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https://doi.org/10.1177/02676583241246739
Second Language Research
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DOI: 10.1177/02676583241246739
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second
language
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Complex dynamic systems
theory as a foundation for
process-oriented research on
second language development
Marijn van Dijk
Wander Lowie
University of Groningen, The Netherlands
Nienke Smit
Utrecht University, The Netherlands
Marjolijn Verspoor
University of Pannonia, Veszprem, Hungary; University of Groningen, The Netherlands
Paul van Geert
University of Groningen, The Netherlands
Abstract
In the past decades, complex dynamic systems theory (CDST) has been used as an important
framework for studying second language development. CDST is a metatheory of change and
focuses on processes. Even though it has been broadly accepted as an inspiring dimension of
research in psychology, sociology and second language development, some scholars have raised
questions about the methodologies used, the interpretation of the data, and the nature of its claims.
Specifically, Pallotti questioned whether CDST generates testable hypotheses, and criticized its
position towards reductionism and generalizability, based on philosophical argumentations. The
present article evaluates the issues addressed, reviews the work that has already been done,
and looks ahead at future CDST applications to research in second language development, by
exploring recent methodological developments in the field.
Corresponding author:
Marijn van Dijk, Faculty of Behavioural and Social Sciences, University of Groningen, Grote Kruisstraat 2/1,
Groningen, 9712TS, The Netherlands
Email: m.w.g.van.dijk@rug.nl
1246739SLR0010.1177/02676583241246739Second Language Researchvan Dijk et al.
research-article2024
Discussion and Commentary
2 Second Language Research 00(0)
Keywords
CDST, complexity, dynamic systems theory, processes
I Introduction
Complex dynamic systems theory (CDST) has been recognized as an important
metatheory (e.g. Hulstijn, 2020), applicable to second language development (SLD)
(Han et al., 2023; Larsen-Freeman, 2017). It is predominantly used as an ontological
lens (a perspective on the nature of reality) that enables us to study principles and
mechanisms of change in SLD (Dörnyei, 2017; Hiver and Al-Hoorie, 2016; Larsen-
Freeman, 1997, 2002; Verspoor et al., 2004). As such, CDST has been recognized as a
framework to account for the dynamic process of second language development, pro-
viding substantive contributions to the field (for an overview, see Hiver et al., 2022).
However, critical reflections have also been formulated. In a recent review paper, the
CDST approach has been criticized by Pallotti (2021) based on philosophical argumen-
tations. After reading this discussion, SLD researchers may conclude that CDST is an
‘empty’ theory, in the sense that it only makes unfalsifiable sweeping statements, has a
problematic view on reductionism, and is unwilling ‘to produce generalized claims’
(p. 1). However, such a conclusion would rest on a misunderstanding of what the theory
stands for. Pallotti’s review points to a number of important challenges for CDST
research and has been a welcome contribution to constructive academic dialogue. It also
shows that some fundamental concepts of CDST can easily be misinterpreted. The pre-
sent article aims to clarify the CDST viewpoint and, in doing so, we will address and
evaluate the main points of criticism, which are whether CDST generates falsifiable
predictions or not, how CDST considers reductionism, and whether it aims to generalize
findings from empirical studies. We will also discuss directions for future applications
of CDST for SLD.
It is important to note that before CDST ideas were introduced to the study of second
language acquisition, the framework had been used in the study of human behavior and
development for some time. In the early 1990s, the main concepts were first applied to
the domain of infant motor coordination and action-perception (e.g. Thelen and Ulrich,
1991). Some years later, studies on first language acquisition (e.g. Van Geert, 1991),
cognitive development (Fischer and Bidell, 1998), and socio-emotional development
(e.g. Fogel, 1993; Lewis, 1996) followed. Currently, CDST ideas are used in a wide
range of topics in psychology and related disciplines, such as parent–child interactions
(e.g. Hollenstein and Lewis, 2006), education (e.g. Van Geert and Steenbeek, 2005), and
psychopathology (e.g. Fried and Robinaugh, 2020). The CDST framework has greatly
influenced the praxis of research in developmental psychology and related disciplines.
Consequently, a greater variety of research questions are currently being addressed,
many of them focusing on change processes and short-term interaction dynamics. It has
also led to the development and applications of new analytical tools (such as Ecological
Momentary Assessment, complex multi-level models with repeated measurements,
Recurrence Quantification Analysis, and Retrodictive Modeling) that are now widely
accepted instruments used in process-based studies in the behavioral sciences.
Regarding the application of CDST to the research of second language development,
pioneering work has been done by Larsen-Freeman (1997, 2002), Herdina and Jessner
van Dijk et al. 3
(2002), and De Bot et al. (2007). These authors have contributed to a new perspective with
a series of theoretical, methodological, and empirical studies, acknowledging the nonlin-
ear and dynamic nature of the developmental process. These early studies have inspired
many other studies in the field of SLD research (e.g. Dörnyei, 2017; Hiver and Al-Hoorie,
2016). Most of these were exploratory in nature and aimed at gathering proof-of-principle
of the specific phenomena of investigation (e.g. variability, nonlinearity). They were often
based on data from single or multiple case studies. Han et al. (2023) have noted that at
present, empirical CDST studies cover an array of topics: from listening strategies (Dong,
2016) to teacher–student questions and answers (Smit et al., 2022), and most focus on
quantitative measures of syntactic and lexical complexity in learners’ productive lan-
guage. In addition, the majority of the studies use longitudinal data from a small sample
of learners and are centered around three theoretical issues: the existence of inter-person
variation in second language development, the existence of complex interactions between
different variables, and the existence of intra-person variability. These issues had previ-
ously been acknowledged and addressed under different theoretical frameworks (such as
sociocultural theory and usage-based approaches), but the CDST perspective offered
interpretations that are rooted in a general process theory, also common in physics and
mathematics. This new theoretical framework opened up the possibility of formulating
specific models of developmental dynamics that explained where individual variation
came from, notwithstanding the possibility that the underlying dynamic principles can be
the same across individuals. At present, CDST is often regarded as a separate ‘branch’ of
second language development research, even though many of the core ideas overlap with
other approaches to second language development, such as the sociocognitive approach
(Atkinson, 2002), the ecology of language learning (van Lier, 2010), emergentist (Ellis
and Larsen-Freeman, 2006) and usage-based approaches (e.g. Tyler, 2010), and cultural-
historical/sociocultural approaches (see de Bot et al., 2013).
