13 July 2000

The Implicit Pedagogy of Chase Play
Stephanie Owens and Francis Steen

Many theorists pondering the existence and funtion of animal and children's play have concluded that the purpose of play is to train skills and acquire and/or organize knowledge (Corsaro, 1985; Fagan, 1975; Bruner, 1972; Vygotsky, 1967; Piaget, 1962). The functional hypothesis of training through play has also been utilized in attempts to explain the purpose of human play. Physical activity play, specifically rough-and-tumble, is proposed to train skills related to the comprehension of and formation of dominance hierarchies for boys (Pellegrini & Smith, 1998; Pellegrini, 1993). Symbolic play is believed to provide practice of skills observed in adults for the purpose of consolidating cognitive schemes (Piaget, 1962). Relatedly, Vygotsky (1967) suggested that play forms a zone of proximal development for the development of higher-level thought. Bruner (1972) writes that play offers an "optional pressure-free opportunity for combinatorial activity (pp. 38)." Because play occurs in a situation that is less pressured and not as costly in which to experiment with strategies and variations of strategies that could be used in the real situation, play functions to minimize the consequences of activities. Features of a skill are mastered in play then recombined in novel ways to provide mastery of the behavior in its entireity for executive use. Symbolic play begins to teach conventions and rules of culture and about conventions and rules in general. (Bruner, 1972). Fagan (1975) posits that the hypothetical function of play is that it is designed as a way to experiment with the world or one's own body to extract a predictive description from simulated examples. Organisms are building a model of the world and of the self.

Not only will we be arguing that play is an adaptation for learning, following the path laid by Bruner and Fagan, but also that pretense, specifically, is an evolved mechanism for learning through the process of imaginative immersion as an agent in a new context and role with accompanying conscious and unconscious changes in probabilities of strategy use via structural learning. The pedagogy of pretense is implicit.

Address the general assumption that nature/evolution produces adaptations for functioning in the world and that cultural
learning is required for training new skills and fostering innovative/creative behavior. Lev Vygotsky is perhaps the most
widely known proponent of this position from his assertion that the higher thought processes develop from sociocultural
learning, specifically from an abstract, sign-based language, and this is what separates cultural man from primitive man,
although on the evolved, physiological level we are the same species. However, there are principled reasons to believe
that natural selection has also constructed adaptations designed for training.

Chase Play as Pretense

Young children, from infancy through the early childhood years, engage in a form of physical activity play with surprising frequency. That form of play is chase. Researchers of play in early childhood do not classify chase play as pretend play but as exercise play, along with jumping rope, bicycling, running and climbing, etc. (Pelligrini & Smith, 1998). We do not deny that chase play does provide an opportunity to exercise but our understanding of chase play must broaden to recognize the elements of pretense intrinsic to this form of play.

When playing chase, children are smiling or have a playface, characterized by a wide open mouth with the corners moving up and out, as in a smile, the eyebrows are raised, and the eyes are open wide. Speech acts within a game are characterized by a rising intonation with a singsong quality, similar to the tone used by a parent speaking to his or her infant. The content of these speech acts must also be interpreted as pretense by the children and adults involved in the game but also by anyone in earshot. When a child says, "Chase me!," she certainly does not mean a "real" chase with the harm that would accompany capture. And she says this with a smile and sometimes followed by the playface. A chaser, especially an adult, makes statements such as "I’m going to get you!" She says this with a playface and really does not intend to even make physical contact with the child. The child usually giggles, laughs, or squeals in response, all the while smiling broadly. Even the squeal ends with a giggle, almost as if the two were combined in some way. The excitement is so intense what would be a giggle becomes one long, high-pitched squeal. An adult was even overheard saying, when she captured a girl and lifted her in the air, "What am I going to do with you? Eat you?" The girl giggled! Certainly she knew her teacher would not eat her "for real." And if a parent overheard this statement, he would not take his child out of the day care. A related behavior indicative of presence in the pretend frame is the frequent behavior of pretending to eat the fleer, complete with the biting and chewing movements with the mouth.

Chase play is also a manifestation of collaborative pretense. On the surface, chase games appear to be verging on the competitive. Chaser and fleer appear to have opposing goals in the game: capture and evade capture. The apparent goal is to capture the fleer with the pretend objective of eating him! However, as many examples throughout this section already suggest, chasers self-handicap. They intentionally refrain from actual capture by pursuing the fleer at a slower pace, by halting all movements to allow the fleer to escape, or by merely grabbing at the fleer with no intention to physically contact her.

Implicit Pedagogy

A primary task of humans, particularly the developing child, is the process of self-construction. Self-construction consists in those activities of the child that have as their primary objective the improvement of the child's motoric, perceptual, emotional, and conceptual organization. These activities take place in a cognitive frame we call the learning mode. By its objectives this frame is distinguished from the executive mode, in which the child seeks to satisfy biological needs of survival such as food, shelter, and rest. The two modes are prototypically different along several dimensions: in their evolutionary history, in their computational design, in the behavior they give rise to, and in their subjective phenomenology. To emphasize that natural selection has acted on the learning mode to optimize the development of the child’s interaction with its environment in such a way as to make optimal use of its neurobiological, cognitive, and cultural resources, we propose to refer to the structure of the learning mode as an implicit pedagogy. The objectives of the curriculum of implicit pedagogy are broadly specified developmental targets (Edelman), but these are reached only in repeated appropriate interactions with the physical and social environment. The child does not need to be and normally would not be conscious of the distal purpose of its spontaneous learning activities. The implicit pedagogy guiding self-construction is typically characterized by adaptations for various forms of nurture, contrasting with the conventional view of natural selection as a struggle between individuals. This evolved pedagogy has three dimensions: motivation, implicit curriculum, and the creation of learning environments.

Let us begin with the motivational dimension. What guides the child's behavior in an indirect manner towards acquiring new skills is her subjective phenomenology, including subtle gradations of experiences such as awe, joy, thrill, boredom, and aversion. Boredom is an extremely important component of implicit pedagogy: it motivates the child not only to cease its current activity, but to move into her zone of proximal development to a new developmental target as specified in the implicit curriculum. The child finds a natural and instinctive pleasure in activities that serve no immediate purpose other than that of improving her overall organization.

Children are highly motivated to play chase. They readily tell us that they find the behavior enjoyable and frequently smile or squeal with delight during the game. Their motivation is closely tied to activators (we’ll need to discuss this concept).

