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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.

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, providing 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 argumentations. 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 present 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 (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 nonlinear 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 language. 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 previously 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 language with non-target forms) to a later state (for instance, using complex target-like idiomatical second language). The CDST perspective on SLD conceptualizes an individual’s multilinguistic system as consisting of many interacting subsystems, emerging in a specific 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 environment. This is called self-organization. Note that these interactions do not just state that ‘everything is related to everything else’. Rather, interactions form specific structures that can be described and observed. The interactions between the relevant subsystems 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 development, 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 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 language 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 factors (internal as well as external, e.g. in learner-directed speech) co-depends on the current 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 language), 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 quantitative 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 phenomena, 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 mathematical modeling of processes, and specific statistical applications and research methodologies (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 developmental 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 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 individuals 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 collection of theoretical perspectives (such as the theory of coordination dynamics, synergetics, chaos theory, bifurcation theory, dynamic network theory), that have in common that they deal with complex systems. Such time-dependent systems of interacting components have various properties (self-organization, emergence, etc.) that can be described and modeled. Many of these perspectives have a firm mathematical basis and thus provide 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 (exploratory 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 theoretical 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 gathering 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 formulated 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 sequence: they are guided explorations of phenomena such as non-linearity, intra-individual 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 theoretical 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 sufficiently captures the important phenomena of interest, whilst doing justice to the complex reality of interacting and changing factors, without losing essential and characteristic features and replacing them by seemingly simple features such as linearity, 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 explaining 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 measures, albeit reductionist, that contain interaction and change. Adopting measures that reflect interactional factors, these simple models improve our understanding of phenomena typical of complex systems, such as changing patterns of variability, sensitivity to initial conditions, nonlinear changes etc. In models of language development, simple, 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 qualitative features that are often observed in empirical data of second language development. First, second language learning varies from linear to discontinuous, from regular to chaotic, 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 generates 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 generalized 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 foundation 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 models 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 properties 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: starting 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 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, representing the process of interest. Only after many individual cases have been made available, 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 generalizations. 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 generalized 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.

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 variability 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 outcomes. 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.

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 individual trajectories of change may be quite different from average trajectories. Other testable hypotheses from CDST concern the special features of the quantitative properties 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 purpose 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, operationalized 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, syntactic 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 development 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.

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 generalizability, 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.

Footnotes

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.

ORCID iDs

Marijn van Dijk

Nienke Smit

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