II The CDST framework
As an overarching framework, CDST aims to explain how an individual moves from an
initial state of being (for instance, using very short simple sentences in the second lan-
guage with non-target forms) to a later state (for instance, using complex target-like idi-
omatical second language). The CDST perspective on SLD conceptualizes an individual’s
multilinguistic system as consisting of many interacting subsystems, emerging in a spe-
cific and dynamic communicative context (Ellis, 2007). The processes involved are not
imposed in the form of a built-in design or explicit external control, but emerge from
dynamic interactions between components of a learner, such as perception, cognition,
memory, attention, and interactions between a learner and their social and material envi-
ronment. This is called self-organization. Note that these interactions do not just state
that ‘everything is related to everything else’. Rather, interactions form specific struc-
tures that can be described and observed. The interactions between the relevant subsys-
tems are assumed to be transactional in nature. This means that during their exchanges,
the components change and shape each other. In the case of second language develop-
ment, this may be mutual interactions between semantics and syntax, or between the
speech of a learner and the speech of a teacher. In this way, a second (third, fourth, etc.)
language emerges from a process of self-organization. Over time, many systems move
4 Second Language Research 00(0)
towards self-reproductive and self-maintaining states. These are called ‘attractors’ (or
‘attractor states’) and can have different kinds of properties. For instance, a second lan-
guage learner may develop towards a single final attractor state of more or less stable L2
proficiency (high or low, dependent on the individual), or move towards a final attractor
state via intermediary attractors that are temporarily stable. Similar to most other types
of natural development, changes that occur during this transactional process are often
nonlinear (see, for example, Murakami, 2016). This means that the magnitude of an
effect is not proportional to the magnitude of its causal factor. In a process such as second
language development, this nonlinearity arises from the fact that the effect of causal fac-
tors (internal as well as external, e.g. in learner-directed speech) co-depends on the cur-
rent state of the system. For this reason, a process can reveal sudden rapid changes,
regressions, phase shifts and discontinuities. Change trajectories have both quantitative
and qualitative properties. The qualitative properties refer to the emergence of something
new or different (e.g. the use of a specific grammatical constructions in a second lan-
guage), whereas the quantitative properties refer to more or less of something (e.g. longer
sentences or a higher frequency of certain constructions). One of the assumptions of
CDST is that the qualitative properties can be meaningfully quantified and that quantita-
tive changes over time describe the development of a certain language capacity.
The insight that second language development has complex interactions and exhibits
large interindividual and intraindividual variation was not new when CDST thinking was
introduced to SLD research. No one has argued that all individuals are identical, that
variables have no or only simple interactions, and that performance is stable over time.
However, CDST provided a general theoretical model encompassing all these phenom-
ena, from which guided exploratory studies could be conducted, for instance with regard
to the structure of variability over time. It also introduced the possibility for mathemati-
cal modeling of processes, and specific statistical applications and research methodolo-
gies (such as the fitting of the aforementioned models and describing patterns of
intraindividual variability) for studying these processes.
In the field of second language learning many studies are based on general linear
models, true score theory and other models that include the notion of measurement error.
For the sake of obtaining results that might be generalized to the population of second
language learners, most studies are based on variables measured at one or two moments
in time and work with group and individual averages. Often, components of a model are
assumed to be additive (which means that the effects of different independent variables
can be added on top of each other in terms of explained variance), and time-dependent
interactions are not analysed. Intra- and inter-individual variability are often treated as
external, random, symmetrically distributed variation added to underlying general devel-
opmental trends (for examples of these approaches, see, for example, Bosch et al., 2020;
Hooper et al., 2011; Xie and Yeung, 2022). Group averages can be meaningful for
answering many types of research questions, such as whether certain groups of second
learners have an advantage over other groups of learners at one point in time. However,
when trying to understand the process of second language development, group averages
are not meaningful, due to the non-ergodic nature of the data (Molenaar and Campbell,
2009). It is therefore broadly recognized that other types of research (based on repeated
measurements and individual trajectories) are needed to capture individual processes of
van Dijk et al. 5
change. The types of analyses are complementary for the study of SLD. For example, if
we know from group studies that the most advanced L2 writers use both more complex
syntactic constructions and more advanced vocabulary, it would be interesting to track in
detail the more advanced process of development. Only dense, longitudinal data of indi-
viduals can offer that kind of information.
