ISB2 23097 Neo-Piagetian Theories of Cognitive Development a0005 Michael F Mascolo, Merrimack College, North Andover, MA, USA Ó 2015 Elsevier Ltd All rights reserved Abstract Neo-Piagetian theories of cognitive development emerged as attempts to preserve core theoretical and empirically supported aspects of Jean Piaget’s seminal theory of intellectual development while addressing criticisms leveled against the theory Neo-Piagetian theories preserve three basic ideas from Piaget’s theory: (1) the unit of cognitive analysis is the scheme or psychological structure; (2) psychological structures undergo qualitative transformation over time; and (3) higher order structures develop through the differentiation and coordination of lower level structures After a brief discussion of similarities and differences among prominent neo-Piagetian theories, one representative approach (dynamic skill theory) is discussed in depth The discussion concludes with a description of recent advances in neo-Piagetian systems theory abspara0010 AU1 p0010 In his theory of intellectual development, Jean Piaget articu- lated a series of questions and ideas that launched the field of cognitive development Piaget’s legacy is most keenly reflected in neo-Piagetian theories of development Neo-Piagetian models emerged in the 1970s and 1980s address criticisms leveled against Piaget’s theory while simultaneously maintaining core principles (Case, 1985; Commons et al., 1998; Demetriou et al., 2010; Fischer and Bidell, 2006; Halford, 1993; Pascual-Leone, 1970) bib4 bib9 AU2 bib7 bib11 bib15 bib23 s0010 Piaget’s Theory of Intellectual Development p0015 According to Piaget, knowing is a form of acting (de Ribaupierre, 23093) The basic unit of cognitive analysis is the scheme, which refers to a structured system of action or thought Schemes function through the dual processes of assimilation and accommodation Assimilation refers to the process by which to-be-known objects are incorporated into existing schemes; accommodation reflects the simultaneous processes of modifying a scheme to incorporate the object For example, to grasp a rattle, an infant incorporates (assimilates) the rattle into her organized grasping action (scheme) while simultaneously modifying (accommodating) her scheme around the particular contours of the incorporated object p0020 Piaget maintained that the structure of a child’s schemes undergoes transformation in a series of broad-based stages over time For Piaget, stages exhibit several important properties First, each stage reflects a qualitatively distinct type of thought or action Children are not simply little adults; they think and act in fundamentally different ways Second, stages form a hierarchical progression with later stages building upon earlier ones Third, the stages form a universal and unidirectional sequence regardless of culture or the content of thought Fourth, Piagetian stages form structures d’ensemble (i.e., ‘structures of the whole’) – generic structures that have wide application to broad ranges of cognitive tasks and conceptual domains Although Piaget acknowledged the phenomenon of décalage – the finding that structurally similar abilities often develop at different times, he nonetheless held that within a stage, systems of thought form broad, integrated wholes International Encyclopedia of the Social & Behavioral Sciences, 2nd edition Piaget suggested that in infancy, schemes operate within the p0025 sensorimotor stage of development Sensorimotor schemes consist of organized systems of action on objects During this time, infants cannot form representations (images) of events without direct sensory contact Symbolic thought emerges between 18 and 24 months of age with the onset of the preoperational stage At this stage, children form representations of events (e.g., words, images) but cannot manipulate them in logical or systematic ways Children gain the capacity for pretend play and deferred imitation During the concrete operational stage (around 6–7 years), with the capacity to think logically using concrete images and representations, children can successfully perform a variety of logical tasks (conservation, class inclusion, seriation, transitivity, etc.) In the formal operational stage (adolescence onward), individuals gain the capacity to think logically using abstract ideas free from particular concrete content Although Piaget is most closely associated with his stage p0030 theory, the concept of equilibration provides the foundation of his theory Equilibration refers to an inherent, self-regulating, compensatory process that motivates the construction of novel patterns of thought over time Equilibrium occurs when an individual is able to assimilate an object to a scheme while accommodating the scheme to the object Disequilibrium occurs when assimilation and accommodation fail; a mismatch arises between object and scheme Disequilibrium prompts reorganization (differentiation and integration) of schemes in an attempt to restore equilibrium For example, recognizing an object as a bunny involves assimilating a rabbitlike object into an existing bunny scheme Although initial attempts to assimilate a kitty into the bunny scheme may be successful, eventually, such attempts will fail as children sense the conflict between the kitty’s features and their representation of a bunny One way to restore equilibrium involves differentiating the initial bunny scheme into two separate schemes – one for bunnies and one for kitties Developmental change occurs through equilibration Critiques of Piaget’s Theory s0015 Table describes eight critical issues that have emerged with