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Title
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The Intrinsic Dynamics of Development
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Author
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van Geert, Paul
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van Dijk, Marijn
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Research Area
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Development
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Topic
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Evolutionary Bases of Development
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Abstract
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In this essay, we discuss an emergent developmental science. It provides an approach to development that redefines its theoretical and methodological basis in the general theory of complex dynamic systems. Its methodological research choices are in line with a focus on actual developmental processes, as they occur in individual cases, such as individual children, families, or relationships. Intraindividual variability based on frequent short‐term as well as long‐term measurements provides an important source of information. Theoretically, we advocate a model of a network of dynamically interacting components, generating a wide variety of developmental trajectories, in line with the idiosyncratic nature of developmental systems.
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Identifier
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extracted text
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The Intrinsic Dynamics
of Development
PAUL VAN GEERT and MARIJN VAN DIJK
Abstract
In this essay, we discuss an emergent developmental science. It provides an
approach to development that redefines its theoretical and methodological basis
in the general theory of complex dynamic systems. Its methodological research
choices are in line with a focus on actual developmental processes, as they occur in
individual cases, such as individual children, families, or relationships. Intraindividual variability based on frequent short-term as well as long-term measurements
provides an important source of information. Theoretically, we advocate a model
of a network of dynamically interacting components, generating a wide variety of
developmental trajectories, in line with the idiosyncratic nature of developmental
systems.
TOWARD A NEW FOUNDATIONAL THEORY
FOR DEVELOPMENT
The word development—or de-velopment—literally means unwrapping. In
whatever it is that develops, there is some hidden thing that can be uncovered by removing the wraps, the wraps metaphorically referring to anything
that hides the essence that will be uncovered. This view on development is
rooted in ancient philosophy and in particular in the Aristotelian notions of
potentiality. Potentiality is defined as the range of possibilities of something,
given the way this thing works, or a possible actuality in the future. Actuality
is defined as being at work here and now, and entails directivity inherent in
the way this thing or phenomenon is “at work.”
This ancient view on potentiality is in a sense revitalized by the modern
(meta-) theory of complex dynamic systems, which has served as a basis for
our own work in developmental psychology. A complex dynamic system
can be defined as a system consisting of many components or elements
that interact with one another, often based on quite simple interaction
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.
1
2
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
principles. These components change over short- as well as long-term time
spans because of their interactions with other components. Typically, these
changes are self-organizing and are coordinated in the form of emergent
properties. An emergent property is a new property of the system, spontaneously originating out of the interactions, not present in any of its parts
and in general not reducible to some sort of sum of the parts. For instance, a
child’s development of the ability for abstract thinking, or for understanding
psychological states of other people (theory of mind), is an example of
emergence and emergent phenomena, unless we see these abilities as simple
collections of skills that were already present. There is very little evidence
for the latter assumption (Fischer & Bidell, 2006).
Emergence is a form of actualizing the potentiality of the system, with
the potentiality given in the changing structure of interactions between
the components. An increasing number of studies are supporting the view
that the development of a child in his or her social and cultural context
can be conceived of as a complex dynamic system. Examples from our
own work concern language development (Van Dijk et al., 2013; Van Geert,
1991), feeding and eating (Van Dijk, Hunnius, & Van Geert, 2012), early
scientific reasoning (Van Der Steen et al., 2014), play and social interaction
(Steenbeek & Van Geert, 2007, 2008; Steenbeek, van der Aalsvoort & Van
Geert, 2014), identity and self-esteem, emotions and conflicts in adolescence
(Lichtwarck-Aschoff et al., 2009), adolescent friendship formation (Schumacher et al., 2014), teacher–child interaction (Steenbeek & Van Geert, 2013),
special education (Steenbeek, Janssen & Van Geert, 2012), and developmental theory formation (Van Geert, 1991, 1998; Van Geert & Steenbeek, 2005a,
2005b).
The assumption of complex dynamic systems as the foundational theory for
development has various consequences for the kinds of research and theory
formation that should be done in developmental psychology.