As said, CDST is a metatheory, which implies that some of its assumptions cannot be
falsified directly, nor do they need to be. It is not a ‘local’ theory as an explanation of
specific observations or a solution to a problem. What we call ‘CDST’ is actually a col-
lection of theoretical perspectives (such as the theory of coordination dynamics, syner-
getics, chaos theory, bifurcation theory, dynamic network theory), that have in common
that they deal with complex systems. Such time-dependent systems of interacting com-
ponents have various properties (self-organization, emergence, etc.) that can be described
and modeled. Many of these perspectives have a firm mathematical basis and thus pro-
vide mathematical evidence for conditional statements: if a process fulfills condition X,
then it will have consequence Y. An example of how a mathematical model predicts a set
of observable phenomena is catastrophe theory (Thom, 1975). Here, the mathematical
model of the cusp catastrophe (which describes a discontinuity between states), predicts
a series of phenomena, such as critically slowing down and anomalous variance.
Critically slowing down refers to a situation in which it takes a long time for a system to
return to a previous equilibrium, whereas anomalous variance describes a situation in
which fluctuations become chaotic. The presence of these phenomena can be tested
empirically, for instance in data of language development (a typical example of this
approach is provided by Ruhland and van Geert, 1998). Thus, the ultimate foundation of
CDST lies in the power of a particular, formal description of reality from which specific
predictions (such as self-organization, emergence, attractors, etc.) follow. CDST thus
serves as a metatheory in that it provides a framework for guided exploration (explora-
tory studies) and the development of ever new theories, e.g. on empirical phenomena
such as second language development. This approach entails much more than the
approach Pallotti cites from Hiver and Al-Hoorie (2020) ‘data are checked against theo-
retical notions and the theory will be strengthened by data supporting it’ (pp. 155). This
exploratory work based on CDST does not consist of ‘wild’, ‘unmotivated’ descriptions,
but instead is embedded in and restricted by the general CDST framework (as described
above). This means that hypothesis formulation is not something preceding empirical
work in a top-down fashion, but as something following exploratory work (data gather-
ing and data analysis). In Karl Popper’s critical rationalism, top-down rationalism and
bottom-up empiricism are related in a cyclical manner. The order Pallotti refers to in this
regard is that theory leads to hypothesis formation, which can be tested empirically. We
argue that the sequence actually consists of four steps: (1) top-down metatheory, (2)
bottom-up guided explorations, (3) top-down theory/hypothesis formation, (4) bottom-
up empirical testing (with eventually a fifth step of adaptation or rejection of the theory,
etc.). Though the predictions in the first step should not be seen as falsifiable hypotheses
(they are assumptions based on the general framework), testing the hypotheses in the
third step is badly needed. We agree with Pallotti that these hypotheses should be formu-
lated with precise definitions and operationalizations. Most of the early CDST inspired
studies (such as Verspoor et al. (2008)) can be subsumed under the second step in the
6 Second Language Research 00(0)
sequence: they are guided explorations of phenomena such as non-linearity, intra-indi-
vidual variability and interactions. As in any good empirical theory, these explorations
must lead to testable hypotheses and should be empirically tested (in the third step and
fourth of the sequence). In the case of CDST research, these hypotheses may concern the
existence of sudden jumps, peaks in variability, specific recurrence patterns, and self-
similarity in second language development. Such hypotheses are testable in empirical
studies with sufficiently dense developmental data (in step 4), for instance by fitting a
mathematical model of coupled equations (e.g. Caspi and Lowie, 2013) or investigating
time-dependent patterns (e.g. Baba and Nitta, 2014). It should also be noted that some of
the hypotheses that may be formulated in the third step of the sequence also owe their
plausibility to their descriptive, predictive and explanatory success in other fields such as
physics, biology and psychology. The final legitimation of the theoretical and empirical
success of CDST has to be based on various criteria, such as theoretical consistency,
theoretical generality, successful prediction or retrodiction, exploration of unexpected
predictions, and bringing together existing phenomena under a single common theoreti-
cal framework.
III Reductionism and generalizability
One of the main points of criticism of Pallotti (2021) is directed at the CDST position
on reductionism. Though some of the pioneering authors in the application of CDST to
SLD may have made bold statements against reductionism and simplistic views of
reality (see, for example, Hiver and Al-Hoorie, 2016; Larsen-Freeman, 2017; Larsen-
Freeman and Cameron, 2008), we stress that CDST does not object to reductionism.
We agree with Pallotti that reductionism is necessary. First, all scientific models are
reductions, i.e. simplifications, of complex phenomena, and virtually nobody would
argue that science needs the complexity of reality to explain the complexity of reality.
The main point is whether the simplification provided in a particular model suffi-
ciently captures the important phenomena of interest, whilst doing justice to the com-
plex reality of interacting and changing factors, without losing essential and
characteristic features and replacing them by seemingly simple features such as linear-
ity, population averages and additivity of influences. It is this type of reductionism that
CDST warns against. Relatively simple models can indeed be very powerful in explain-
ing underlying mechanisms (e.g. Caspi, 2010; Van Dijk et al., 2013; Van Geert, 1991,
1998, 2003, 2023). However, the focus should also be on change processes and their
important characteristics.
CDST theorists are constantly reducing complex phenomena of interacting and
changing factors to simple models. This is done for instance in the study of relational
aspects of various behavioral and social phenomena including language development but
also in the emergence of excellent performance (Den Hartigh et al., 2016; Van Geert,
1991, 2023). A crucial common feature of these simple models is that they contain meas-
ures, albeit reductionist, that contain interaction and change. Adopting measures that
reflect interactional factors, these simple models improve our understanding of phenom-
ena typical of complex systems, such as changing patterns of variability, sensitivity to
initial conditions, nonlinear changes etc. In models of language development, simple,
van Dijk et al. 7
coupled logistic equations are ways of reducing the almost infinitely complex stream of
linguistic production and exchange to very basic dynamic principles, explaining typical
nonlinear phenomena of first language development (Van Dijk et al., 2013; Van Geert,
1991). In a recent publication, Van Geert (2023) proposes a model of second language
development in the form of a simulation model. This model generates important qualita-
tive features that are often observed in empirical data of second language development.