p0035 regard to Piaget’s theory Regarding Piaget’s stage theory, Demetriou (2006) stated, “whenever a replication study http://dx.doi.org/10.1016/B978-0-08-097086-8.23097-3 AU3 Four neo-Piagetian theories Problem Pascual-Leone Case Fischer Demetriou Unit of psychological analysis Figurative and operative schemes basis in action and internalized action Difficulty specifying scheme independent of task; task ability changes with task First-order subjective operators (schemes) and second-order metasubjective operators Executive control structures Processing potentials Hypercognitive system Specialized structures of thought Nature of change Qualitative structural change Evidence of higher order abilities at lower stages Structures D’Ensemble Broad-based stages of structures of logicomathematical Intelligence Decalage between emerging abilities; age of emergence varies with area, task, context, etc Qualitative changes in structure; quantitative changes in working memory capacity Task analysis yields structure of actions needed to perform a given task Qualitative changes in structure; quantitative changes in working memory capacity Development organized around series of different central conceptual structures Skill: Capacity to control elements of acting, skill and feeling within particular contexts and psychological domains Qualitative and quantitative transformation of skills in context Hierarchical progression Logical skills involve hierarchical progression Predicted sequences not always hold Tied to task and nature of task sequence Universality Single universal sequence of stages Variation in particular trajectories by culture; final stages not always reached Tied to task and nature of task sequence Hierarchical progression within development central conceptual structures Different central conceptual structures develop through fixed and universal stage structures Change processes Equilibration Differentiation and integration to adapt to cognitive conflict; maturation of physical structure; active experiencing of world; social transmission of cultural knowledge Difficulty specifying how process of differentiation arises from cognitive conflict Role of affect Affect merely provides energetics of adaptive action; schemes the work of adaptive action Affect more differentiated and plays stronger role than Piaget suggested Constructive operators foster Hierarchical coordination of executive control change: Content operator structures; changes in (C) produces accommodative change working memory engendered by brain as schemes encounter development and conflict; learning operator myelinization (L) coordinates schemes into higher order units; mental energy (M) indicates central computing space; interrupt operator (I) inhibits irrelevant schemas Cognition and affect are Affect operator (A): Affective generated by different schemes activate systems that influence cognitive schemes, and each other over time vice-versa Role of context and culture Sensory and social conflict stimulates development Change context, change skill; scaffolding Change arises through dialectical exchange between organism and physiosocial context Children must have access to cultural activities to construct central conceptual structures Structural change in specialized structures of thought; quantitative change in processing potentials Specialized structures of thought (e.g., class, causality, number, space, verbal, social domains of thought) each mediated by their own symbol systems Hierarchical progression within development central conceptual structures Development tied to local domains, tasks and contexts; variation is rule rather exception; task analysis indicates structure Higher order skills build on lower level skills; multiple paths to any particular form of skill Different central conceptual Alternative pathways of structures develop through structural change in fixed and universal stage different domains, tasks, contexts, cultures, and structures individuals Change in speed of Differentiation and processing, control of coordination of lower level processing and actions into higher order representational capacity; skills; social scaffolding metarepresentation and and contextual support; symbolic individuation discontinuities in brain growth and development Affect plays central role in organizing consciousness, psychological structures and the pathways through which they develop Context and cultural tools play direct role in formation and functioning of skill Self-oriented processes generate emotional feelings Quantitative differences in processing potentials and content among cultures ISB2 23097 Piagetian principle Neo-Piagetian Theories of Cognitive Development Issue To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication t0010 Table To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development remained close to the original Piagetian conditions, the same phenomena were observed in more or less the same way at more or less the same age.” However, when researchers modified the nature or complexity of Piagetian tasks, children showed evidence of logical abilities earlier than Piaget indicated (Bryant and Trabasso, 1971) Research shows that children often pass structurally similar tasks at different ages (e.g., mass is conserved before volume; Gelman and Baillargeon, 1983) Studies show that children function at higher levels when provided with contextual support than in the absence of support (Fischer et al., 1993; Vygotsky, 1978) Cross-cultural research indicates variation not only in the age at which children are able to perform Piagetian tasks, but also in the form of thinking