However, current developmental psychology hardly has anything like an
overarching theory of development, consisting of a set of first principles
or basic mechanisms of development. The picture that emerges from what
is probably still the main practice of research is that development can be
described as a broad connection of phenomena, such as attachment, the
child’s theory of mind, bullying, executive functioning, and so forth, that are
under the control of a comparably wide variety of independent variables.
For many researchers, “explain” still basically means to reduce the interindividual variability of a particular phenomenon across the population to the
interindividual variability in a set of other variables. Current developmental
psychology is now slowly moving away from being a theoretical and is
looking more and more into the dynamics of change.
The Intrinsic Dynamics of Development
3
EMERGING TRENDS IN DEVELOPMENTAL THEORY
FORMATION AND RESEARCH
There are two important issues on how to explain and study development,
which are now undergoing a radical revision.
The first issue deals with the meaning of intraindividual variability, that
is, fluctuations and changes in the way developing persons carry out particular activities that refer to underlying psychological variables, such as a
child’s mastery of syntax, its understanding of theory of mind, its reasoning
in science and technology problems, and so forth. A related issue deals with
the question of whether models based on studying groups (representative
samples) can tell us anything about individual trajectories.
The second issue deals with the basic mechanisms of development, namely
how particular variables can be said to explain various developmental phenomena.
INTRAINDIVIDUAL VARIABILITY AND INDIVIDUAL DEVELOPMENTAL TRAJECTORIES
Individual development is hardly ever a regular—linear or stepwise—
process. Although some general order obviously exists across children (for
instance, when learning how to walk, they go through roughly the same
“stages”), a much more irregular—almost chaotic—picture emerges when
looking at individual pathways (for instance, infants use many different
strategies of locomotion at the same time and show temporal improvements
as well as regressions). When reviewing the literature on early development,
it becomes clear that this type of (intraindividual) variability is prominent
in various domains, for instance, in motor and mental development (e.g.,
Freedland & Bertenthal, 1994; McCall, Eichorn, & Hogarty, 1977; for a
thorough review see Van Dijk & Van Geert, 2014). However, although
intraindividual variability is a rather universal finding, its importance has
not been recognized for a long time. The reason for this is that intraindividual variability is (traditionally) conceived of as being merely a reactive
phenomenon. The moment-to-moment irregularities are seen as the result of
context changes, which are considered to be independent of development.
A more methodological traditional explanation for variability is that it
is caused by measurement error. This interpretation originates from true
score theory (Cronbach, 1960; Lord & Novick, 1968; Nunnally, 1970), which
states that each observed psychological score is the result of both a “true
score” plus an “error term.” Thus, although behavior may look irregular
because of “noise,” the underlying latent variables (the psychological
constructs) are considered to be rather stable. These viewpoints (context
dependency a measurement error) largely overlap, but the difference is
4
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
that the measurement error concept frames it in terms of psychological
measurement, and thus offers a methodological solution, which is averaging
over the irregularities.
With the emergence of the theoretical framework of complex dynamic systems in psychology, a new view on variability was put forward, which was
that variability should be seen as a driving force of development (Lewis,
2000; Thelen & Smith, 1994; Van Geert; 1994; Van Geert & Van Dijk, 2002).
This theoretical approach defined development as a self-organizing system
of many components that constantly interact with each other and the environment. Variability was argued to reflect a system’s flexibility and to offer
the system room for exploration. According to this theory, variability is seen
as a generator of change by means of Darwinian principles of variation and
selection (Thelen, 1985). This idea was already introduced with the theorem
of operant conditioning by Skinner (1937), which states that learning is critically dependent on the consequences of the of the individual’s intrinsically
variable behaviors. In this sense, variability is a precondition for development because it enables the individual to adapt to new situations. Within a
particular developmental system, structural reorganizations occur at transition points, periods of instability where old patterns break down and new
ones emerge (Lewis, 2000). Variability is important because its presence can
be used to detect these transition points (Granott, Fischer & Parziale, 2002).
