will be operating from a different base than those for whom it is a first or second language (Jessner et al., 2016). Soft assembly and historical contingency offer a way of conceptualizing both global and universal changes as well as local, variable, and individual performance (Thelen and Bates, 2003).
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A system denotes a set of interconnected parts, which function in coordination together. In both product and process views of language, language operates as a system, not merely a collection of components. In the latter case, it is a dynamic system. It is not necessary for a dynamic system to be invariable, bounded, or without exception (Larsen-Freeman and Cameron, 2008). Indeed, as I have already indicated, a dynamic system is perpetually changing, never ending—in the case of language, emerging from the bottom-up interaction of multiple speakers in communicative exchanges, where both parties’ language resources are affected (Larsen-Freeman, 2011: 49). The mutual influence does not lead to reification. Indeed, language should not be seen
as an entity but instead as a space in which an infinite number of possible trajectories may be realized. None of these trajectories comes into being until language is used in a specific context … Context, in this sense, does not mean just the physical space; it includes the intentional or inter-subjective space between users.
(Larsen-Freeman and Freeman, 2008: 161)
It is important to remember that complex systems are comprised of multiple levels. In the case of ELF, we can point to individual human beings, their contacts zones, and globalized networks—nested levels that are mutually influencing each other. This does not imply that the changed use at an individual level is immediately taken up at all levels, for change takes place at different rates at different levels (MacWhinney, 1999). As with other complex systems, language-using patterns are heterochronous (Lemke, 2000). A language event on some local timescale may simultaneously be part of language change on longer timescales. The point is that both novel patterns and established ones co-exist, which make complex systems at one and the same time both variable and stable. Systems function toward stability while simultaneously changing in response to internal and external phenomena (Clarke et al., 2016).
CT also helps us expect that what emerges from an interaction will be distinctive—not entirely predictable from an analysis of its antecedents.
Similarly, we cannot assume that because the participants we study use English as a lingua franca, this will necessarily lead to the emergence of particular forms of speech (like a preference for zero realization of the [-s] variable). In short, it is simply difficult, if not impossible, to claim with any certainty that a specific language scenario will necessarily generate specific speech forms and lead to the adoption of specific norms of interaction and interpretation.
(Mortensen, 2013: 39)
Thus, the language resources of individual ELF users, i.e., people who use English in contexts where it serves as a lingua franca, may overlap, but will never be identical, not only because of the users’ different language profiles and their use of English to satisfy their unique needs, but also because of their history of interactions with others. Furthermore, each language user has in principle the right to extend the language. In addition, language in use is not only for the purpose of communication but is also a tool that allows speakers to manage their identities and even to resist adopting ongoing changes present in the speech of other members of the community (Labov, 1966), so we see tremendous variation (Steels and Buels, 2017).
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In concert with a CAS view of ELF, Baird et al. (2014) underscore
the importance of viewing language from multiple dimensions in which its contextual embodiment is crucial, and its isolation and compartmentalisation is problematic. This leads Larsen-Freeman and Cameron to state that “language cannot be usefully segregated from its ecology” (2008: 79).
(Baird et al., 2014: 181)
Challenging native-speaker privilege
Language as a CAS has also contributed to challenging the privileging of English native speaker norms. Because language as a CAS is realized in, and affected by, different contexts, there should be no one usage that is universally privileged, independent of purpose and audience. The following excerpt from the front matter of the respected American Heritage Dictionary (pointed out by a member of its usage panel, Anne Curzan, 2016) makes this clear.
The Usage Panel should not be thought of as an academy empowered to rule on all questions of disputed usage. That is an expedient that the English-speaking world has rejected since the 18th century, and in a world where English is established as the language of a heterogeneous international community, the idea that any group or individual might arrogate the authority to fix standards seems not only illiberal but absurd.