First, second language learning varies from linear to discontinuous, from regular to cha-
otic, and from optimal to suboptimal, which can be simulated with the same model,
depending on the parameter values in the model. This demonstrates that a relatively
simple model is able to predict differences between individuals. Second, the model gen-
erates intra-individual variability that changes over time. This shows that simple models
– strongly reduced versions of reality – are well able to describe complex processes.
This leads us to the issue of generalizability. According to Pallotti (2021), CDST
researchers ‘chronicle’ how different aspects of SLD evolve and interact over time, but
are unwilling to go beyond such descriptions. He argues that there seems to be resistance
against trying to explain and predict the phenomena at hand in order to produce general-
ized knowledge. This criticism is supported with several citations, such as one by De Bot
and Larsen-Freeman (2011) where they argue ‘Instead of generalizable predictions, then,
we are content to point to tendencies, patterns, and contingencies’ (p. 23), and from De
Bot (2011) who argues for ‘a soft approach towards falsification, in which single cases
are not assumed to refute a theory completely, since there will be individual variation that
comes into play’ (De Bot, 2011: 126). Although individual case studies form the founda-
tion of observations and theory formation about change over time, this does not mean
CDST-inspired research cannot inform us about general principles and mechanisms of
the language developmental process beyond the individual case.
At this point, the notion of generalizability needs to be clarified. In many cases of
SLD research, generalizability relates only to the extent to which a statistic obtained for
a particular sample of cases or observations (e.g. an average, a standard deviation) is also
true of an encompassing or overarching set of observations, like the categorical contrast
between monolinguals and bilinguals (e.g. Bialystok and Viswanathan, 2009). The most
extreme case of a generalizability issue is the question to what extent an individual case
provides information that is true of the population (usually defined by some – socially
constructed – category, e.g. ‘man’, ‘women’, ‘child’, ‘learner of the Chinese language’,
etc.) from which this individual is a member. The behavioral sciences suggest that mod-
els based on inter-individual variability in a population are ‘general’ and that individual
processes are specific cases of the general model. However, if we want to understand
change processes, we need many repeated measurements of the same individuals over
time and investigate changes that occur. Once many of such detailed process descriptions
are available, researchers can begin to study the extent to which individual process prop-
erties occur across a wider population. This type of generalization is similar to what is
common in qualitative research, where the focus is on understanding the nuances and
patterns of social behavior.
For a CDST researcher, the pattern of generalization of findings runs as follows: start-
ing from a hypothesis regarding specific features of the underlying dynamics of certain
linguistic variables (as in step 3 of the sequence described in paragraph 1.), this
8 Second Language Research 00(0)
hypothesis is first tested against the data of concrete, i.e. individual processes (as in step
4 of the sequence). The first test of the hypothesis can occur with a small number of cases
(or even a single case). This provides some first, nontrivial support for it, which must be
the beginning of a further empirical validation process with more individual cases, rep-
resenting the process of interest. Only after many individual cases have been made avail-
able, first attempts at producing general knowledge are possible. This ‘general’ knowledge
however does not mean that there is one model – or one solution – that fits all individuals
in a population. It may also mean that there are different models or different solutions for
different (groups of) individuals. Just as in the replication of mean scores, the use of
multiple case studies leads to a cumulative ‘substantiation’ of observations (Al-Hoorie
et al., 2023). For a CDST researcher, population generalizability (in the meaning of ‘to
what extent is the information obtained from a particular sample, beginning with one
person or one case, true of the population to which the particular case belongs’) is just
another generalization question, which can be answered incrementally, by increasing the
number of individual cases with which a particular dynamic model is tested (Van Geert
and De Ruiter, 2022).
To summarize, CDST generates testable hypotheses, reduces reality and makes gen-
eralizations. CDST aims to discover dynamic mechanisms and phenomena of change
processes that emerge over time. To do so, reality has to be reduced to essential aspects
that do justice to the complexity of interacting and changing factors that can only be
observed at the individual level. Such findings at the individual level can then be gener-
alized in a population of learners by testing specific hypotheses to substantiate a dynamic
model (Al-Hoorie et al., 2023).
IV Leading questions for a CDST research program
In CDST research, much work on SLD has already been conducted (Hiver et al., 2022).
The way forward can be found in the continuation of ambitious and multiple case studies
with dense data to come to an understanding of the process of development and in testing
hypotheses that are derived from the earlier explorations. The focus of these studies
should remain on the level of the individual learners. Similarities among (groups of)
individuals and consistently occurring patterns might in turn contribute to generalizable
conclusions about the process of second language development. In addition, new and
innovative methodologies may go beyond individual cases, while acknowledging the
complex dynamic and nonlinear development of SLD.
Future directions of CDST research in the field of SLD should be aimed at testing
specific hypotheses about the process of change, as the overwhelming majority of CDST
studies (82%) is still exploratory and not falsificatory in nature (Hiver et al., 2022). We
will sketch some of the most important lines of research below that would deserve to be
pursued; these are studies aimed at:
investigating the randomness (or patternedness) of intra-individual variability.
testing whether certain patterns of intra-individual variability are associated with
more (or less) optimal long-term outcomes.
describing developmental trends and language emergence.
van Dijk et al. 9
testing temporal relations between different language variables (or between
speakers).
developing and applying new methodological tools.