Studying intraindividual variability can thus provide insight into how the
system is changing.
Already in 1994, Thelen and Smith urged developmental psychologists to
treat intraindividual variability as data and to use it in their analyses, instead
of averaging it out by means of smoothing techniques. In the two decades that
have followed, more and more researchers have started to act accordingly
and have started to take variability seriously. Innovations in computation
and software have been a driving force in this development. Many methods have been developed with regard to data analyses and description and
have been applied to a wide variety of topics in human development, for
instance, in the domain of motor coordination (by authors such as Thelen,
Ulrich, and Smith), cognitive and language development (by authors such
as van Geert, Fischer, Case, and Granott), and emotional/social development
(by for instance Fogel, Granic, and Lewis).
Studying intraindividual variability requires taking repeated measures of
the same behavior across time, and the time scale of measurement must be
able to both fit the real-time behaviors and to capture long-term change. A
highly suitable approach to study the relations between these time scales is
offered by Flynn and Siegler (2007) and Lavelli, Pantoja, Hsu, Messinger, and
Fogel (2006). This method considers fine-grained information of real-time
The Intrinsic Dynamics of Development
5
behavior essential for grasping macro-level change processes (Lavelli et al.,
2006; Siegler, 2006).
In order to analyze patterns of variability, some simple descriptive
techniques have been proposed, such as the moving min/max graph, the
skewness analysis, and peak analysis (Van Geert & Van Dijk, 2002; van Dijk
& van Geert, 2007). Other measures are developed to describe qualitative
variability of interaction behaviors. For instance, Lewis and colleagues
(Hollenstein, 2013; Lewis, Lamey, & Douglas, 1999) developed the state
space grid (SSG) method, which has become increasingly popular in a
broad domain of developmental research, such as parent–child interactions
(see for instance Hollenstein, Granic, Stoolmiller, & Snyder, 2004; van Dijk
et al., 2012), teacher–child interaction (Mainhard, Pennings, Wubbels, &
Brekelmans, 2012), and young children’s peer relationships (Martin, Fabes,
Hanish, & Hollenstein, 2005).
In addition to focusing on its frequency or magnitude, variability can also
be analyzed in terms of its structure. Methods employing tools from the field
of nonlinear dynamics—such as fractal and spectral analysis—can be used
to classify patterns in terms of pink noise. Pink noise is also called 1/f scaling
and consists of a wavy, a periodic, fractal pattern, which is considered to be
the signature of self-organization. Other promising methods are offered by
recurrence quantification analysis (RQA) and cross-RQA, which can also be
used to detect transitions in the temporal structure of a pattern (Marwan,
2008; Marwan, Romano, Thiel, & Kurths, 2007; Webber & Zbilut, 2005). These
methods offer measures that express the degree of determinism/flexibility
in time series. Although these techniques are rather new in the field of
human development, they have been successfully applied to a variety of
topics, such as syntactic coordination during language development (Dale
& Spivey, 2006), reading in dyslexia (Wijnants et al., 2012), motor control
(Wijnants, Bosman, Hasselman, Cox, & Van Orden, 2009), and problemsolving behavior (Kloos & van Orden, 2009).
When studying patterns of intraindividual variability, questions of a more
fundamental nature also arise. One of the most notable findings from developmental studies that are based on time series is that individual development
is idiosyncratic. This finding leads us to the question of how we can generalize from these highly individualized patterns to more general knowledge
about developmental processes. In relation to this, Molenaar and Campbell
(2009) have argued that developmental models based on aggregated group
data do—by definition—not apply to individual processes, because of the
nonergodic nature of these processes. In relation to this, the meaning of the
concept of “generalization” should also be reconsidered. Currently, generalization is mainly viewed in terms of “sample generalization” of explained
variance in a sample (see van Geert, 2011). However, we have argued before
6
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
that generalizability should be conceived in terms of how individual development relates to an underlying developmental theory (van Geert, 2011).