itself (Saxe, 1991) Other theorists suggested that Piaget’s concepts of assimilation and accommodation were vague and difficult to assess (Klahr and Wallace, 1976) Still others suggested that the theory failed to account for the importance of affect (Fischer et al., 1990) and language (Matusov and Hayes, 2000) in the process of development and that (3) higher order forms of psychological structure arise through the differentiation and hierarchical coordination of lower level schemes Table and Figure show similarities and differences among prominent neo-Piagetian approaches bib3 Pascual-Leone’s Theory of Constructive Operators bib13 AU4 Juan Pascual-Leone (1970) launched the traditional of neo- p0045 Piagetian theories Drawing on information processing psychology, Pascual-Leone proposed his theory of constructive operators (see 23082; 23083) Pascual-Leone differentiated two basic categories of operations These include subjective operators (akin to Piagetian schemes) and metasubjective operators In any given situation, a variety of first-order operative and figurative (content) schemes are activated In the traditional conservation task, activate schemes for understanding height and width of the beakers, the fluidity of liquid, and so forth The multiplicity of schemes sets the stage for the production of cognitive conflict For example, a child may notice that when pouring water from a tall and thin beaker to a short and wide one, the amount of water appears to change Metasubjective operators are second-order processes that operate on first-order operators (schemes) Pascual-Leone differentiated a series of metasubjective operators, the most prominent including the Content (C), Learning (L), Mental Energy (M), and Interrupt (I) operators (Other operators include the Content (C), Space (S), Field (F), and Affect (A) operators.) Metasubjective operators function to bib26 AU5 bib25 bib18 bib12 bib22 s0020 Neo-Piagetian Models of Development p0040 Neo-Piagetian models of development preserve three core aspects of Piaget’s theory: (1) knowing involves the invocation of schemes or psychological structures; (2) that psychological structures undergo qualitative transformation in development; 20–23 e+7 AU14 f0010 Figure e PascualLeone B A A1 A2 B1 B2 Substage (5–7 years) A B Substage A1 B1 (3.5–5 years) A2 X B2 A or B B1 B2 Substage (1.5– years) A B systems (18–24 months) Substage A1 B1 A or B (12–18 m) A2 X B2 Sensorimotor systems (12–13 months) Substage (4–8 m) A B Substage (1–4 m) A or B Case Abstractmappings (14–15 years) Proportional / = x /8? reasoning (11–12 years) Single abstraction Simple math Dimensionalization (length, relations weight); counting on (add) (9–10 years) Quantitative Conservation dimensions (7–8 years) Coordination of proto-quantitative dimensions (5–6 years) Proto-quantitative dimensions (3–4 years) Representational mappings (3.5– years) A1 A2 B1 B2 Algebraic Which is bigger: reasoning 4/5 or 7/8? (13–14 years) If x = 3n + & n = 4, x=? Representational systems (6–7 years) Substage (2–3.5 years) Substage A1 (8–12 m) A2 Generalized If x = y + z and variables x + y + z = 20, (15–16 years) specify x Abstract systems (17–18 years) System of representational systems (10–11 years) Representations Dimensional Substage (7–9 years) System of sensorimotor Sensorimotor actions Substage (11–13 years) Single representation Understands increasing < > decreasing, cardinality, ordinality Recite numbers, absolute (big) and comparitive (bigger/smaller) judgment Infant Core (0-2 yrs) Sensorimotor mappings (7–8 months) System of reflex systems (4 months) Reflex systems (12–13 weeks) Reflexes e+k Interrelational e+2 e+1 B1 B2 Substage A1 B1 (9–11 years) A2 X B2 A or B e+3 7? A1 Substage (13–15.5 years) A2 Abstractions e+6 e+5 e+4 Sensorimotor Months Age Years 10–11 18 12 11 10 Abstract dimensional 17–18 14–16 Abstract principles (21–23 years) A1 B1 Substage (15.5–19 years) A2 X B2 Reflex mappings (7–8 weeks) Single reflexes (3–4 weeks) Fischer s0025 bib23 Single act Infant core Subitizing, iconic (0–2 years) encoding Number Class Cause Space domains Verbal Demetriou Social AU6 To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development create new schemes in order to resolve contradictions among competing schemes For example, the C operator adjusts the content of schemes to accommodate to novel experience The L operator creates higher order schemes by coordinating two or more activated schemes (e.g., coordinating schemes for judging height and width into an understanding that changes in height are compensated by changes in width) The I operator inhibits the activation of schemes that are irrelevant to a given task (e.g., inhibiting the tendency to rely on perceptual differences in height to make judgments about volume in the conservation task) These operators work together adaptively in the context of cognitive conflict to construct novel schemes that function to resolve cognitive contradiction p0050 Perhaps the most frequently invoked construct proposed by Pascual-Leone is the concept of mental energy or M space M places a limit on the amount of information that can be held in mind at any given time Pascual-Leone proposed that maturation of the capacity of the M operator is the primary source of cognitive developmental change (see 23064) In development, increases in M capacity allow children to hold increasing numbers of schemes in mind while performing cognitive tasks According to Pascual-Leone and Johnson (1991), between birth and years of age, sensorimotor M space (e) increases by one scheme every months For symbolic schemes, the capacity of the M operator (k) increases