The second dimension of implicit pedagogy is that of structuring the child’s activity according to an implicit curriculum. We propose that the child is guided by a systematically unfolding and cumulative sequence of target values that constitutes an implicit curriculum. Although the implicit curriculum internally regulates the child, her performance is enhanced in an environment enriched by adult interactions. Discuss some elements of our findings here.

What guides the child’s behavior in an indirect manner towards these objectives is its subjective
phenomenology, including subtle gradations of experiences such as awe, joy, thrill, aversion, and boredom (Baars). An
important corollary of this model is that the child finds a natural and instinctive pleasure in activities that serve no immediate
purpose other than that of improving its overall organization. We propose that the child is guided in this manner towards a
systematically unfolding sequence of target values that constitutes an implicit curriculum that defines a cumulative
developmental trajectory (Owens and Steen).

Autopoiesis involves the related developmental dimensions of assembly, organization, and training. The autopoiesis hypothesis of the origin and function of pretense makes the claim that pretense is a suite of computational processes that evolved in response to pressures from natural selection to train complex cognitive adaptations. A more detailed description of these computational processes may help clarify the claim that it is central to autopoiesis. In the framework of human development, autopoiesis is the process of regulating and guiding the child towards more complex skills. We have suggested it relies on two central strategies: it structures the child’s learning activities according to an implicit curriculum and it motivates the child through the conscious experience of a subjective phenomenology. We now wish to add a third: autopoiesis utilizes pretense as a way of creating a learning environment for the child. These three strategies add up to what we term an implicit pedagogy. The notion of an implicit pedagogy should be elaborated. We need to draw the parallels to explicit pedagogy and to extend the notion to include the collaborative participation of adults and other experts in the child’s development.

Autopoesis is faced with two kinds of opportunities/constraints: speed of epigenesis and the use of information located in the
environment (behavioral integration into the environment). The solution to this adaptive problem is implicit pedagogy.

Natural selection will favor a robust system. On the one hand, the system needs to be robust enough to withstand impoverished
circumstances. On the other, there will be adaptive pressures to make use of opportunities - rich informational resources - if
they are available. Children are faced with informational and nutritional resources. This is an adaptive problem = how do you
time the resource allocation on the nutritional and informational dimensions? The implicit curriculum is the embodiment of the
solution of the adaptive problem. It optimizes resource abstraction in a neurobiological developmental stage. Given the
neurobiological resources available at the moment, the child should know how to abstract the resources.

Without this:

1 - would not optimize - would learn arbitary information
2 - would not optimize - would not be using available capacity

The implicit curriculum schedule for information abstraction needs to be aligned with biological changes. Would be selected
against if these were not synchronized.

Ironic aspect - debate about nature-nurture - people assume that with a genetic model, we would favor nature over nurture.
With this model, an emphasis on either nature or nurture would be maladaptive.

There is a constant ceiling effect. Children are always pushing the limits. The ceiling is constantly moving up, creating space that
the child can then move into.

Ceiling effect = the child's cognitive activities are always making maximal use of its neurobiological resources.

Neurocomputational abilities will always be pushing against the neurobiological limits. Pushing against the ceiling does not cause
the ceiling to rise. An evolutionary account would not expect this to happen, but the child should be pushing against it or the
space available would be a wasted resource.

Evolutionary pressures on the implicit curriculum = Natural selection would act against a curriculum that wasted resources. No
advantage to spare cognitive resources. The implicit curriculum motivates children to make use of all cognitive resources all the
time.

Pascual-Leone and van Geert = if a child is pedagogically deprived (without expert interaction during play), development
appears stage-like because the available neurobiological resources are wasted.

Theories of child development have contrasted the view that cognitive change is driven by learning, as proposed by Vygotsky
and others, with the view that it is driven by organic changes, such as proposed by Piaget and his school. Both sides claim or
have amassed an impressive body of evidence.

In an evolutionary perspective, however, it is not possible to maintain this opposition. The challenge of autopoiesis is precisely
to integrate them. Much of the information the child needs to build itself is located in the environment. We might think of this as
the distributed cognition of life itself. While the genes contain the core instructions, their capacity is constrained. Natural
selection will have favored storing only that information which cannot reliably be found in the environment. The precise strength
of bones and muscles, for instance, need not be stored in the brain, since gravity and the activity of the infant reliably provides
the necessary parameters. This is also true for cognitive tasks. The child must build itself in the environment in which it finds
itself, and it must do so faced with the twin constraints of epigenesis and information processing.

The cultural constructivist model, which may be more extreme than Vygotsky's proposals, is still widespread both in
psychology and in the humanities. It holds that epigenetic change is largely or entirely irrelevant to the process of cognitive
growth. In this perspective, the brain is at all times adequate to the child's learning opportunities, and development is entirely
driven by the culturally mediated acquisition of new skills and modes of thinking.

In the model proposed by Piaget, the child's learning takes place within the space provided by organic development. Given a
certain neurobiological profile, there are certain tasks the child is capable of learning and others that remain beyond its reach. In
any developmental stage, there is a ceiling effect beyond which new skills or skills of a new complexity will not be acquired.
The epigenetic system is seen to be robust: even if the child is not trained or taught, new cognitive skills will nevertheless come
on-line on time as directed by organic changes in the child's brain.

The notion of stages has been somewhat undermined by the work of Pascual-Leone and van Geert. They found that in a
situation where the child receives adequate educational support, development is gradual and continuous.

These debates can usefully be placed in an adaptationist perspective.In describing the two major dimensions of constraints of
development, learning and epigenesis, they in effect pose an adaptive problem, which is to optimize learning through the
simultaneous development of both.

The task of learning is inherently complex. With Vygotsky, we can think of it being structured like a man-made edifice, where
certain tasks can only be learned on the basis of previous learning, like bricks placed on bricks. The architectural plan of the
building is achieved because the learning is scaffolded by adults in the community. The growth of the child's neuroanatomy is
similarly cumulative; each step depends on an infinite series of previous steps.