EXPLAINING DEVELOPMENT
How can development be explained? Let us focus on a single variable or
dimension of development, such as a child’s frequency of use of nouns in
its sentence constructions, a child’s level of reasoning in science problems, a
child’s motivation to focus on a particular type of school task, and so forth.
Suppose we would have studied a representative sample of children and
found a positive correlation between age and the level of reasoning. It is
tempting to interpret this correlation as evidence for a linear relationship
between age and reasoning. That is, with every unit increase in age, we may
assume a corresponding unit increase in level of reasoning. If the sample is
big enough and really representative of the population of children, we might
be tempted to treat this linear model as a general model of reasoning growth,
and assume that, as it is a general model, it must apply to every individual
child in the population of interest. Treated as a model of individual change,
the correlation basically suggests that the next state of the variable “level of
reasoning” is equal to the preceding state plus some constant value that is
characterized by a certain level of stochastic variation:
yt+1 = yt + a + e
or, in the form of the change formula
Δy
=a
Δt
However, the time-serial data we have on individual change processes
hardly if ever show this sort of overall simple linear increase. Individual
change processes are characterized by various patterns of change, such
as S-shaped change, inverted J-shaped change, discontinuous change,
stepwise changes, inverted U-shaped change, overlapping waves, changing
variability, temporary regressions, or stepwise changes each of which is
preceded by temporary regression (e.g., Van Geert, 1998 for an overview).
What we should do now is to try to define mathematical expressions for
the iterative change pattern that, first, correspond with theoretically feasible
causal principles of developmental change and, second, generate the developmental patterns found in individual trajectories (Van Geert, 1991, 1994;
Van Geert & Steenbeek, 2005a, 2005b).
The first principle that such growth models entail is that the amount of
change depends on what is “already there,” that is, is proportional to the
The Intrinsic Dynamics of Development
7
current level of the variable:
yt+1 = yt + yt ⋅ a
or in the form of the change formula
Δy
=y⋅a
Δt
A second general principle of growth is that it depends on intrinsically
limited resources. That is, as a variable approaches the limit set by the limited resources, growth will decline in a way that is proportional to the level
already attained. Both principles can be combined into the logistic growth
equation (it was first discussed in the context of population growth by the
nineteenth century Belgian mathematician Verhulst):
(
)
1–yt
yt+1 = yt + yt ⋅ r ⋅
K
(for K being a limiting factor corresponding with the set of available
resources).
The change in a variable also depends on the influence from other variables, for instance, acquisition of syntax depends to a greater or lesser extent
on the quality and availability of syntactic “input” from the environment,
but also on the presence of a critical mass of words in early language development (e.g., Marchman & Bates, 1994). In line with the general assumption
that growth depends on what is already there, the effect of other variables
can be represented as follows:
Δy
= vi ⋅ y ⋅ s i
Δt
(for s being an influencing factor which can be positive, in which case we call
the variable vi a supportive variable, and a competitive variable in case the
value is negative).
In a growth process, a variable may affect another one not by its level but by
the amount it changes, that is, its increase or decrease. For instance, the increase
of a particular variable, such as a child’s knowledge of multiplication and
division, may consume shared resources such as practice time or effort at the
time this particular knowledge is explicitly taught or practiced by the child
(Fischer & Bidell, 2006). In this case, the effect of the variable v on the variable
y occurs via its first derivative, and can be written as
Δy
= Δvi ⋅ y ⋅ wi
Δt
(for w a parameter that can again be supportive or competitive, i.e., positive
or negative).
8
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
Finally, variables can be connected in various ways and connections can be
reciprocal, symmetrical, or asymmetrical. For instance, the level of a particular skill can be positively affected by skill-specific motivation, but on the
other hand, the skill-specific motivation can be positively (symmetrically)
or negatively (asymmetrically) affected by the level already attained. The
relationships can in principle also be indirect, as when a particular skill positively affects the increase in motivation that affects the growth of another
skill, which then positively or negatively affects the first skill.