1 Studies aimed at investigating the randomness (or patternedness) of
intra-individual variability
Variability is one of the well-acknowledged characteristics of complex dynamic systems
and has been documented as the manifestation of the interaction of multiple subsystems.
Future studies can be directed by conducting thorough analysis of the patterns of varia-
bility that occur in second language development. It can be empirically tested whether
these patterns are different from a random pattern and, if so, how the temporal structure
of the data can be described. Techniques such as spectral and fractal analysis might be
used to quantify the degree in which a pattern resembles pink noise, which is considered
to reflect an optimal combination between stability and flexibility (Van Orden et al.,
2011). For instance, Plat et al. (2018) demonstrated that L1 word naming showed a more
optimal variability pattern than L2 word naming, indicating a differential degree of
automatized and controlled processing in L1 and L2. Another way of quantifying the
temporal structure of the variability is by means of (Cross) Recurrence Quantification
Analysis (Marwan et al., 2007). Cox and Van Dijk (2013), for instance, analysed how the
moment-to-moment variability of the language of a young child was related to moment-
to-moment variability of the child-directed speech of the parent. The results showed that
these patterns were significantly different from a random pattern, and were ‘coupled’ to
one another. Moreover, this degree of coupling became looser in the course of a year,
indicating an increased flexibility in the parent–child dialogue. The hypothesis that the
‘coupling’ between learner and teacher becomes less rigid over time is also relevant for
the study of second language development and would provide understanding of how the
language of a language learner is connected with the language input.
2 Studies aimed at testing whether certain patterns of intra-individual
variability are associated with more (or less) optimal long-term outcomes
Another future direction of research might focus on investigating whether certain types
of variability are associated with other process characteristics and developmental out-
comes. Variability is seen as a precursor of (or even a necessity for) change (Bassano and
Van Geert, 2007; Thelen and Smith, 1994; Van Geert, 1994, 2004). In addition, it has
been hypothesized that certain types of variability are more optimal than others. Within
the field of SLD research, several (multiple) case studies on the topic have described
such patterns (e.g. Baba and Nitta, 2014; Chang and Zhang, 2021; Gui et al., 2021;
Larsen-Freeman, 2006; Lesonen et al., 2017; Lowie et al., 2017; Penris and Verspoor,
2017; Pfenninger and Kliesch, 2023; Spoelman and Verspoor, 2010; Verspoor and de
Bot, 2022; Verspoor et al., 2008). However, the hypothesis that (non)optimal variability
predicts (long term) learning outcomes can be tested with greater rigor, for instance by
means of cluster analysis, or other types of multivariate analysis.
10 Second Language Research 00(0)
3 Studies aimed at describing developmental trends and language
emergence
Several CDST studies (e.g. Lowie and Verspoor, 2019; Lowie et al., 2017) in SLD
have aimed at illustrating that language learning is not always linear and that indi-
vidual trajectories of change may be quite different from average trajectories. Other
testable hypotheses from CDST concern the special features of the quantitative prop-
erties of second language use, such as sudden jumps, specific recurrence patterns,
and self-similarity (e.g. Lowie et al., 2014). Such studies should go beyond the pur-
pose of exploration, and focus on describing how certain linguistic variables are
acquired in terms of their shapes of change. A relevant hypothesis is that a certain
shape of change (for instance, a jump-wise development) is related to more optimal
long-term learning outcomes. This hypothesis can be tested, for instance through
change point analysis (see, for example, Baba and Nitta, 2014). Previous studies
covered dimensions such as motivation (Dörnyei et al., 2014; Elahi Shirvan and
Teherian, 2023; Papi and Hiver, 2020), or speaking and writing skills, operational-
ized as complexity, accuracy and fluency (CAF) measures (see Chan et al., 2015) or
by holistic ratings. However, many dimensions of SLD and the way in which they
interact remain underexplored.
4 Studies aimed at testing temporal relations between different language
variables (or between speakers)
The study of the dynamical relations between different (developing) variables has been
the focus in several CAF-inspired studies (e.g. Penris and Verspoor, 2017; Spoelman
and Verspoor, 2010). For instance, one testable hypothesis is that the interactions
between specific variables (development in lexical complexity, lexical accuracy, syn-
tactic complexity, and syntactic accuracy) can be modeled in empirical data of SLD. In
such a model, each individual has their own path of development, but the underlying
mechanisms are similar (see, for example, Caspi, 2010; Van Dijk et al., 2013). This
means that one growth model with the same underlying dynamics can be fitted with data
of multiple individuals that may – on the surface – look very different from each other.