by one scheme every years from 3- to 15-years of age Thus, as indicated in Figure 1, total M space is calculated as the sum of M space required for sensorimotor (e) and symbolic (k) schemes (M ẳ e ỵ k) p0055 To understand developmental changes in children’s task performance, it is necessary to understand the nature and number of schemes that children must hold in mind in order to perform different types of tasks To achieve this goal, a researcher can perform a task analysis, which involves identifying the component operations and representations required to complete a task Having performed a task analysis, a researcher can identify the number of schemes necessary to perform the task successfully Developmental change does not occur in a holistic, stagelike matter At any given point in time, a child’s cognitive abilities are defined by a child’s available schemes, the capacity of M space, and the cognitive demands of particular tasks bib24 s0030 Case’s Staircase Model bib4 AU7 include the sensorimotor (birth to 18 months), interrelational (1½–5 years), dimensional (5–11 years), and vectoral (or abstract dimensional) stages (11 years through adulthood) Within each stage, control structures develop through four levels: predimensional, unidimensional, bidimensional, and integrated bidimenional The substages develop in a cyclic and iterative way in that the last substage within each stage (the integrated bidimensional substage) corresponds to the first substage (predimensional) of the next broad stage of thought (The cyclic nature and development of executive control structures will be explained further in the discussion of Fischer’s (1980) dynamic skill theory.) Case proposed that developmental progressions are organized around different central conceptual structures (Case et al., 1996) These consist of “networks of semantic nodes and relations that have an extremely broad (but not system-wide) domain of application” (Case et al., 1996: p 5) Central conceptual structures organize a suite of executive control structures around a common core Case and his colleagues amassed evidence for the existence of a series of central conceptual structures, including those for quantity, space, social relations, narrative, motor action, and music Like Pascual-Leone, Case held that changes in attentional p0065 capacity are responsible for stage progression Case suggests that processing capacity involves the integration of two basic components: operating space and short-term storage space Operating space refers to the capacity required to execute goal-related operations Short-term memory space corresponds to the number of representational schemes on which an individual can focus in a single act of centration For example, the act of counting the number of items on a grocery list is composed of two integrated components: the goal-related operations corresponding to counting each item, and the monitoring of representations that arise from successive counts (‘1 item,’ ‘2 items,’ etc.) Counting acts require operational space whereas the monitoring the representational outcomes requires short-term storage space Case held that total processing capacity (i.e., operating space plus short-term storage space) does not change in ontogenesis Instead, he suggested that the ability to execute operations becomes increasingly efficient over time, which frees processing space for short-term storage Case suggested that increasing efficiency of executive operations results from changes in brain structures that mediate the processing of information, as well as increasing myelinization of neuronal axons bib10 bib6 bib6 bib5 p0060 Case’s (1985, 1992) model of cognitive development builds upon and extends Pascual-Leone’s approach Case’s model contains three main components: The theory of executive control structures, the invocating of working memory capacity as the source of conceptual change, and developmental change organized around central conceptual structures For Case, the primary unit of thinking is the executive control structure, which consists of “an internal mental blueprint, which represents a subject’s habitual way of construing a particular problem situation, together with his or her habitual procedure for dealing with it” (Case, 1985: p 68.) The concept of executive control structure incorporates both the figurative and operative aspects of thinking into a single structure Similar to Piaget, Case proposed that executive control structures develop through four basic stages As indicated in Figure 1, these bib4 Halford’s Relational Complexity Model bib15 s0035 bib17 Halford’s (1993; Halford et al., 2012) relational complexity p0070 model of cognitive development is based on the idea capacity limitations in working memory are not simply a function of the number of representational units that can be retained at any given time, but instead reflect the complexity of the relations between representational units Halford’s relational complexity metric is defined in terms of arguments and relations, and can be represented as follows: RELATION (argumenti, argumentj, etc.) Binary relations include relations between two arguments; ternary relations involve three arguments; quaternary relations involve four interrelated arguments, and so forth For example, the relation LARGER-THAN (dog, cat) expresses the binary To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development relation ‘dog is larger than cat’; the ternary relation ADDITION (1, 3, and 5) indicates an additive relation between three numbers Halford and his colleagues have assessed children’s capacity to perform different types of representational