It is clearly not possible to optimize these two dimensions of cognitive development separately. Since much of the information
needed for the development of appropriate brain structures is located not in the genes but in the external environment, or more
broadly in the child's action in and construction of the environment, a developmental process that proceeded by leaps and starts
in either dimension would be wasteful. This is most obviously the case in the constructivist postion. If at any given time there is
always sufficient neural capacity to perform any possible cognitive task, there is an implausibly chronic capacity underutilization.
On the other hand, if neural capacity lags what the child is expected to learn, teaching will be ineffective. Similar objections hold
against Piaget's suggestion that epigenetic development build neurobiological structures on a fixed schedule, as it were creating
a large room in which the child was given space to grow. Eventually, through learning, he would grow to fill up all the available
space and thus trigger the ceiling effect. In the meantime, however, there would be wasted neural capacity. Seen from the other
side, organic changes that become decoupled from learning runs the risk of going astray, as information located in the
environment is vital for meaningful epigenetic development.

The adaptive task facing autopoiesis can thus be reformulated. On the one hand, a one-sided focus on epigenetic change risks
the underutilization of information located in the environment. On the other, an excessive emphasis on extracting environmental
information runs up against the problem of an insufficient neural substrate to accomodate the learning. Such inefficiencies form
the scene of opportunity for beneficial mutations. Natural selection acts in precisely such circumstances, resulting through
differential reproductive success in organisms that have a superior design. We propose to conceptualize the solution to this
adaptive problem in the notion of an implicit curriculum. It is hypothesized to be designed to maintain a developmental
trajectory where learning processes at all times tend to make full use of neurobiological resources.

The gradual development that Pascual-Leone and van Geert observe under educationally favorable conditions is in line with the
predictions of this model. We would not expect a stage-like development. In place of the image of the child entering a large and
spacious room and slowly growing until his head hits the ceiling, we propose the image of a child that is at all times playfully and
energetically banging against the ceiling. At the same time, the ceiling is constantly receding, creating additional computational
capacity. The task of implicit pedagogy is to motivate the child to keep pushing up against the ceiling at all times even as it
constantly recedes. The ceiling effect, in this view, is the normal situation, the optimal cutting edge of the child's development
and the constantly moving target of implicit pedagogy.

The appearance of stages can be explained in part as an artifact of Piaget's methodology, in part as a useful if somewhat
misleading heuristic, and in part as the effect of selective deprivation. Children who receive inadequate educational attention
may in periods be unable to make full use of their neurobiological capacities -- a problem that surely persists. Similarly, children
who do not receive adequate nutrition may show a disrupted developmental trajectory.

Dialectical Constructivism / Working Memory as the Nexus of Cognitive Development

What is the significance of the learning-mode hypothesis for modeling the developmental trajectory of the child? It allows us to
articulate a position that is intermediate between genetic determinism and a cultural constructivism.

Following Pascual-Leone (1970) and Case (1995), we propose to treat working memory as the critical locus of this cognitive
development. Pascual-Leone (1970) was the first to propose that working memory growth plays an important role in
influencing children's cognitive development, and that this growth is controlled by epigenetic rather than by experiential factors.
In more recent work, Pascual-Leone and Johnson (1999) have elaborated this model into what they term dialectical
constructivism. Case (1995) may also have contributed to this development, or his version may be preferable to us; the point
is that the theory has been broadened to provide a pivotal role to experiential learning in interaction with epigenetic changes.

Dialectical constructivism may be contrasted with Piaget’s model of learning. Piaget proposed the developmental trajectory of
the child was largely determined by epigenetic changes. Assimilation of new behaviors and cognitive skills take place
continually, but accomodation takes place according to the epigenetic schedule. Could you elaborate on this? The term
dialectical constructivism suggests that Pascual-Leone argues for a model where experience engages dialectically with
epigenesis and that they somehow drive each other; I’m not sure we really need to get into this debate at all. All we really need
is a model that says the child uses its resources to make progress and this progress is gradual. So far, or model is entirely
experiential and makes no mention of epigenetic changes. Rather than relying on an epigenetic schedule of events, we propose
there are target values that set the implicit curriculum – but this curriculum must be followed for the development to take place.
We do not require epigenetic changes (e.g. in memory capacity) to accompany this implicit curriculum, though clearly the model
could if we wanted to. Minimally, we might say that we don’t address this dimension but that our model is not closed to it.

Let us add to this the notion of evolved templates. We propose that the implicit curriculum is evolved; it specifies an orderly
sequence of target values. There is also another area where we propose evolution may have played a role, not by fixing
development in terms of epigenetic stages, but by providing constraints for learning. This model provides an alternative to the
rationalist/empiricist dichotomy: as we go into in greater detail below, we suggest that the child’s learning may be critically
guided by evolved templates that act as vitally necessary constraints on learning.

Working Memory as the Nexus of Cognitive Development

In terms of our description of developmental progress, we need a theory that says roughly the following: the child at any given
time has a certain repertoire of behavioral and cognitive skills. Some skills are securely mastered; these are chunked into
compact procedures in working memory (references here). Others can be undertaken on the basis of existing skills, but they
require the cognitive resources of large parts of working memory, including that of conscious attention (Baars, possibly
Pascual-Leone 1999). Finally, some skills exist only in the child’s zone of proximal development (Vygotsky). We should try to
visualize this in some way – the child’s attention is like – what would be a good metaphor – like a searchlight or like the shadow
of the moon crossing the earth’s surface, or like a penumbra, or like a virus scanning display that looks at files sequentially
through a magnifier, or like a flame thrower or a welder’s torch that burns snow or wood or grass as it moves along,
compacting it and turning it into ashes or water (more compact forms), and then moving on.

Learning consists precisely or at least in part in the process of turning new information into compact procedural chunks (this
may be to reductive – ideas and references?). This raises the question of how this information is simplified. We raise the
possibility that evolved templates may play a role in providing the required constraints for generalizing in appropriate ways.
Once this has been accomplished, the skill has been mastered. Working memory has been freed up; specifically, consciousness
is no longer required.

The event of mastery has consequences in three concatenated dimensions of implicit pedagogy. First, there is a change at the
motivational level, mediated at the locus of subjective phenomenology: the child becomes bored. This is the diagnostic that tells
the child, or the observer, that the task has been mastered. In cognitive terms, the freeing up of working memory and of
conscious information-processing capacity is accompanied by the production of a subjective phenomenology of spare and
underutilized capacity, which is experienced as aversive. Second, and in consequence, there is a change relating to the
structuring of the child’s activity according to the implicit curriculum. Boredom is an extremely important component of implicit
pedagogy: it motivates the child not only to cease its current activity, but to move into its zone of proximal development to a
new developmental target as specified in the implicit curriculum. Third, and again in consequence, this will arouse the child’s
efforts to create a suitable learning environment through means of pretense. We emphasize that these three concatenated effects
are design features of an evolved system of autopoiesis. When the attention of a bored child drifts and he or she begins to
daydream, we see this as implicit pedagogy in action, though we do not of course wish to argue that explicit pedagogy should
be subordinated to the objectives of implicit pedagogy..