(American Heritage Dictionary, 2011: xii)
Along with a rejection of native-speaker privilege is the recognition that what constitutes an “error” is subject to interpretation. Curzan (2016) addresses the polysemy of the term “error,” pointing out that there are three instances of what might be called “an error” in English. One is the use of double negation, which once was common in Old and Middle English, but now only exists in non-standard varieties of English. The second is a deviation from formal standard English, such as the increasingly common use of the subject pronoun they as singular (e.g., I was talking to a friend of mine, and they told me). The third is a construction that no native speaker of English would use. However, going a step further, with regard to this third category, Jenkins (2000: 160) makes the point: “There really is no justification for doggedly persisting in referring to an item as “an error” if the vast majority of the world’s L2 English speakers produce and understand it.”
Interestingly, some child language researchers now describe what might have earlier been termed “an error,” not as an error or mistake, but rather as an innovation (see also Larsen-Freeman, 2016). For instance, Achimova (2008) writes about the “innovations” that children learning English as their native language exhibit. Achimova’s justification is that “[w]e refer to forms like goed as innovations, not mistakes because a child does not yet know the whole system of a language and simply tries to fill in the gaps in the grammatical system creating new forms” (2008: 7). This same logic would seem to apply to other language learners/users, and perhaps even more so to ELF users because ELF is used in a multilingual context (Jenkins, 2015), and thus what appears to be an error from a monolingual English point of view may, in fact, be an innovation from a multilingual point of view.
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The fact of the matter is that, from a CT perspective, ELF users have the capacity to create their own forms with meanings and uses (morphogenesis) and to expand the meaning potential of English (Larsen-Freeman and Cameron, 2008). For instance, Björkman, (Chapter 21, this volume) observes that ELF users often choose the English periphrastic comparative form (e.g., more narrow, more cheap) over the inflected form (narrower, cheaper). However, there are good reasons for this choice. Besides, many native English speakers choose to do the same (Larsen-Freeman and Celce-Murcia, 2015). The history of English is the loss of grammatical inflections (Curzan, 2016). Clearly, the form of comparatives in English is changing in this regard, and perhaps ELF users are in the vanguard in this instance and elsewhere.
To return to the point about innovations and errors, CT offers support for the position that there is no principled basis for distinguishing between an innovation and an error because both are contingent upon the speakers’ perception of, and acting on, the affordances in the context to create meaning, not in their applying a fixed set of rules. In fact, instead of applying rules, there is a tendency for speakers to reuse existing forms as much as possible, even if the forms already have other functions. This exaptation serves a useful purpose.
If a new invention is based on the exaptation of an existing word or construction in a slightly different context, then there is a higher chance that the hearer might guess this new meaning than if a radically new invention is made. Hence the exapted invention has a higher chance to propagate and survive in the communal language.
(Steels and Beuls, 2017: 32)
This process of bricolage works in both directions. Since ELF interactions are multilingual, it is possible not only for inventions to surface in English, but for new forms to be adopted into the contact language. For example, speakers of German now use the expression “Das macht sinn” (That makes sense), which is not endemic to German, but is rather a back translation from English into German (Herdina, personal communication).
Much of the discussion so far has centered on the use of language for meaning-making and communicating. While these are no doubt core functions of language use, challenging native-speaker privilege also extends to using one’s language resources to negotiate one’s identity and to manipulate one’s languages resources to one’s benefit as well, what Kramsch and Whiteside (2008) refer to as “symbolic competence.” Symbolic competence “is defined within a complexity theoretical framework as the ability to position oneself advantageously, to be aware of the historicity of words, to reframe and change the context of the interaction” (Kramsch and Whiteside, 2016). In other words, in keeping with CT as a metatheory, symbolic competence is dynamic, flexible, and locally contingent (Kramsch, 2009).
Implications for methodology
As was mentioned in the introduction, Overton’s definition of a metatheory has implications for what he calls “observational exploration.” Although the study of language development from a Complexity Theoretic perspective is still in its infancy, second language development researchers have sought to identify research methods that are more consistent with CT as a metatheory (Larsen-Freeman, 2015). At the least, it is felicitous if such methods are longitudinal, multiscalar, and localized, and ones that consider individual variability in the developing language resources of second language learners (Verspoor et al., 2011; Dörnyei et al., 2015). To these characteristics, Hiver and Al-Hoorie (2016: 750 ) add,
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CDST [complex dynamic systems theory] is grounded in the phenomenological reality of the social world and calls for approaches that emerge from the needs of inquiry (Morin, 2008), which we believe complements the recent pivot toward a more transdisciplinary, problem-focused orientation to research methodology (King and Mackey, 2016).