tasks (e.g., transitivity, class inclusion, hierarchical classification, cardinality, etc.) that vary in relational complexity They found that relational complexity was directly related to the age of acquisition of target skills (Andrews and Halford, 2002) Halford has shown that unlike performance on Piagetian tasks, (which show decalage in different conceptual domains) children acquire the capacity to perform tasks at the same level of relational complexity at the same time, regardless of domain or task variables (Halford and Andrews, 2006) Halford’s relational complexity theory is not a stage theory in the sense of Piaget’s theory Instead, like PascualLeone’s theory, Halford is able to track gradual developmental changes in children’s thinking by identifying the relational complexity of the tasks that they are able to perform However, like Case’s (1985) theory, Halford’s theory predicts that tasks reflecting the same level of relational complexity will be passed around the same age bib1 bib16 bib4 capacities include processing speed, control of processing, and storage Processing speed refers to the tie needed for the system to process the meaning of information; control functions regulate the activation and inhibition of relevant and irrelevant information in any given task Storage is mediated by a multidimensional system for retaining and operating on information in real time Baddeley’s (2012) Information is retained in specialized information processing buffers (e.g., phonological, visual) where they are operated on by central executive processes Demetriou suggests that each of these three systems p0080 undergoes systematic change in development Specific domains of thought (structural systems) undergo qualitative change in accordance with Case’s (1985) model To illustrate, developmental changes in the quantitative structural system are indicated in Figure Hypercognitive processes also change For example, children under the age of about 7–8 years show limited awareness of the nature and functioning of their own psychological processes After about 7–8 years, children use their awareness increasingly of their psychological states to predict, plan, and regulate their thinking and acting Finally, core capacities show steady change over time Demetriou and his colleagues (Demetriou and Mouyi, 2011) have shown that core capacities (processing speed, control processing, and information storage) increase systematically with age While such provide the broad resources for the construction of higher order thought structures, the processes of metarepresentation and symbolic individuation mediate their actual construction Metarepresentation processes identify and abstract similarities between mental experiences (integration); symbolic individuation processes tag novel mental experiences (differentiation) bib2 AU8 bib4 bib8 s0040 Demetriou’s Analysis of the Developing Architecture of Mind bib9 p0075 For over 25 years, Andreas Demetriou et al (2010) have worked toward a comprehensive model of the architecture of the developing mind As indicated in Figure 2, Demetroiu suggests that the human ‘mind’ is organized into three levels of interacting systems: Specific structural systems, hypercognitive systems, and core capacities Specific structural systems consist of organized domains of representation and operational abilities and are constituted by different symbol systems These include categorical, verbal, quantitative, causal, spatial, and social systems of operations Hypercognitive systems consist of systems of higher order control structures (sometimes called metacognitive structures) that govern self-understanding, selfmonitoring, and self-regulation Hypercognitive processes map elements of specific structural systems onto each other in the constructive integration of everyday activity Core Dynamic Skill Theory: A Neo-Piagetian System Model Psychological Development s0045 The discussion now turns to an in-depth illustration how neo- p0085 Piagetian theory – in particular, Fischer’s dynamic skill theory (Fischer, 1980; Fischer and Bidell, 2006; Mascolo and Fischer, in press) – accounts for structural changes in psychological development In Fischer’s (1980) approach, a skill refers to an individual’s capacity to control elements of thinking, feeling, and acting within specified contexts and within particular task domains As in Case’s (1995) theory, a skill is a type of control structure; it refers to the configuration of action over which an individual exerts control within a given context The concept of skill differs from the Piagetian notion of scheme Unlike the concept of scheme, skills are not properties of individuals Instead, they are properties of individuals-within-contexts Changes in context typically result in change in behavior, and vice-versa Action is always a joint product of person and context Contexts differ in how they contribute to individual activity p0090 Skill theory differentiates three types of contexts: Low support, high support, and scaffolding By orienting attention to important features of a task, high support contexts support the production of a person’s optimal level of functioning – the highest level one can perform on one’s own In low support contexts, individual operate at their everyday functional levels, typically several levels lower than their optimum For example, students who are able bib10 bib11 bib21 bib10 Hypercognitive systems Developmental levels Builds models of all other aspects of mind; maps lower level structures onto each other f0015 Figure Core capacities (speed, span, control) Specific structural systems (verbal, numerical, social ) Abstract Dimensional Interrelational Sensorimotor AU9 To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development to understand complex ideas while attending a lecture (high support) often find that their understanding declines when studying at home (low support) This occurs because at home, students not benefit from the support of a lecture to orient their attention toward central ideas p0095 A third type of context provides individuals with scaffolding Scaffolding occurs when a more accomplished individuals break down, structure, direct and assist a less expert person in completing a task (Mascolo, 2005) Scaffolding differs from high support Under conditions of scaffolding, another person carries part of the load of a task; in high-support situations, individuals complete tasks on their own, albeit under conditions that orient attention Under scaffolded conditions, individuals perform at levels that exceed their optimal levels, thus fostering learning and development (Vygotsky, 1978) (see 23094; 23098) p0100 A second way in which the concept of skill departs from Piagetian theory is that skills are not general structures There are no general, decontextualized or all-purpose skills Skills that operate within different conceptual domains (e.g., conservation, classification, reading words, social interaction, etc.) develop somewhat independently and at different rates Development in domain (e.g., conservation) does not necessarily predict development in other domains (e.g., classification), or even in conceptually similar tasks (conservation of number vs conservation of volume) It is only possible to track developmental sequences for particular skills within particular domain, social contexts, and assessment conditions bib20 bib26 s0050 The Web of Development p0105 Given the above, it follows that individuals never operate at any single level of development Instead, they operate within a developmental range – a series of levels that vary with task, domain, context, emotional state, and so forth Given such dynamic variation, there can be no broad-based stages of development It is thus not helpful to think of a person or a person’s abilities as being ‘in a stage’ of development Development does not move through a series of fixed steps; development operates more like a constructive Web As indicated in Figure 3, a constructive Web is composed of multiple converging and diverging pathways or strands Such strands can represent the developmental courses of different individuals, different domains of thought in groups of children, or different domains of skill within the same individual (e.g., writing, arithmetic, social skills) Within particular individuals, skills in different domains develop along different pathways For example, writing and arithmetic skills tend to develop along relatively independent pathways However, skills for responding in writing to math problems require convergence among different reading, writing, and arithmetic skills s0055 Tracking the Development of Psychological Structures p0110 Skills develop through the hierarchical coordination of lower level action systems into higher order structures Figure presents the levels of hierarchical organization of a developing skill based on Fischer’s dynamic skill theory (Fischer, 1980; Fischer and Bidell, 2006) Skills develop iteratively through four broad tiers: Reflexes consist of innate action elements (e.g., sucking bib10 bib11 Scaffolded level Optimal level Functional level Development Figure f0020 a nipple placed in the mouth; see 23137); sensorimotor actions refer to acquired actions directed toward objects (e.g., reaching for a seen ball) Representations consist of symbolic meanings about concrete aspects of the world (e.g., ‘Eating candy is fun’); abstractions consist of higher order representations of intangible and generalized aspects of the world (e.g., “Conservation is the idea that the quality of something remains the same despite a change in appearance”) Within each broad tier, skills develop through four levels: A single set refers to a single organized reflex, action, representation, or abstraction Mappings refer to coordinations between two or more sets, whereas systems consist of coordinations of two or more mappings A system of systems arises from the intercoordination of at least two systems and is the equivalent of the first level of the next broad tier of skills For example, a system of sensorimotor systems creates a single representational set Dynamic skill theory identifies four broad qualitatively distinct tiers comprising a total 13 specific levels s0060 Development in Infancy Development in infancy spans two broad developmental tiers – p0115 reflexes and sensorimotor actions (see 23071) Reaching for objects is an example of a sensorimotor action After a series of levels of prereaching develop during the reflex tier, beginning at around 15–17 weeks of age, infants enter the sensorimotor tier of development As a result, they gain the capacity to construct single sensorimotor actions Sensorimotor actions consist of controlled actions on objects in the environment Using sensorimotor actions, in high support contexts, an infant can produce the first successful reaches toward objects When posture is supported, an infant can direct arm movements toward a seen object, grasp a toy placed near her hands, or move a grasped toy toward her mouth Such single sensorimotor acts are represented as follows (Figure 4): Beginning around 7–8 months of age, infants gain the p0120 capacity to bring together two sensorimotor acts into AU10 To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development