However, new and exciting methodologies have emerged in adjacent fields, such as
psychology, in recent years. For instance, dynamic network models have been proposed
to understand how depressive symptoms are interrelated and how a network can show
properties of ‘getting stuck’ in a specific state (Wichers et al., 2021). In a similar vein,
dynamic network models may be used to understand how different linguistic variables
are interdependent and how the structure of the network of second language develop-
ment as a whole can be described (Freeborn et al., 2023). In earlier studies, coupled
(logistic) equation models have been successfully used to model the dynamic relation
between different levels of vocabulary development (Caspi and Lowie, 2013; Van
Geert, 2023). Such models can be tested against empirical data and describe the extent
to which specific cases (individual processes or samples of individual processes) can be
subsumed under a similar general model, in which individual cases are represented by
specific individual parameter values.
van Dijk et al. 11
5 Studies aimed at developing and applying new methodological tools
Finally, the challenge of testing CDST-inspired hypotheses is methodological in nature. Not
only is it quite difficult to collect large data sets with many participants and lots of repeated
measurements, but more importantly there is clear lack of analytical tools to capture both
intra-individual change and interindividual differences. New nonlinear group analyses are
promising, like the use of generalized additive modeling (GAM) (Kliesch and Pfenninger,
2021; Verspoor et al., 2021), to generalize beyond the individual. In GAMs the nonlinear
trend is analysed, while taking into account the individual variability over time. For the
modeling of multiple case studies, several promising suggestions have been made by Hiver
and Al-Hoorie (2020). Also, new techniques have recently been used in data analyses, like
Latent Growth Curve Modeling (Elahi Shirvan and Teherian, 2023), Parallel-Process
Growth Mixture Modeling (Yu et al., 2022) and Retrodictive Qualitative modeling.
V Conclusions
Based on philosophical argumentations, Pallotti has pointed to a number of important
challenges to CDST research concerning testable hypotheses, reductionism and general-
izability, and has identified instances of rather unfocused explorations. Although open
exploration forms a necessary step in the development, CDST research has grown well
beyond that point. The present article has argued that a CDST approach to investigating
the actual processes of development, testable hypotheses must start at the individual
level (trajectories of individual learners, individual dyads, individual classrooms, i.e.
specific cases in which a time series of behavior can be observed). Findings might then
be generalized if similar patterns are found in other individuals. There is also no doubt
that in analysing data, reductionism is needed to trace variables over time, but within
CDST theory, the focus is on how these variables interact and develop. CDST research
now needs more focused research centered around answering process-based research
questions, guided by testing of informed hypotheses about change, development and
nonlinear network relations. With this article we hope to have contributed to a better
understanding of the position of CDST in SLD research. We also hope to have inspired
researchers to continue the development of new methodologies to warrant a sustainable
future for research based on CDST ideas.
Acknowledgements
We would like to thank Jan Hulstijn and one anonymous reviewer for their constructive feedback
to our manuscript.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/
or publication of this article.
Funding
The authors received no financial support for the research, authorship, and/or publication of this
article.
12 Second Language Research 00(0)
ORCID iDs
Marijn van Dijk https://orcid.org/0000-0002-2823-1455
Nienke Smit https://orcid.org/0000-0002-2672-9794
References
Al-Hoorie AH, Hiver P, Larsen-Freeman D and Lowie W (2023) From replication to substantia-
tion: A complexity theory perspective, Language Teaching 56(2): 276–291.
Atkinson D (2002) Toward a sociocognitive approach to second Language acquisition. The
Modern Language Journal 86: 525–45.
Baba K and Nitta R (2014) Phase transitions in development of writing fluency from a complex
dynamic systems perspective. Language Learning 64: 1–35.
Bassano D and van Geert P (2007) Modeling continuity and discontinuity in utterance length: A
quantitative approach to changes, transitions and intra-individual variability in early gram-
matical development. Developmental Science 10: 588–612.
Bialystok E and Viswanathan M (2009) Components of executive control with advantages for
bilingual children in two cultures. Cognition 112: 494–500.
Bosch LJ, Segers E, and Verhoeven L (2020) First and second language vocabulary affect early
second language reading comprehension development. Journal of Research in Reading 43:
290–308.
Caspi T (2010) The dynamics of L2 vocabulary development: A case study of receptive and pro-
ductive knowledge. Revista Brasiliera de Linguistica 13: 437–62.
Caspi T and Lowie W (2013) The dynamics of L2 vocabulary development: A case study of recep-
tive and productive knowledge. Revista Brasileira de Linguística Aplicada 13: 437–62.
Chan H, Verspoor M, and Vahtrick L (2015) Dynamic development in speaking versus writing in
identical twins. Language Learning 65: 298–325.
Chang P and Zhang LJ (2021) A CDST perspective on variability in foreign language learners’
listening development. Frontiers in Psychology 12: 601962.
Cox RFA and van Dijk M (2013) Microdevelopment in parent–child conversations: From global
changes to flexibility. Ecological Psychology 25: 304–15.
De Bot K (2011) Epilogue. In: Verspoor M, De Bot K, and Lowie W (eds) A dynamic approach
to second language development: Methods and techniques. Amsterdam: John Benjamins, pp.
123–28.
De Bot K and Larsen-Freeman D (2011) Researching second language development from
a dynamic systems theory perspective. In: Verspoor M, De Bot K, and Lowie W (eds) A
dynamic approach to second language development: Methods and techniques. Amsterdam:
John Benjamins, pp. 5–24.
de Bot K, Lowie W, Thorne SL, and Verspoor M (2013) Dynamic systems theory as a theory
of second language development. In: Mayo M, Gutierrez-Mangado M, and Adrián M (eds)
Contemporary approaches to second language acquisition. Amsterdam: John Benjamins, pp.
199–220.
De Bot K, Lowie W, and Verspoor M (2007) A dynamic systems theory approach to second lan-
guage acquisition. Bilingualism: Language and Cognition 10: 7–21.
Den Hartigh RJR, Van Dijk MWG, Steenbeek HW, and van, and Geert PLC (2016) A dynamic
network model to explain the development of excellent human performance. Frontiers in
Psychology 7: 532.