The implicit pedagogy is timed by epigenetic changes. The curriculum is related to epigenetic changes in a systematic manner.

What is the relation between implicit pedagogy and epigenetic change?

1.The strong theory would be that epigenetic change is causally related to the curriculum. Claims that epigenetic change is
contingent upon satisfactory progress along the implicit curriculum. (Constructivist position.) Evidence suggests the
degree of deprivation would need to be very high to disrupt epigenetic development.
2.The implicit curriculum optimizes the child’s cognitive effort by anticipating epigenetic change.
3.The implicit curriculum is irrelevant to cognitive development, which is driven by epigenetic change.

Working memory changes and the relation to pretend play:

1.Epigenetic change in working memory capacity
2.Skills that can be performed with this new level of capacity must be learned and rehearsed.
3.Play can become as complex as possible within that level of capacity, assisted by adults and practiced alone. And, as the
change to the next level approaches, scaffolding can provide the intitial exposure and practice of the skills available at
that new level.
4.As skills are practiced to the point of chunking within each level, they become automated and can be used in a
self-regulatory manner, as opposed to reliance on external mediators or adult scaffolding. This is what allows for
increasingly complex forms of play within a level of capacity.

The third dimension of implicit pedagogy is the activity of creating appropriate learning situations. This raises the question of the reference object or event in chase play. As Vygotsky noted in the context of explicit pedagogy, adults and older children scaffold the child’s development into her zone of proximal development. Adults also often provide working memory and other cognitive resources that enable the child to solve certain problems before her own neurobiological development would allow it – a form of distributed cognition. Finally, adults are typically able and often motivated to participate in furthering the child’s implicit curriculum. In these situations, the adults are frequently as unaware of their role as teachers as the children are of the pedagogical purpose of their activities.What is the image schema that is being activated in chase play? Based on several dimensions of evidence we have been led to hypothesize that the template for early chase play (up to about the age of 5?) is predator avoidance. Also discuss affordances.

Affordances: In implicit pedagogy, the notion that in the learning mode, people perceive objects and events in ways that allow
them to define suitable learning situations; cf. J.J. Gibson.

High-frequency substitute events in the environment are utilized as affordances for modeling low-frequency reference events; the image schemas or templates derived from the reference events guide the action in the pretend play.

Humans must learn an incredible amount of information in order to live successfully in the social group. We must understand the external and internal artifacts of human existence. Most of this information must be learned during the brief period of childhood; however, many of the events that could possibly provide the necessary learning experiences occur rarely. We propose play to be a learning mode in which low frequency, improbable events are practiced. During pretense, encounters with highly probable events (objects, peers, etc.) are taken advantage of in order to practice infrequent interactions. This solution to the adaptationist problem of learning necessary procedural and declarative information from rare events is possible, because during play similarities between features of the frequently encountered objects and events (i.e. affordances) and the real, improbable event are extracted and utilized.

Now let us consider the logic behind the pretend play of chase in the context of implicit pedagogy:

  1. the implicit curriculum specifies that the child must be able to evade predators
  2. this skill must be acquired gradually in a safe and predator-free environment
  3. this is accomplished by seeking out high-frequency local affordances
  4. playmates are suitable substitute objects for the reference objects, predators
  5. they help to provide a safe yet effective learning environment
  6. chase play is accompanied by a subjective phenomenology: the thrill of being chased
  7. this pleasure motivates the child to create and sustain a suitable learning environment

Note that the first two points relate to the structuring dimension of implicit pedagogy, the middle three to the dimension of creating a suitable learning environment, and the last two to the motivational dimension. This should be written out in full, perhaps in three paragraphs.

The adult chaser that provides a scaffold for the child’s learning experience relies on activators or cues from the child to regulate this activity. The task of the adult is as it were to formulate a problem for the child: in most cases, it is simply the problem of how to get away from a predator in hot pursuit. When the child squeals with excitement, the implicit teacher knows that the correct problem has been posed – the problem that, as it were, is the very lesson in that day’s implicit curriculum. Similarly, for the child herself, the excitement that expresses itself as a squeal as it were labels the activity as intensely right. It is not necessary or even easily conceivable to seek a justification for being chased; it is unproblematically fun and inherently worthwhile. Yet by several other measures the behavior is paradoxical: the child does not in fact fear the aide and has no reason to run away from him, and besides, even if it did, the flight would in most cases be pointless, since she knows the aide can easily catch up with her if he wanted to.

Structural Learning

To understand the function of chase play, we need to consider the general design of the learning mode. We propose the learning mode is organized according to a set of complementary pedagogical methods: achieving a specified standard and exploring the possibility space this new skill makes possible. Exploring this possibility space is done by adjusting and calibrating the new skill in context. As the child is learning a new skill, its performance must be tuned to its environment, its playmates, and its own internal phenomenology. Learning can thus be modeled in relation to the three levels of consciousness outlined above:

In all three cases, we see that the basic developmental target is proposed to include a practical skill as well as the acquisition of the ability to manage that skill through self-knowledge. This discovery of oneself in action is as vital a part of play as the acquistion of the skill itself, which would be largely useless without the accompanying self-knowledge.

In a metaphor of structural learning, we might think of the developmental target as having a core value that must be achieved: say, the ability to run at top speed while looking over your shoulder. Surrounding this core value (or standard) is a large possibility space of things that the new skill makes possible: you can run to a structure and climb it, you can run behind a structure, you can run to an adult or other protector, and so on.

Because chase play models an adversarial situation, the developmental target cannot remain at the stereotypical level. We hypothesize that the child will be motivated to explore the far reaches of the possibility space that its new-found skills give access to. In these explorations the child learns to develop strategies that are slightly unpredictable; the discovery of such strategies should be a source of particular delight to the child.

The third layer of theory regarding structural learning is the Distributions of Associations model developed by Siegler: as strategies that are learned and practiced, they are unconsciously given different weightings for confidence and the probability of success.