Reach Toy Grasp Move Toy (diffuse) Toy to mouth Glass Tall Glass Short or Glass Glass Thin Wide f0045 Figure f0025 Figure Reach Grasp Object Object Tall Short Glass Glass Thin Wide f0030 Figure Figure To point Front of toy Turn Look To point Back of toy f0035 Figure Bear at point Bear at point Grasp Look Bear at point Bear at point Leg Position Move Forward Leg Position Bear walk f0040 Figure a sensorimotor mapping At this level, an infant is able to fully coordinate distinct acts of looking and reaching into a seamless action In so doing, an infant can reach for an object to grasp it, or reach for an object in order to look at it (Figure 5) p0125 At this level, infants can reroute their reaches around barriers placed between themselves and target objects If an adult tries to block a child’s reach, he can redirect the reach around the obstacle Beginning around 11–12 months of age, infants are able to coordinate two sensorimotor mappings into a sensorimotor system (S3) In so doing, infants can coordinate multiple acts of looking and reaching in order to explore an object from a variety of angles Such coordinations are the equivalent of Piaget’s concept of tertiary circular reaction (Figure 6) s0065 Development through the Representational Tier p0130 Beginning around 18–24 months of age, children gain the capacity to coordinate two sensorimotor systems into a system of sensorimotor systems, which is the equivalent of the first level of the next tier of development – single representational sets Using single representations, children form symbolic meanings in the absence of their referents For example, using single representations, a child can pretend that a teddy bear can walk In so doing, a toddler can use one sensorimotor system of actions (e.g., holding and moving the teddy bear) to regulate a second such system (e.g., making the bear move forward) in order to represent the symbolic act of walking (Figure 7) f0050 Single representations take different forms in many p0135 different modalities (e.g., pretend play, imagery, word use) Single representations are the rough equivalents of a single declarative sentence Beginning around ½ to years of age, children gain the capacity to coordinate two single representations into a representational mapping At this level, children begin to represent different relations between ideas (e.g., cause/ effect; before/after; bigger/smaller; part/whole; reciprocity, and so forth) For example, children can compare the relative height of liquid poured into two glasses or the relative width of liquid poured into two glasses, but cannot keep both in mind simultaneously Given a tall thin glass and a short wide glass filled with the same amount of liquid, a child can correctly indicate that the liquid in one glass is higher or wider than the other (Figure 8) By 6–7 years of age, children can begin to coordinate two p0140 representational mappings into a seamless representational system At this level, a child can hold in mind a relationship between two relationships In the traditional Piagetian conservation task, children are able to relate one representational mapping for comparing changes in height from tall to short to another mapping connecting changes from in width from thin to wide (Figure 9): Using this structure, children solve the conservation task by p0145 understanding that the amount of liquid remains the same in both glasses because changes in the height of the liquid in the glasses are compensated for by changes in width Developing through the Abstract Tier s0070 Throughout the representational tier, a child’s thinking remains p0150 concrete Beginning around 10–11 years of age, in high support contexts, preteens gain the capacity to abstract what is common across multiple representational systems and coordinate them into a single abstraction Using a single abstraction, a youth can represent intangible aspects of a single idea free from concrete content For example, a teen can generalize across commonalities between conservation of mass and conservation of volume tasks to construct an abstract (content free) understanding of conservation: Despite a change in appearance, the quality of a phenomenon remains the same (Figure 10) Abstractions develop through the same iterative process that p0155 occurred in previous tiers (see 23024) Around 14–15 years of age, using abstract mappings, a teen can hold in mind the relationship between two abstractions For example, a teen To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development Tall Long Ball Sausage Wide Thin Conservation Quality stays same despite change in appearance Tall Short Glass Glass Wide Thin epigenetic one, the role he assigned to the environment was rather limited In postulating a universal stage sequence, Piaget did not allow that schemes could develop in significantly different ways in different sociocultural contexts According to contemporary epigenetic systems models of development, different developmental pathways self-organize as a product the interplay among diverse aspects of the person– environment system over time (Gottlieb, 2002; van Geert, 2000) One such model of the person–environment system is displayed in the top panel of Figures 4–12 (Mascolo and Fischer, in press) In this model, psychological structures are the emergent product of coactions that occur among systems that operate both within and between individuals The integrative organization of individual action is indicated in the left panel of Figure 13 In any given context, (1) nonconscious appraisals of one’s relation to one’s environs (e.g., judgments of danger, goal