Dong J (2016) A dynamic systems theory approach to development of listening strategy use and
listening performance. System 63: 149–65.
van Dijk et al. 13
Dörnyei Z (2017) Conceptualizing learner characteristics in a complex, dynamic world. In: Ortega
L and Han Z (eds) Complexity theory and language development: In celebration of Diane
Larsen-Freeman. Amsterdam: John Benjamins, pp. 79–96.
Dörnyei Z, Macintyre PD, and Henry A (2014) Motivational dynamics in language learning.
Bristol: Multilingual Matters.
Elahi Shirvan M and Teherian T (2023) Affordances of the microsystem of the classroom for for-
eign language enjoyment. Human Arenas 5: 222–44.
Ellis N (2007) Dynamic systems and SLA: The wood and the trees. Bilingualism: Language and
Cognition 10: 23–25.
Ellis N and Larsen-Freeman D (2006) Language emergence: Implications for applied linguistics.
Applied Linguistics 27: 558–89.
Fischer KW and Bidell TR (1998) Dynamic development of psychological structures in action
and thought. In: Damon W and Lerner RM (eds) Handbook of child psychology: Theoretical
models of human development. Hoboken, NJ: John Wiley and Sons, pp. 467–561.
Fogel A (1993) Developing through relationships; Origin of communication, self and culture.
Chicago, IL: The University of Chicago Press.
Freeborn L, Andringa S, Lunansky G, and Rispens J (2023) Network analysis for modeling com-
plex systems in SLA research. Studies in Second Language Acquisition 45: 526–57.
Fried EI and Robinaugh DJ (2020) Systems all the way down: Embracing complexity in mental
health research. BMC Medicine 18: 205.
Gui M, Chen X and Verspoor M (2021) The dynamics of reading development in L2 English for
academic purposes. System 100: 102546.
Han Z, Kang EY, and Sok S (2023) The complexity epistemology and ontology in second lan-
guage acquisition: A critical review. Studies in Second Language Acquisition 45: 1388–412.
Herdina P and Jessner U (2002) A dynamic model of multilingualism: Perspectives of change in
psycholinguistics. Bristol: Multilingual Matters.
Hiver P and Al-Hoorie A (2016) A dynamic ensemble for second language research: Putting com-
plexity theory into practice. The Modern Language Journal 100: 741–56.
Hiver P and Al-Hoorie AH (2020) Research methods for complexity theory in applied linguistics.
Bristol: Multilingual Matters.
Hiver P, Al-Hoorie AH, and Evans R (2022) Complex dynamic systems theory in language learning:
A scoping review of 25 years of research. Studies in Second Language Acquisition 44: 913–41.
Hollenstein T and Lewis MD (2006) A state space analysis of emotion and flexibility in parent–
child interactions. Emotion 6: 656–62.
Hooper SR, Costa LJ, McBee M, et al. (2011) Concurrent and longitudinal neuropsychological
contributors to written language expression in first and second grade students. Reading and
Writing: An Interdisciplinary Journal 24: 221–52.
Hulstijn J (2020) Proximate and ultimate explanations of individual differences in language use
and language acquisition. Dutch Journal of Applied Linguistics 9: 21–37.
Kliesch M and Pfenninger SE (2021) Cognitive and socio-affective predictors of L2 micro-devel-
opment in late adulthood: A longitudinal intervention study. Modern Language Journal 105:
237–66.
Larsen-Freeman D (1997) Chaos/complexity science and second language acquisition. Applied
Linguistics 18: 148–65.
Larsen-Freeman D (2002) Language acquisition and language use form a chaos/complexity the-
ory perspective. In: Kramsch C (ed.) Language Acquisition and Language Socialization:
Ecological perspectives. London: Continuum, pp. 33–46.
Larsen-Freeman D (2006) The emergence of complexity, fluency, and accuracy in the oral and
written production of five Chinese learners of English. Applied Linguistics 27: 590–619.
14 Second Language Research 00(0)
Larsen-Freeman D (2017) Complexity theory: The lessons continue. In: Ortega L and Han Z (eds)
Complexity theory and language development: In celebration of Diane Larsen-Freeman.
Amsterdam: John Benjamins, pp. 11–50.
Larsen-Freeman D and Cameron L (2008) Complex Systems and Applied Linguistics. Oxford:
Oxford University Press.
Lesonen S, Suni M, Steinkrauss R, and Verspoor M (2017) From conceptualization to construc-
tions in Finnish as an L2. Pragmatics and Cognition 24: 212–62.
Lewis MD (1996) Self-organizing cognitive appraisals. Cognition and Emotion 10: 1–25.
Lowie W, Plat R, and de Bot K (2014) Pink noise in language production: A nonlinear approach
to the multilingual lexicon. Ecological Psychology 26: 216–28.
Lowie W, van Dijk M, Chan H, and Verspoor M (2017) Finding the key to successful L2 learning
in groups and individuals. Studies in Second Language Learning and Teaching 7: 127–48.
Lowie WM and Verspoor MH (2019) Individual differences and the ergodicity problem. Language
Learning 69: 184–206.
Marwan N, Romano MC, Thiel M, and Kurths J (2007) Recurrence plots for the analysis of com-
plex systems. Physics Reports 438: 237–329.
Molenaar PC and Campbell CG (2009) The new person-specific paradigm in psychology. Current
Directions in Psychological Science 18: 112–17.
Murakami A (2016) Modeling systematicity and individuality in nonlinear second language devel-
opment: The case of English grammatical morphemes. Language Learning 66: 834–71.