It would seem that research methods with these design features are also suitable for researching ELF (Baker, 2015).
Another dimension of methodology that might be attended to, given CT, is to frame investigations in multilingual terms, one where what emerges from ELF interactions is a pluralistic interplay of language resources, resulting from the mutual influence of all relevant languages in the exchange. Another important consideration has to do with the importance of context. CT makes it clear that similar mechanisms may lead to different outcomes as they interact with different features of the context. Central to these contextual features are the understandings, choices, actions, and interactions of the speakers involved (Moss and Haertel, 2016).
One other way that CT may help with the study of ELF is in the former’s encouragement to interrogate dichotomies (Morin, 2007). Such an attitude might help to overcome the tendency to dichotomize native and non-native uses of English. It recognizes that dichotomies can be useful when used heuristically, such as the one between mono- and multi-lingualism, but like all heuristics, they are simplifying moves (Larsen-Freeman, forthcoming). Baird (2012: 10) has written thusly about ELF:
Dichotomising along the lines of “standard” vs. “non-standard,” “ENL/normative” vs. “ELF/expressive” or perhaps worse “creative” vs. “conforming” is to vastly oversimplify the linguacultural landscapes in which language is performed, the backgrounds and roles of the interlocutors, and the contextual identification processes involved in interactions.
Conclusion
Some have argued that theories from the physical sciences are inappropriate to apply to more human concerns; however, linguists are increasingly drawn to CT for the analogical insights it affords,
a linguistic system emerges in the same way as other “emergent phenomena” (the way systems are seen in the science of complexity), through the addition and/or disuse of the strategies that the interactants develop in the here and now of their communicative acts.
(Mufwene et al., 2017: 20)
If one accepts the analogy, there is guidance available in CT as a metatheory and support for it from the study of ELF: the need to acknowledge the dynamicity, nonlinearity, and open-endedness of ELF communication and speakers’ positionings, which lead to the emergence of innovative, and the retention of established, patterns, partly attributable to English and partly traceable to the interplay with the other languages present. The guidance and support include the need to foreground the spatial, temporal, and intersubjective contextualization of ELF speakers’ interactions, attending to speakers’ adaptive moves and the inevitable variability that accompanies the adaptation. While any of these defining characteristics of ELF could be looked at singly, an advantage to adopting CT is that it offers a coherent framework from which to view the whole. A corresponding point is that in order to avoid becoming awash in holism, it is necessary to demarcate a focal system of interest. It must be recognized that in drawing boundaries, certain aspects of a multidimensional process are foregrounded, with the result that other dimensions are backgrounded. Any claims, therefore, must remain modest and provisional (Cilliers, 2001).
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Further reading
Baird, R., Baker, W., and Kitazawa, M. (2014). The complexity of ELF. Journal of English as a Lingua Franca, 3, pp. 171−196.
De Bot, K., Lowie, W., and Verspoor, M. (2007) A dynamic systems theory approach to second language acquisition. Bilingualism: Language and Cognition, 10, pp. 7−21.
Larsen-Freeman, D. (2016). A successful union: Linking ELF with CAS. In L. Lopriore and E. Grazzi (Eds.), Intercultural Communication: New Perspectives from ELF (pp. 15−29). Rome: Roma Tres Press.
Larsen-Freeman, D. (2016). Complexity Theory and ELF: A matter of teleology. In M.-L. Pitzl and R. Osimk-Teasdale (Eds.), English as a lingua franca: Perspectives and prospects. Contributions in honour of Barbara Seidlhofer (pp. 139−146). Berlin: De Gruyter Mouton.
Mufwene S., Coupé, C., and Pellegrino, F. (Eds.). (2017). Complexity in language: Developmental and evolutionary perspectives. Cambridge: Cambridge University Press.
References
Achimova, A. (2008). Verb innovations in spontaneous speech of children. In T. Marinis, A. Papangeli and V. Stojanovik. (Eds.), Proceedings of the child language seminar 2007–30th anniversary (pp. 4−14). Reading: University of Reading.