Such connections can in principle be highly idiosyncratic, that is, typical
of a particular individual, for instance during the development of specific
interests in children. However, some connections are highly systematic, particularly in educational contexts. Education often takes place in the form
of highly regulated forms of interactions between adults and children, or
between teachers and students. The teacher will adapt his or her level of help
and instruction—for instance, with regard to science reasoning—to the needs
of the students, that is to say, to the level, for instance of science reasoning,
the students have already attained. This adaptation is meant to facilitate the
students’ learning. Adaptation and learning thus become a coupled process
of mutual fine-tuning. This process can be described in the form of coupled
dynamic equations for learning–teaching processes in general (Van Geert &
Steenbeek, 2005a, 2005b), and for processes of child-directed speech and language acquisition (Van Dijk et al., 2013).
The general point is that the variables describing a complex developing
system are, in principle, connected in a wide variety of ways. That is, such
a complex system can be described by a network of interacting variables, the
interactions of which are described in the form of theoretically generalized
growth equations (Van Geert, den Hartigh, Steenbeek, & Van Dijk, submitted) (Figures 1 and 2).
It is likely that the networks of interacting variables characterizing developmental systems have a network structure comparable to that of a small
world networks (Van Geert et al., submitted). That is to say, the number of
direct dynamic connections between any two variables is relatively small,
but any variable is likely to be associated with any other variable in an indirect way, that is, via a few intermediary, directly connected variables. Small
world properties can be found in a large variety of networks, including the
pattern of connectivity in the brain (Bullmore & Sporns, 2009).
It is interesting to observe that the network model governed by the
above mentioned equations naturally produces a wide variety of temporal
trajectories that show many of the qualitative phenomena that have been
described in the literature (Fischer & Van Geert, 2014; Van Geert et al.,
submitted). It generates sequences of S-shaped growth, stepwise growth,
temporal regressions, inverted U-shaped growth, long-term couplings
The Intrinsic Dynamics of Development
9
3.5
3
Level of growers
2.5
2
1.5
1
0
1
12
23
34
45
56
67
78
89
100
111
122
133
144
155
166
177
188
198
210
221
232
243
254
265
276
287
298
309
320
331
342
353
364
375
386
397
408
419
430
441
452
463
474
485
496
0.5
Time in steps
(a)
Grower 1
Grower 2
Grower 3
Grower 4
Grower 5
Grower 6
Grower 7
Grower 8
Grower 9
Grower 10
3.5
3
Level of growers
2.5
2
1.5
1
0
1
12
23
34
45
56
67
78
89
100
111
122
133
144
155
166
177
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210
221
232
243
254
265
276
287
298
309
320
331
342
353
364
375
386
397
408
419
430
441
452
463
474
485
496
0.5
Time in steps
(b)
Grower 1
Grower 2
Grower 3
Grower 4
Grower 5
Grower 6
Grower 7
Grower 8
Grower 9
Grower 10
Figure 1 (a,b) A typical outcome of a network model of 10 connected growers
representing 10 variables from a developing system. Trajectories show simple
S-shaped forms (e.g., grower 3), stepwise change (e.g., grower 4), inverted
U-shape (e.g., grower 1), and temporal overshoot (e.g., grower 5).
between variables, and sequences of overlapping waves. In addition, the
model generates predictions for the distribution of exceptional (excellent)
performance levels, which are not symmetrically distributed and are in
fact highly skewed (Simonton, 2001). The model generates developmental
trajectories in which the predictability of the final level of a particular
developmental variable or ability increases with age. It also predicts that
heritability, defined as a correlation with genetic endowment, increases with
increasing age, as is demonstrated by empirical data.
10
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
Grower 10
Grower 8
Grower 6
Grower 9
Grower 1
Grower 7
Grower 2
Grower 4
Grower 5
Grower 3
Figure 2 The pattern of connections leading to the developmental trajectories
represented in Figure 1a. Blue arrows represent positive (supportive), orange
arrows negative (competitive) relationships from one grower to another. The
strength of the relationship is represented by the arrows’ thickness. The final level
of the growers is represented by the size of the circles. Many relationships are
indirect (e.g., a positive relationship from grower 5 to 9 to 3 to 6 to 4).