Pallotti G (2021) Cratylus’ silence: On the philosophy and methodology of Complex Dynamic
Systems Theory in SLA. Second Language Research 38: 689–701.
Papi M and Hiver P (2020) Language learning motivation as a complex dynamic system: A global
perspective of truth, control, and value. The Modern Language Journal 104: 209–32.
Penris W and Verspoor M (2017) Academic writing development: A complex, dynamic process.
In: Pfenniger S and Navracsics J (eds) Future research directions for applied linguistics/sec-
ond language acquisition: Volume 109. Bristol: Multilingual Matters, pp. 215–42.
Pfenninger SE and Kliesch M (2023) Variability as a functional marker of second language devel-
opment in older adult learners. Studies in Second Language Acquisition 45: 1004–30.
Plat R, Lowie W, and de Bot K (2018) Word naming in the L1 and L2: A dynamic perspective on
automatization and the degree of semantic involvement in naming. Frontiers in Psychology
8: 2256.
Ruhland R and van Geert P (1998) Jumping into syntax: Transitions in the development of closed
class words. British Journal of Developmental Psychology 16(Pt 1): 65–95.
Smit N, van Dijk M, de Bot C, and Lowie W (2022) The complex dynamics of adaptive teach-
ing: Observing teacher–student interaction in the language classroom. IRAL – International
Review of Applied Linguistics in Language Teaching 60: 23–40.
Spoelman M and Verspoor M (2010) Dynamic patterns in the development of accuracy and
complexity: A longitudinal case study on the acquisition of Finnish. Applied Linguistics 31:
532–53.
Thelen E and Smith LB (1994) A Dynamic Systems Approach to the Development of Cognition
and Action. Cambrigde, MA: The MIT Press.
Thelen E and Ulrich BD (1991) Hidden skills: A dynamic systems analysis of treadmill stepping
during the first year. Monographs of the Society for Research in Child Development 56:
1–104.
Thom R (1975) Structural Stability and Morphogenesis. New York: Benjamin-Addison-Wesley.
Tyler A (2010) Usage-based approaches to language and their applications to second language
learning. Annual Review of Applied Linguistics 30: 270–91.
van Dijk et al. 15
Van Dijk M, van Geert P, Korecky KK, et al. (2013) Dynamic adaptation in child–adult language
interaction. Language Learning 63: 243–70.
Van Geert P (1991) A dynamic systems model of cognitive and language growth. Psychological
Review 98: 3–53.
Van Geert P (1994) Dynamic systems of development: Change between complexity and chaos.
London: Harvester Wheatsheaf.
Van Geert P (1998) A dynamic systems model of basic developmental mechanisms: Piaget,
Vygotsky, and beyond. Psychological Review 105: 634–77.
Van Geert P (2003) Dynamic systems approaches and modeling of developmental processes. In:
Valsener J and Connolly KJ (eds) Handbook of developmental psychology. London: Sage,
pp. 640–72.
Van Geert P (2004) Dynamic modelling of cognitive development: Time, situatedness and variabil-
ity. In: Demetriou A, Raftopoulos A, Demetriou A, and Raftopoulos A (eds) Cognitive devel-
opmental change: Theories, models and measurement. Cambridge: Cambridge University
Press, pp. 354–78.
Van Geert P and De Ruiter N (2022) Toward a process approach in psychology: Stepping into
Helaclitus’ River. Cambridge: Cambridge University Press.
Van Geert P and Steenbeek HW (2005) The dynamics of scaffolding. New Ideas in Psychology
23: 115–28.
Van Geert PLC (2023) Some thoughts on dynamic systems modeling of L2 learning. Frontiers in
Physics 11: 408.
Van Lier L (2010) The ecology of language learning: Practice to theory, theory to practice.
Procedia – Social and Behavioral Sciences 3: 2–6.
Van Orden GC, Kloos H, and Wallot S (2011) Living in the pink: Intentionality, wellbeing, and
complexity. In: Hooker C (ed.) Philosophy of complex systems: Handbook of the philosophy
of science: Volume 10. Amsterdam: Elsevier, pp. 629–74.
Verspoor M and De Bot K (2022) Measures of variability in transitional phases in second language
development. IRAL – International Review of Applied Linguistics in Language Teaching 60:
85–101.
Verspoor M, De Bot K, and Lowie W (2004) Dynamic systems theory and variation: A case study
in L2 writing. In: Aertsen H, Hannay M, and Lyall R (eds) Words in their places: A festschrift
for J. Lachlan Mackenzie. Amsterdam: Free University Press, pp. 407–21.
Verspoor M, Lowie W, and Van Dijk M (2008) Variability in second language development from
a dynamic systems perspective. Modern Language Journal 92: 214–31.
Verspoor M, Lowie W, and Wieling M (2021) L2 developmental measures from a dynamic per-
spective. In: Le Bruyn B and Paquot (eds) Learner corpus research meets second language
acquisition. Cambridge: Cambridge University Press, pp. 172–90.
Wichers M, Riese H, Hodges TM, Snippe E, and Bos FM (2021) A narrative review of network
studies in depression: What different methodological approaches tell us about depression.
Frontiers in Psychiatry 12: 719490.
Xie Q and Yeung SS (2022) Do vocabulary, syntactic awareness, and reading comprehension in
second language facilitate the development of each other in young children? Learning and
Instruction 82: 1–8.
Yu H, Peng H and Lowie WM (2022) Dynamics of language learning motivation and emotions:
A parallel-process growth mixture modeling approach. Frontiers in Psychology 13: 899400.