Vygotsky recognized that themes, stories, and roles enacted in play illustrate a child’s understanding of and learning of
sociocultural information. Children do not construct a conceptual world with no input but must learn it from those around them
(cognition distributed in the environment as we would say). Vygotsky believed there existed two essential and interrelated
components of play:

1.the imaginary situation
2.rules implicit in the imaginary situation placed on action occurring in pretense by virtue of the role adopted during play


Continuum of Development

Explicit imaginary situations ______________________ Implicit imaginary situations with explicit rules
with implicit rules (pretense)



Vygotsky also stated that play creates a zone of proximal development. In this ZPD, children learn to satisfy their desires by
voluntarily obeying self-chosen rules. Personal satisfaction is enhanced through cooperation in rule-governed activities
(implications for moral development).

In our terms, play provides an expanded possibility space beyond one’s present capabilities. Vygotsky stated that in play, the
child first liberates thought from the immediate external environment (mapping); this marks the beginning of independent,
coherent organization of thought. The child begins to separate meaning and vision/action/object thus creating a sustainable
imaginary scenario in which meanings can be cleaved from their referents.

In pretend play, children make use of resources in their social world (what we term affordances): roles; plans for action, stories,
scripts; objects and settings (Vygotsky).

"Play should be studied on its own terms as one expression of imaginative activity that draws and reflects back
upon the interrelated domains of emotional, intellectual, and social life." (Nicolopoulou, p. 13)

The play world is an experimental theatre in which children explore and master the social world. Play expresses individual
desires (Freud, Piaget) yet is also a vehicle for learning (V. Paley).

The Role of Pretense

Consider the following adaptive problem:

at birth, the newborn is faced with the prospect that at some point in the future, it will be pursued by a predator – easily a terminal experience

before the predator appears, the cues required to trigger the construction of the evasive behavior are absent

after the predator has appeared, there is no time to construct the appropriate behavior

Play is the mammalian solution to this type of adaptive problem

Feed a reptile and provide it with a safe environment, and it will lie perfectly still

Feed a young mammal and give it everything it needs, and it will make use of its surplus resources to play

Play relies heavily on a complex cognitive adaptation, pretense

In pretense, the child is able to rehearse expensive or dangerous low-frequency events and activities by making use of cheap, safe, and high-frequency features of the environment as opportunities for learning

The child spends a great deal of his time in the learning mode rather than in the executive mode, scanning the environment for pedagogical affordances – materials and opportunities for play – rather than for food, resources, and shelter.

V. The Predator-evasion Hypothesis

Chase play appears to mimic the behavior of predators chasing prey

The activators belong to the domain of predators: growling, stalking, looming, and rearing

The elicitors mimic the behavior of prey: glancing behind, running away, hiding, climbing to get out of reach

When the game ends in a capture, the chaser frequently pretends to eat the fleer, or claims to be about to do so

On the evidence of the activator cues and the children’s responses, we hypothesize that chase play is an adaptation to train predator evasion


VI. Chase Play in the Context of Implicit Pedagogy

The implicit curriculum specifies that the child must be able to evade predators

This skill must be acquired gradually in a safe and predator-free environment

This is accomplished by seeking out high-frequency local affordances

Playmates are suitable substitute objects for predators

They help to provide a safe yet effective learning environment

Chase play is accompanied by a subjective phenomenology: the thrill of being chased

This pleasure motivates the child to create and sustain a suitable learning environment

It may be objected that chase play is not a form of pretense In chase play, neither the children nor the adults are conscious of chase play as a preparation for predator evasion Chasers and fleers adopt the roles of predator and prey without any apparent awareness of role play We propose chase play is a form of unconscious pretense

VIII. What Do Children Learn From Playing Chase?

Motor skills such as running, dodging, climbing, creeping, crawling, and hiding; combinations of such skills; smooth and high-speed transitions between them

The motor skills are learned as part of the environment -- that is to say, the child not only learns to hide but learns to interpret the environment in terms of motoric opportunities: the kinds of features that are possessed by places to hide, to jump, to climb, and so on.

These motor skills involve not just training but self-discovery: the child not only needs to learn to run, but he or she needs to learn how fast she is able to run, to evaluate how fast a chaser is going to catch up, to allocate strength in optimal ways, and so on.

Other-directed interpretive skills related to the gestures and motions of the chaser

These other-directed interpretive skills are learned as part of an effort to decode the intentions of the chaser – to make the chaser more predictable, to anticipate the chaser's movements

These interpretive skills may also involve monitoring the effect on the other of your own behavior, thus setting the stage for deceptive moves

Self-directed interpretive skills: how to respond to one's own fear, one's own terror, one's own emotions

Self-directed interpretive skills relate to being able to act in response to emotion, practicing being excited, and so on.

These self-directed skills become vitally important later on as a form of self-knowledge and may be considered a requisite to moral developments

IX. Structural Learning - 1

In these three levels of skill, the basic developmental target is proposed to include a practical skill as well as the acquisition of the ability to manage that skill through self-knowledge.

This discovery of oneself in action is as vital a part of play as the acquisition of the skill itself, which would be largely useless without the accompanying self-knowledge.

We propose the learning mode is organized according to a set of complementary pedagogical objectives:

achieving a specific developmental target

exploring the possibility space this new skill opens up

Exploring this possibility space is done by adjusting and calibrating the new skill in context.

The two objectives are pursued together.

As the child is learning a new skill, its performance must be tuned to its environment, its playmates, and its own internal phenomenology.


IX. Structural Learning - 2

Applying this model to chase play, we might think of the developmental target as having a core value that must be achieved: say, the ability to run at top speed while looking over your shoulder.

Surrounding this core value (or standard) is a large possibility space of things that the new skill makes possible: you can run to a structure and climb it, you can run behind a structure, you can run to an adult or other protector, and so on.

Because chase play models an adversarial situation, the developmental target cannot remain at the stereotypical level.

The child must adapt its basic skills to the specific needs of the chase.

We hypothesize that the child will be motivated to explore the far reaches of the possibility space that its new-found skills give access to.

In these explorations the child learns to develop strategies that are slightly unpredictable; the discovery of such strategies should be a source of particular delight to the child

Structural learning finally involves largely unconscious changes in the levels of confidence and probability of success assigned to these strategies (Siegler)

Conclusion

In very tentative tones, should state that theories of explicit pedagogy are incomplete as long as their relation and
possibly their dependence upon implicit pedagogy is not understood. It seems probable that the mechanisms that
regulate implicit pedagogy remain vital in subsequent sociocultural learning. Although the similarities between
implicit and explicit pedagogy are striking, we have not superimposed the structure of good, effective explicit
pedagogy on these evoloved systems, we conclude instead that explicit pedagogy has been founded on these
basic structures.