The study of network models of development has great promise for the
future, but many problems have yet to be solved. One question concerns
a shift in explanatory emphasis. Standard models, based on interindividual variability obtained over big representative samples of individuals, typically focus on component-dominant forms of explanation. That is to say, they
try to explain the variance of a particular phenomenon across individuals
by estimating the independent contributions of major variables or components, for instance, the contribution of the variable “intelligence” to the variable “school performance.” Network models, however, focus on explaining
how dynamic interactions between many directly and indirectly connected
variables generate highly specific patterns of intraindividual variability, for
instance, in indicator variables such as reaction time in reading (Wijnants,
The Intrinsic Dynamics of Development
11
Hasselman, Cox, Bosman & Van Orden, 2012), or moment-to-moment emotional and behavioral expressions of self-esteem (De Ruiter-Wilcox, den Hartigh, Cox, Van Geert, & Kunnen, submitted). Another question concerns the
as yet unsolved tension between self-organization either into stable attractors
or into critical states. A stable attractor is a self-sustaining stable state of the
system, for instance, a child using a particular strategy to solve a broad range
of problems, irrespective of whether the strategy leads to correct solutions
are not. A critical state is one in which the system moves toward a particular
form of instability, where a relatively minor experience or event may cause
the system to rapidly change toward a new attractor state. Theorists such as
Piaget already had the intuition that a developing system changes in the form
of a succession of states (Piaget’s famous stages). Each stage, with the exception of the final one, automatically moves toward a point of instability, where
relatively minor events cause it to rapidly reorganize into a different pattern,
that is, a different developmental stage. This type of process is very similar to
what the theory of self-organized criticality (Bak, 1996) would predict, but the
empirical data for verifying its existence in long-term developmental changes
still need to be collected. On the other hand, analyses of the fractal structure
of time-serial patterns in developing systems have demonstrated properties
such as self-similarity over various time scales, which also comply with the
mechanism of self-organized criticality.
DEVELOPMENTAL PSYCHOLOGY: AN EMERGENT SCIENCE
OF EMERGENCE
The emerging trend that we discussed in this essay concerns the emergence
of a new kind of developmental science: It is new in the sense that it redefines
its basis in the general theory of complex dynamic systems, and new in the
sense that it redefines its methodological research choices in line with a focus
on actual developmental processes, as they occur in individual cases, such as
individual children, families, or relationships.
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PAUL VAN GEERT SHORT BIOGRAPHY
Paul van Geert (1950) holds a doctoral degree from the University of Ghent
(Belgium) and is a Professor of developmental psychology at the University
of Groningen in the Netherlands since 1985. He has had a pioneering role in
the application of dynamic systems theory to a broad range of developmental
areas, including early language development and second language acquisition; cognitive development in the context of learning–teaching processes;
and social development including social interaction and identity. His main
aim is to better understand the general nature of developmental dynamics,
that is, nature of the mechanism(s) that drive and shape a developmental process in an individual, as the individual, given his or her biological properties
and potentialities interacts with his or her actively explored and transformed
environment. He has been Fellow at the Center for Advanced Studies in the
Behavioral Sciences and has held visiting professorships at the Universities
of Torino (Italy), Paris V and Reims (France), Trondheim (Norway), and Harvard University (Mind–Brain–Education programme). For his research and
an overview of his artwork, see www.paulvangeert.nl
MARIJN VAN DIJK SHORT BIOGRAPHY
Marijn van Dijk (1972) studied developmental psychology at the University of Tilburg. In 2004, she defended her PhD thesis at the University of
Groningen, on variability and ambiguity in early language acquisition. She
currently works as an Associate Professor at the Department of Developmental Psychology at the same university. Her research themes are early
interaction and development (language and feeding) and the dynamics of
learning in primary education. Most studies are focused on change processes
and the observation of interaction behaviors in naturalistic circumstances.
http://www.rug.nl/staff/m.w.g.van.dijk/research
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