A dynamic systems model of cognitive and language growth.

“van Geert (1991) noted that the accelerating lexical growth curve has to drop at some point, or children would have to be learning astronomical numbers of words.”

“The extended logistic growth equation gives rise to different, often nonlinear forms of development [16, 52, 53], which are typically observed in the domain of sports [9, 19, 27, 37].”

“…studies linking short-term variability in motor skills, cognitive performance, and language use with long-term development and distal outcomes have generated a considerable body of knowledge about the mechanisms that promote or constrain developmental change (Siegler, 2006; van Geert, 1991).”

“Mathematical Model of CDS The scaffolding model we adjusted from van Geert and Steenbeek (2006) for the present study has two major components. The first is the adaptation in the parent expressed as It in the model (I stands for input, i.e., the language addressed to the child), which depends on the tendency of the pa…”

“In these cases qualitative changes in behaviour arise from small continuous changes in the underlying mechanisms of information processing (McClelland, 1995; van Geert, 1991; van der Maas & Molenaar, 1992).”

“…our view, research from this theoretical perspective has made substantial contributions to the field of motor development (Thelen & Ulrich, 1991) and language development (Van Geert, 1991, 1993) but has yet failed to make serious inroads into other aspects of developmental research and theorizing.”

“In general, these findings are in line with modern neo-Piagetian models of cognitive development from childhood to adulthood (331-335).”

“Most of their work has focused on applications of modeling techniques to cognitive developmental questions (and particularly those related to motor and perceptual development) (Schutte, Spencer, & Schoner, 2003; van der Maas et al., 2006; van Geert, 1991).”

“First, the sociometric status of the participants was determined on the basis of repeated measures of a rating test (Asher, Singleton, Tinsley, & Hymel, 1979), which was analysed with the computer program SS-rat (for a detailed description of SS-rat, see Maassen, Akkermans, & Van der Linden, 1996).”

“Dynamic systems models (Fischer & Bidell, 1998; Fischer & Pare-Blagoev, 2ooo; van Geert, 1991, 1998, 2ooo) have offered new ways to analyze developmental data.”

“In terms of our concerns, we focus on dynamic growth theory (Van Geert, 1991, 1994).”

“The parameters of the function can be varied depending on learning opportunities, individual characteristics, and their interaction (Van Geert, 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.”

“…1994; Lewis, 1995), for example, in the context of the dynamic systems approach to the development of cognition and action (Thelen & Smith, 1994; van Geert, 1991), Ecological Systems Theory (EST; Bronfenbrenner, 1992) and its successors, such as the Phenomenological version of EST (Hall et al.,…”

“Finally, van Geert (1991, 1994, 1998) challenged the developmental community to think dynamically in order to generate realistic models of change.”

“That is because in recent years, these two fields have undergone a conceptual shift—from a static framework that assumes stable skills and linear change to a dynamic one that focuses on natural variability, as well as patterns of order, in learning and development (Fischer & Bidell, 1998; Thelen & Smith, 1994; van Gee…”

“Recently, an alternative conceptualization of productive vocabulary growth suggests a continuous and smoothly accelerating curve with no single point of acceleration (Bates & Carnevale, 1993; Bloom, 2000; vanGeert, 1991).”

“Citation for published version (APA): van Geert, P., & van Dijk, M. (2021). Thirty years of focus on individual variability and the dynamics of processes.”

“Indeed, such a process appears implicitly in models like that of van Geert (1991) and Elman et al. (1996), which describe vocabulary acquisition as a simple differential equation in which the rate of acquisition is a function of the current lexicon size.”

“In psychology (e.g., Nowak, 2004; Nowak et al., 1990, 2000; van Geert, 1991, 2003)—among many other disciplines—how complexity is at work over time has been modeled mathematically with iterative functions that parsimoniously account for emerging properties such as stability and resistance to…”

“This is captured well in the focus on future ‘‘attractors’’ in the Dynamic Systems Theory applications in psychology (Lewis, 2000; Tsuda, 2001; van Geert, 1991, 1994).”