American heritage dictionary of the English language (2011). 5th ed. Boston, MA: Houghton Mifflin.
Baird, R. (2012). English as a lingua franca: The study of language practices. Englishes in Practice: Working papers of the Centre for Global Englishes, University of Southampton 1, 3–17.
Baird, R., Baker, W., and Kitazawa, M. (2014). The complexity of ELF. Journal of English as a Lingua Franca, 3, pp. 171−196.
Baker, W. (2015). Culture and identity through English as a lingua franca: Rethinking concepts and goals in intercultural communication. Berlin: De Gruyter Mouton.
Beckner, C., Blythe, R., Bybee, B., Christiansen, M.H., Croft, W., Ellis, N.C. Holland, J., Ke, J., Larsen-Freeman, D., and Schonemann, T. (2009). Language is a complex adaptive system: Position paper. Language Learning, Supplement 1, pp. 1–26.
Byrne, D. and Callaghan, G. (2014). Complexity theory and the social sciences: The state of the art. Abingdon: Routledge.
Cilliers, P. (2001). Boundaries, hierarchies, and networks in complex systems. International Journal of Innovation Management, 5, pp. 135–147.
Clarke M., Trujillo, A., Hubbard, R., and Loven-Santos, C. (2016). Balancing mandated innovation and personal/professional development. A paper presented at COTESOL, Denver, November 4.
Curzan, A. (2016). Survey says . . . : Determining what usage is and isn’t acceptable. A plenary addressed delivered at the International TESOL Convention, Baltimore, April 8.
Dörnyei, Z., MacIntyre, P.D., and Henry, A. (Eds.). (2015). Motivational dynamics in language learning. Bristol: Multilingual Matters.
Ellis, N.C. and Larsen-Freeman, D. (Eds.). (2006). Language emergence: Implications for applied linguistics [Special issue]. Applied Linguistics, 27(4).
Gleick, J. (1987). Chaos: Making a new science. New York: Penguin.
Herdina, P. and Larsen-Freeman, D. (forthcoming). Language and complexity.
Hiver, P. and Al-Hoorie, A. (2016). A dynamic ensemble for second language research: Putting complexity theory into practice.Modern Language Journal,100(4), pp. 741–756.
p.59
Hülmbauer, C. (2013). From within and without. The virtual and the plurilingual in ELF. Journal of English as a Lingua Franca 2(1), pp. 47–73.
Jenkins, J. (2000). The phonology of English as an international language. Oxford: Oxford University Press.
Jenkins, J. (2015). Repositioning English and multilingualism in English as a lingua franca. Englishes in Practice 2015, 2, pp. 49–85.
Jessner, U., Allgäuer-Hackl, E., and Hofer, B. (2016). Emerging multilingual awareness in educational contexts: From theory to practice. The Canadian Modern Language Review/La Revue canadienne des langues vivantes, 72, pp. 157–182.
Juarrero, A. (2000). Dynamics in action: Intentional behavior as a complex system. Emergence, 2, pp. 24−57.
Kramsch, C. (2009). The multilingual subject. Oxford: Oxford University Press.
Kramsch, C. and Whiteside, A. (2008). Language ecology in multilingual settings: Towards a theory of symbolic competence. Applied Linguistics, 29, pp. 645−671.
Kramsch, C. and Whiteside, A. (2016). Annotated bibliography on symbolic competence. A presentation at the University of Arizona, February 26.
Labov, W. (1966). The social stratification of English in New York City. Washington, DC: Center for Applied Linguistics.
Larsen-Freeman, D. (2011). A complexity theory approach to second language development/acquisition. In D. Atkinson (Ed.), Alternative approaches to second language acquisition (pp. 48−72). Abingdon: Routledge.
Larsen-Freeman, D. (2015). Ten “lessons” from CDST: What is on offer. In Z. Dörnyei, P. MacIntyre, and A. Henry (Eds.), Motivational dynamics in language learning (pp. 11–19). Bristol: Multilingual Matters.