Chase Play Data


The task of specifying an evolved pedagogy is one of making the implicit explicit. In the model we’ve developed so far, we
proposed that there is a central skill specified as a developmental target and that this skill opens up a possibility space in which
various strategies can be developed. In play behavior, this means that the child engages in strategies that work and, as it were,
tailors the performance of the target skill to the local circumstances relevant to solving the specified task. What we assumed,
without making explicit, is that the criteria for what works must already be known to the child. These criteria must be taken
from the executive mode. That is to say, the motivational dimension relating to the choice of strategies must be determined by
evolution in the executive mode.

In the case of chase play, this means that the children should be motivated by learning mode specific inference systems, to
create make-believe dangerous situations. These situations would not be enjoyable in the executive mode and yet they are
highly enjoyable in the learning mode. This circumstance demonstrates that the learning mode constitutes an independent set of
adaptations and suggests that is has a distinct evolutionary history. However, the goals of the pretend play should nevertheless
be constrained or specified by motivational adapations that belong to the executive mode. In the case of chase play – or, as
Gene Learner suggested, play fleeing – this model suggests that the goal should be a successful escape. The children should
not enjoy being caught. Captures generally appear during a game and the game merely continues afterwards. They possibly
serve as a negative feedback device that changes the confidence level associated with the preceeding evasion strategy and
indicates what skills need to be further practiced.

In regard to very young children, we are seeing an apparent enjoyment at being captured and pretend-eaten. We suggest
this is because the children at that age, when they are first practicing being chased, are focusing on a different problem than the
older preschool children. From the point of view of the predator-evasion hypothesis, the lack of serious attempts by very small
children to escape capture seems anomalous. However, we must consider the possibility that the implicit curriculum at this
young age is geared to training pretense rather than fleeing. The chase play system must come on line. Children must become
habituated to feeling extremely excited to the point of fear and yet at the same time feel safe. This situation has a somewhat
surprising entailment that small children will treat pretend eating as an activator. It will not serve to mark the end of the game
but will make the child more excited and will cue the child to the domain of predator evasion. This difference between chase
play in very young children and preschoolers suggests that even within this age period there is a clear progression of
developmental and pedagogical goals.

The distinction between the motivation to create learning situations derived from the learning mode and motivations to select
strategies that work derived from the executive mode become even more important in the case of fictional stories. On the one
hand, stories must present situations that are suitable for learning new strategies. These situations will be experienced as
enjoyable in a story although in real life they would be terrifying. The constraints that are placed on which strategies should be
adopted for dealing with this fictional situation, however, do not derive from the learning mode but from the executive mode. It
would not be productive to train capacities for pursuing strategies that lead to outcomes that would be aversive in real life.
Structural learning must be constrained by what you really want to happen. At the same time, the situations that are created
through pretense are not situations that you would desire to happen to you in real life. They are designed because they present
suitable learning situations.

Fictional stories make certain things more apparent that can then inform chase play and vice versa. Some of the entailments
that spring from the learning mode are more visible in chase play. When children are delighted by situations that in real life
would be terrifying, this strongly suggests the presence of a distinct motivational system – an implicit pedagogy. In stories, on
the other hand, the necessity of producing outcomes that would be desireable in real life become much more prominent.

A successful story must have two components. It must not only describe outcomes which are desireable in the real world
but it must create realistic situations in which probable strategies can be applied to reach those outcomes. Under normal
circumstances, good stories typically focus on moments of difficulty, since the easy ways to reach desirable solutions have
generally already been taken. This is due to what we may refer to as the principle of relevance, proposed by Sperber and
Wilson in the context of speech act theory. A criterion for the construction of an appropriate learning situation is that it must in
some way be perceived to be relevant

As the emergent theoretical focus is pretense as a learning mode characterized by an implicit, unconsciously driven curriculum
and pedagogy on the part of the child and mediated by an adult, certain behaviors in chase games need to be sampled during
observation periods. Specifically, self-handicapping behaviors must be fleshed out in greater detail. When do players
self-handicap? What is the nature of self-handicapping? What functions might self-handicapping perform and how might these
relate to an implicit understanding on the part of the adult of the child's developmental level in chase? In order to gain a better
understanding of the nature of implicit pedagogy, signs of mediation provided by an expert chase player should be recorded in
detail if they occur. The pretend lunge, for instance, is performed when self-handicapping, as the fleer is not captured due to an
alteration in the timing and intent of the gesture. The behavior appears to provide an exaggerated cue that is framed by the
chaser (adults use this in chase with children) possibly to highlight a means of initiating a chase game.


Chase Play Project

2000-1-10 Theoretical Note

A General Description Of Implicit Pedagogy

Rubin, Fein, and Vanderberg (1983) offer a set of criteria for the identification of play behavior. The first criterion is that play is
intrinsically motivated. Play is also an activity engaged in for its own sake with no thought of the goals of behavior. The behavior
is child-directed. The activities can be nonliteral. External rules are not imposed in play, and any rules emerging from the activity
can be negotiated and modified (Sancho & Spodek, 1998). These criteria, among other lists, have been proposed to guide
attempts to define play and to aid in the classification of behaviors as play. As this phenomenon is manifest in many diverse
forms, the act of defining play has been problematic. How does chase play shed light on this dilemma? Can a definition of play
be formulated to account for the extreme diversity in play behavior?

Perhaps play can be categorized into three broad classes: Motoric, intentional, and narrative play. Motoric pretense may take
the form or early play in infancy or of chase play. Object substitutions would be considered intentional play. Narrative play is
characterized by the assumption of roles and scripts to guide play activity. Obviously, these three classes could not be
considered discrete categories; considerable overlap can and does occur during play. But on the surface, these forms of play
appear to be quite different. What, if anything, might they have in common?

Humans must learn an incredible amount of information in order to live successfully in the social group. We must understand the
external and internal artifacts of human existence. Most of this information must be learned during the brief period of childhood;
however, many of the events that could possibly provide the necessary learning experiences occur rarely. We propose play to
be a learning mode in which low frequency, improbable events are practiced. During pretense, encounters with highly probable
events (objects, peers, etc.) are taken advantage of in order to practice infrequent interactions. This solution to the adaptationist
problem of learning necessary procedural and declarative information from rare events is possible, because during play
similarities between features of the frequently encountered objects and events (i.e. affordances) and the real, improbable event
are extracted and utilized.