“Having pioneered in dynamic systems for quite some time now (see Van Geert and Steenbeek, 2005, for a recent overview), I cannot be but supportive of their vision and their hope that this particular approach will lead to a fuller understanding of second language acquisition that is not only of theoretical but also of…”

“A powerful tool in dynamic systems is construction of mathematical models of processes of development and learning ( van Geert, 1991 ).”

“Van Geert, P. (2009) Complex dynamic systems of development.”

“Third, developmental psychopathologists modeling and computer simulation (e.g., Gottman et al., 1997; van Geert, 1991), and stateare uniquely interested in linking the study of normal and atypical development (Cicchetti, space depictions of system variability (e.g., Thelen & Smith, 1994).”

“Applying the DS perspective (Lewis, 2000b, 2005; Thelen & Smith, 1994, 2006; van Geert, 1991, 1994, 2009), moral motivation can be viewed as a complex dynamic system within which moral judgment and action emerge.”

“Fields as diverse as cognitive neuroscience (cf. Port & Van Gelder, 1995), developmental psychology (e.g., van Geert, 1991; Smith & Thelen, 1993; Thelen & Smith, 1994), organizational behavior (Axelrod & Cohen, 1999; Guastello, 1995), and political sociology (e.g., Axelrod, 1984) are being reframed…”

“The iterative or recursive nature of the application of the mechanism of change is a fundamental feature of dynamic models (Van Geert & Steenbeek, 2005a, 2005b; Weisstein, 1999), which makes them very different from the linear regression model that most researchers in the educational and developmental sciences will be…”

“With its emphasis on the developmental process, DST has tracked the developmental psychology research on growth (e.g., Thelen & Smith, 1994; van Geert, 1991; van Gelder, 1998; van Gelder & Port, 1995), in particular, the work of van Geert (1991) on L1 acquisition.”

“…have proven particularly useful for modeling the dynamics of such phenomena as personality development (Nowak et al., 2005), language development (van Geert, 1991), cognitive development (van Geert, 1998), talent development (Den Hartigh et al., 2018; Den Hartigh, van Dijk et al., 2016), and…”

“Over time, the interaction between these growers shifts from competition to support as both stabilize (VAN GEERT, 1991).”

“For instance, it is known that the parent’s level of adaptation to the mean length of utterance (MLU) of the child (in terms of parental MLU in CDS) appears to depend on the child’s current linguistic level (Phillips, 1973; Van Dijk et al., submitted).”

“…sub-systems interact as ‘connecting growers’ as they have a positive correlation, whereas others compete for the limited resources as ‘competing growers’ which suggests trade-off effects or inverse relationships between the advanced growers and the less advanced ones (Van Geert, 1991; Zheng, 2016).”

“Van Geert, P. (2009) Complex dynamic systems of development.”

“Throughout the 90s, researchers in cognitive and language development used the DS lens to examine real-time performance and profiles of developmental change (e.g., Smith, 1995; van der Maas & Molenaar, 1992; van Geert, 1991).”

“However, idiosyncratic theories can in principle be subsumed under nomothetic laws, i.e. laws that apply to every individual process (Van Geert, 1991; Molenaar, 2013; Steenbeek, Janssen & Van Geert, 2012; Van der Steen, Steenbeek, Van Dijk, & Van Geert, 2014).”

“Logistic growth analysis takes a first step toward nonlinear growth analysis by starting with logistic growth rather than linear growth (van Geert, 1991).”

“Verspoor et al. (2011) is an edited book in which the methods and techniques, used to visualize variability and test for meaningful jumps, were described in great detail and these will form the basis for the current study.”

“For example, van Geert (1991) described the expansion of vocabulary during the one-word stage in a state space with four dimensions, namely number of acquired words, growth rate (e.g. 0.5–2 words per day), carrying capacity (1–500 words) and feedback delay.”

“As illustrated across a wide range of content areas, dynamic systems theory has been valuable as an impetus, and tool, for conceptualizing developmental processes (e.g., Bosma & Kunnen, 2001b; Fogel, 1993; Thelen & Smith, 1994; Van Geert, 1991).”

“... & Valsiner, 1997; Lewis, 2000; Lewis & Granic, 2000; Newell & Molenaar, 1998), where researchers have relied on the theory to inform their study of infants’ and children’s progression through theoretical stages of development, the emergence of new behavioral forms and patterns during development, and changes in pa…”