Larsen-Freeman, D. (2016). Complexity theory and ELF: A matter of teleology. In M.-L. Pitzl and R. Osimk-Teasdale (Eds.), English as a lingua franca: Perspectives and prospects. Contributions in honour of Barbara Seidlhofer (pp. 139−146). Berlin: De Gruyter Mouton.
Larsen-Freeman, D. (forthcoming, 2017). Complexity theory: The lessons continue. In Z.-H. Han and L. Ortega (Eds.), Complexity theory and language development: In celebration of Diane Larsen-Freeman. Amsterdam and Philadelphia, PA: John Benjamins.
Larsen-Freeman, D. and Cameron, L. (2008). Complex systems and applied linguistics. Oxford, Oxford University Press.
Larsen-Freeman, D. and Celce-Murcia, M. (2015). The grammar book: Form, meaning, and use for English language teachers. 3rd ed. Boston, MA: National Geographic Learning/Heinle/Cengage Learning.
Larsen-Freeman, D. and Freeman, D. (2008). Language moves: The place of “foreign” languages in classroom teaching and learning. Review of Research in Education, 32, pp. 147–186.
Larsen-Freeman, D. and Tedick, D. J. (2016). Teaching world languages: Thinking differently. In D. Gitomer and C. Bell (Eds.), Handbook of research on teaching (5th ed.) (pp. 1335−1387). Washington DC: American Educational Research Association.
Lemke, J. (2000). Across the scales of time: artifacts, activities, and meanings in ecosocial systems. Mind, Culture and Activity, 7, pp. 273–290.
MacWhinney, B. (Ed.) (1999). The emergence of language. Mahwah, NJ: Lawrence Erlbaum Associates.
Maturana, H.R. and Varela, F.J. (1987). The tree of knowledge. Boston, MA: New Science Library.
Mauranen, A. (2012). Exploring ELF: Academic English shaped by non-native speakers. Cambridge: Cambridge University Press.
Morin, E. (2007). Restricted complexity, general complexity. In C. Gershenson, D. Aerts, and B. Edmonds (Eds.), Worldviews, science and us: Philosophy and complexity (pp. 5–29). Singapore: World Scientific.
Mortensen, J. (2013). Notes on English used as a lingua franca as an object of study. Journal of English as a Lingua Franca, 2, pp. 25–46.
Moss, P. and Haertel, E. (2016). Engaging methodological pluralism. In D. Gitomer and C. Bell (Eds.), Handbook of research on teaching (5th ed., pp. 127−247). Washington DC: American Educational Research Association.
Mufwene, S., Coupé, C., and Pellegrino, F. (Eds.). (2017). Complexity in language: Developmental and evolutionary perspectives. Cambridge: Cambridge University Press.
p.60
Overton, W. F. (2007). A coherent metatheory for dynamic systems: Relational organicism-contextualism. Human Development, 50, pp. 154–159.
Seidlhofer, B.. (2011). Understanding English as a lingua franca. Oxford: Oxford University Press.
Steels, L. and Beuls, K. (2017). How to explain the origins of complexity in language: A case study for agreement systems. In S. Mufwene, C. Coupé, and F. Pellegrino (Eds.), Complexity in language: Developmental and evolutionary perspectives (pp. 30–47). Cambridge: Cambridge University Press.
Thelen, E. (2005). Dynamic systems theory and the complexity of change. Psychoanalytic Dialogues, 15, pp. 255−283.
Thelen, E. and Bates, E. (2003). Connectionism and dynamic systems: Are they really different? Developmental Science, 6, pp. 378−391.
Thelen, E. and Smith, L. (1994). A dynamic systems approach to the development of cognition and action. Cambridge, MA: The MIT Press.
Thompson, E. and Varela, F.J. (2001). Radical embodiment: Neural dynamics and consciousness. Trends in Cognitive Science, 5, pp. 418−425.
Van Lier, L. (2000). From input to affordance: Social-interactive learning from an ecological perspective. In J.P. Lantolf and S.L. Thorne (Eds.), Sociocultural theory and second language learning (pp. 155−177). Oxford: Oxford University Press.
Verspoor, M., de Bot, K., and Lowie, W. (Eds.) (2011). A dynamic approach to second language development. Methods and techniques. Philadelphia and Amsterdam: John Benjamins.