In play, behaviors are practiced. Bruner (1976) had a similar idea in mind in a discussion of the function of play. He considers
an important aspect of play to be that it occurs in a safe (protected), pressure-free context and affords the opportunity to
practice individualized combinations of subcomponents that comprise complex behaviors. The complex behavior is learned via
observation or may be instinctual knowledge that must be practiced to unfold developmentally. Due to the complexity, the
overall behavior is parsed into manageable subcomponents that provides an opportunity for independent practice of each. With
mastery of parts, the subcomponents are then reintegrated and the complex behavior is rehearsed as a whole (Bruner, 1972).
Under pressure (i.e. the "real" situation), performance would disintegrate without this pressure-free opportunity for rehearsal.
We modify Bruner's account of play as practice by adding that rather than practicing discrete subcomponents in a linear fashion
there is a cumulative effect. Practiced behaviors may begin as simple subcomponents of a whole that, in their development, gain
in difficulty and complexity. Cognitively, how does pretense provide a learning opportunity? Steen (personal communication)
developed the notion of rewritable agent registers. These define the parameters for interactions with objects and others during
pretense. Agent register contents (i.e. information about the self) can be decoupled, which allows for the discard of local detail
of the registers during pretense while extracting and retaining the structural relations between the high-frequency event in
pretense and the low-frequency real event. What does this mean?

Chase games, for instance, are frequently occurring during early childhood. These games are characterized by an understanding
of cues to initiate, maintain, and terminate games; many motoric strategies to capture or evade capture; and by age 4, a
coherent pretense narrative guides play. We hypothesize the purpose of this universal form of play to be the evasion of
predators. An understanding of intention is necessary to register the state of affairs between ones' own situation and the
presence of a predator. Behavioral strategies, such as climbing, hiding, and dodging would be necessary components of
predator avoidance. During a chase game, a child's agent registers are loaded with the specifics of their role in the game (e.g.
fleer, chaser, monster, cheetah, etc.), and an understanding of the role guides the behaviors appropriate for that position. The
local detail of the pretense situation, such as the narrative, the identity of other players, the playground terrain, etc. is discarded;
but the structural relations between the game and the improbable event of encountering a predator are retained. The similarities
between the two events may be the strategies and consequences of their use and comprehension of intentional cues, such as
eye-direction detection.

Interestingly, the role preferred by children in chase is that of the fleer; the chaser is providing a service to the fleers.

Footnote: According to Provine 1996), "chimpanzee laughter occurs almost exclusively during physical contact, or
during the threat of such contact, during chasing games, wrestling or tickling." He notes that "The individual being
chased laughs the most."

Role reversals seem to be frequent, providing all with an opportunity to be chased. The narratives providing a coherent
pretense theme in 4-year-old chase generally involve animals, monsters, and cartoon (Pokemon) characters. These children
engage in some pretend "eating" of others when captured.

A most fascinating aspect of chase games observed thus far is a preference to play games with an adult in the role of chaser.
We view this as another indication of the preference of the fleer role; this preference may also provide evidence for a
pedagogical interaction between expert and novice players. The concept of play as a learning mode can be further expanded
with an understanding of an evolved, implicit pedagogy.

Utilizing a Piagetian framework, Clarke (1999) developed a description of the emergence of chase play beginning in early
infancy with peek-a-boo games. She adheres to Piaget's theory of cognitive development in the assertion that early chase play
provides assimilative practice of sensory-motor schemes of object permanence. By age 5, chase games begin to be
characterized by the loose use of rules; and around 7 years of age, chase play has evolved into rule-governed games, such as
tag. This description is also consistent with the Piagetian paradigm. Nonsocial, unrealistic, and fantastic features mark early
thought processes. Realistic thought, which is logical and rule-bound, does not emerge until the concrete operational period
around age 7 to 8 years. Clarke, possibly unknowingly, violates the theory by including the role of the caregiver in chase play,
thus endowing the behavior with a social component.

Piaget believed pretend play to be a solitary activity. Sociocultural researchers have criticized this position on the grounds that
Piaget ignored the social context of his own children (specifically the role of Mrs. Piaget) and that later researchers focused on
non-adult directed contexts and overgeneralized their findings to characterize play behavior in the home. Current research
indicates active involvement of caregivers in initiating, guiding, and elaborating their child's pretend play behavior, thus creating a
zone of proximal development (ZPD) in which the child can perform increasingly sophisticated behaviors resulting in the novice
approaching expert levels in play. Vygotsky posited the function of pretend play to be the necessary process for later creative
and abstract thought. Therefore, not only does caregiver interaction during play create a ZPD for more advanced play behavior
but pretend play itself creates a ZPD for the emergence of higher level thought. Vygotsky and later researchers have
concentrated primarily on object substitutions in pretend play and have formulated a developmental trajectory of this play
behavior. In the beginning phases, around 24 months of age, mom initiates more object substitutions, a role that is gradually
usurped by the child around the age of 28 months. Also by 28 months, the child is directing mom's play behavior in pretense,
which was also a primary role for mom when the child was younger. The presence of child speech during later solitary play that
is correlated with external adult speech of earlier guided play is given as evidence of scaffolding in the acquisition of pretend
play. A second line of reasoning put forth as evidence of scaffolding is the repetition of behaviors in solitary play that are exact
replicas of behaviors guided by mom in earlier collaborative play sessions.

Clarke's (1999) developmental progression of chase play is also interpretable from the Vygotskian paradigm because it follows
a similar trajectory in relation to the caregiver. Hence, a ZPD is created for chase play behavior. Peek-a-boo games, stationary
chasing, "I'm gonna get you" games, and crawl chasing are generally initiated by adults and occur with adults as play partners.
Only in crawl chasing (the last stage of infancy chase behavior) does the infant assume the role of chaser. At age 2, children first
begin to initiate chase play with adults as preferred play partners. The older 2-year-old begins to play chase with peers.

Researchers in the Vygotskian tradition have noted the occurrence of scaffolding provided by adults during play interactions
with children. This scaffolding creates a situation in which the child can perform at higher levels, due to the assistance given by
the adult. Children prefer adult interaction to peer interaction during play in early childhood; and with adult interaction, play
periods lengthen and play is more sophisticated than similar play with peers or alone. Contrary to these researchers, we believe
that there are differences between this form of scaffolding and that appearing in what we have termed explicit pedagogy.
Explicit forms of pedagogy are consciously planned and structured, guided by a known curriculum and knowledge of optimal
outcomes, and the intentional assessment of level of goal attainment. The adult rather than the child usually direct explicit
pedagogy and the accompanying curriculum.

The mainstream understanding of scaffolding conforms to the qualities of explicit pedagogy. The teacher assesses a child's
actual level of development and guided instruction is consciously and painstakingly planned in light of this information and
knowledge of curricular objectives. Play, as an implicit pedagogy involving the use of scaffolding is a slightly divergent concept
than that ascribed to explicit pedagogy. In play, activities are child-directed, rather than adult determinations of play activities.
The role of the adult is to assist in play.

How does the adult assist in play? Perhaps the role of the adult is that of model and mediator. Adults demonstrate increasingly
complex behaviors in play. Adults may also assist in the expression of play as a mediated learning experience (MLE). Feurstein
defines an MLE as an interaction with the environment via a human mediator. The mediator frames, filters, and schedules
stimuli, thus increasing the salience of certain affordances in the environment. This behavior would influence the clarity of
perception of the relations between the high-frequency event and the low-frequency event. This form of mediation influences the
transfer of knowledge form a specific context to other environments. Mediation also fosters higher and more efficient levels of
function and adaptation, leading eventually to self-regulation of learning from direct stimuli sans mediation.

Although pedagogical concepts of scaffolding and mediated learning are useful in a description of implicit pedagogy, they, in
their entirety, cannot be mapped directly onto this conception of pedagogy. Only specific entailments of the concepts will be
useful; one outcome of this project may be a description of these similarities. Fundamentally, we must disagree with Vygotsky
and other Vygotskian play theorists on one point. Vygotsky believed pretend play to be taught in an explicit manner to children;
play is learned through social interaction. Because play interactions with adults do entail pedagogy, the agency of the child in the
play frame was ignored. Children in collaborative play with "expert" play partners are not learning to play but playing to learn.
This learning is developmentally driven, and the contents of learning can be universal, as in chase play, or culturally specified, as
in object substitution and narrative play. Adult interaction facilitates the unfolding of an internally motivated curriculum and
provides the cultural information necessary to learn context-specific information. As a result, in development, learning through
play becomes increasingly self-regulated. What follows are the proposed features of an implicit pedagogy.

We must begin with the notion of consciousness and its partner, the unconscious. (We will flesh this out in greater detail at a
later date.) Children have an innate, unconscious developmental curriculum. This curriculum specifies no ultimate goals but
contains basic objectives that may be in the form of baseline measures of necessary abilities and understandings of universal and
cultural knowledge. Pretense, the learning mode, is a conscious learning strategy. When in the pretend frame, those aspects of
the learning process, such as contextual affordances, are customized to local circumstances of the pretend world containing
high-frequency occurrences. These local circumstances are discarded, as the structural information is stored. This act of storage
would, in effect, update the curriculum and indicate fulfillment of objectives.

The role of the "expert" in collaborative play with children, most frequently an adult, is similar to the mediator as proposed by
Feurstein; the "expert" may also employ the technique of scaffolding to assist learning in the child's zone of proximal
development (ZPD). For these roles to be filled, however, the adult must, in some way, assess the current functioning of the
child. Steen (personal communication) suggests three possible means of assessment of a child's actual level of performance and
understanding during pretend play:

1 - The adult possesses a conscious model of the child's implicit curriculum. The curriculum has been made explicit with life
experience/maturity in a culture and as a human. The adult, in play interactions, would "test" the child to assess the actual level
and would provide necessary pedagogical intervention to facilitate development. This scenario is highly unlikely. The learning
goals of play, the act of assessment, and the use of intervention techniques are not realized by adults when playing with children.
Assessment and pedagogy may be carried out without conscious or deliberate adult action, as in the transcendence criteria of a
MLE (Kouzlin, 1991).

2 - The adult possesses a half-conscious theory of the child's implicit curriculum. During play, the adult would assess the child
and unconsciously choose pedagogical behaviors and content knowledge appropriate to the specifics of the situation. Although
assessment of a child's abilities and understandings would be conscious ("What happens if I...?"), the effects of this assessment
would be unconsciously registered and would then function to regulate behavior in the play interaction.

3 - Play is entirely child-directed. The child has no explicit theory of her own curriculum but is conscious of the current context.
The conscious lesson plan may only be experienced phenomenologically as a desire to engage in a certain pretense behavior.
The child will physiologically sense a "fit" between the lesson plan and the context during an active search of the environment for
affordances that will effectively train behavior. If certain objectives have not been met but developmentally the child is ready to
experience content in play, the triggers indicating a "fit" become more sensitive resulting in more abstract forms of object
substitution to enact the lesson plan. If no "fit" between the current plan and the environment is discovered, this state will also be
consciously experienced. In this scenario of implicit pedagogy, the adult does as the child directs in play. Adults may perceived
cues of readiness that guide behavior, albeit unconsciously because through selection of play behavior cues have become
invariant or standardized. Adult conscious experience in collaborative play would be centered on contextual variants. (E.g. of
child direction = chase with 2 1/2 -year-old who could not change the direction of the chase and another 2 1/2 -year-old who
refused to continue play when grandmother made the game complex by catching him from behind when he was the chaser)

Bernard Baars (personal communication) suggests a possible cue indicative of the fulfillment of a conscious objective may be
habituation. The idea is that as objectives are satisfied in learning from extracted environmental affordances, the activity or use
of the object will become boring for the child, who will move on to another activity or a more complex form of the behavior.

Glossary

Explicit pedagogy: an explicitly formulated pedagogy; more broadly, a method or plan consciously devised by an expert to
achieve a pedagogical result in a learner.

Image schema: a object and/or event schema developed through structural learning and utilized to interpret perceptions, guide
actions, and draw inferences (cf. Mandler 1992).

Scaffolding: an expert's interaction with a learner, characterized by providing just enough support for a cognitive task, that
serves to create a cognitively appropriate social learning situation. Scaffolding directs attention to important dimensions of
problems and provides a context for observational learning. (Vygotsky 1962).

Template: an evolved representation in the infant's mind, such as of a generic predator, that has inferential, emotional, sensory,
and motoric dimensions. It serves to motivate and guide pretend play and may play a role in structural learning.

 

 

Top Chase Play Home Bibliography

CogWeb