blockage) generate (2) emotional feelings (e.g., fear, frustration) and (3) action tendencies (flee, fight) Thereupon, emotional feelings (4) provide feedback that amplifies the importance of appraised events and selects them for (5) conscious awareness within working memory In this way, psychological structures that operate in working memory arise from the interplay of nonconscious cognitive and emotional processes (see 25003; 24058; 25007) Thus, although psychological structures regulate action, they not so autonomously; they selforganize as a product of the dynamic interplay among processes that operate both within and between individuals (see 23122) To illustrate the emergent self-organization of psychological p0175 structures in real time, consider two brothers engaged in parallel play After B referred to L as his ‘little brother,’ the following interaction occurred: bib14 f0055 Figure 10 bib21 Kinetic energy Transformed into Potential energy f0060 Figure 11 Matter contained in objects Mass Can be converted to energy e = mc2 Capacity to work Energy Can be converted to mass f0065 Figure 12 can represent the concept of conservation in terms of the inverse relationship between the loss of kinetic energy is lost (e.g., the slowing of the velocity of a ball thrown into the air) and the gain in potential energy (gravitational potential) (Figure 11) p0160 Using abstract systems, 17- to 18-year-olds begin to coordinate two abstract mappings into an abstract system At this point, for example, a youth can represent relationships between two abstract aspects of one concept and two abstract aspects of another One can, for example, represent the concept that matter can neither be created nor destroyed in terms of Einstein’s principle relating the abstract concepts of energy and matter (e ¼ mc2) (Figure 12) p0165 The final level of skills emerges in early adulthood with the capacity to coordinate two or more abstract systems into abstract principles – highly abstract representations that organize multiple abstract ideas and large bodies of knowledge Such skills only arise in individuals with extensive experience in particular domains of activity (e.g., advance training in a discipline) u0010 L: (Playing) No I’m not a little brother I’m big B: (Gently) I know you’re not little, but (in a slightly sing-song u0015 ‘teaching’ voice) you’re When someone is younger than another brother, they call that a little brother L: Oh (Slightly whining) I’m not (with rising intonation) little u0020 (looks toward O) The bottom panel of Figures 4–12 shows the emergent p0195 structure of thinking, feeling, and acting as it operated both within and between the two brothers The left and right panels identify the structure of B’s and L’s activity, respectively For each boy, the diagram identifies (1) the appraisal that organized affective and cognitive activity, (2) the emotional expressions produced by the appraisal, and (3) the structure of the child’s skilled action The symbol between the two panels identifies the ways in which the boys adjusted their behavior in relation to each other In this situation, the little brother’s slightly sad complaint that “I’m not little; I’m big” operated at the level of representational mappings (Fischer’s, 1980) Responding empathically to the little boy’s plea, the big brother modified the affective quality of his action, and, operating at the level of representational systems, attempted to console his brother As indicated in this example, psychological structures are not isolated cognitive systems encapsulated within discrete individuals Instead, they are integrative structures of thinking, feeling, and action that self-organize as interlocutors adjust their processes to each other over time bib10 s0075 Recent Advances: The Dynamic Self-organization of Integrative Psychological Structures p0170 Epigenesis refers to the idea that psychological and behavioral structures emerge in development as a product of dynamic coactions between genes and a series of nested environments Genes and environment are inseparable as causal processes in development Although Piaget’s equilibration model is an AU11,12 To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo-Piagetian Theories of Cognitive Development Person–environment system (e) Physical and sociocultural context Conscious meanings (b) Object Appraisal Events Motives Action tendency Emotional feeling (d) (c) Mutual regulation (a) Other’s action Action Skill structure Motive-relevant appraisal Emotional expression You’re not little Want to be big Me You Big brother Motive Be big brother Gaze Play Brother - Little brother Face Neutral Event You are sad Voice Soothing Direct Assert Me Me Not a little brother I’m big Motive Be seen as big - Event B says I’m little Gaze Face Voice Shift to high Wide eyes Play Brother Little brother Big brother Structure of dyadic action f0070 Figure 13 s0080 Psychological Structures Are Dynamic Constructions p0200 Psychological structures self-organize in both real and developmental time To say that they self-organize implies that there is no single, fixed or isolated genetic, psychological or sociocultural plan that directs the course of development The pathways of development are neither fixed nor predetermined Instead, they emerge over time as a product of richly interactive person–environment interactions Novel skills coevolve with the formation of novel forms of cultural life Rather than thinking of development in terms of fixed pathways, it is better to think of developmental pathways themselves as emergent outcomes That is, while we sometimes walk along pathways that have already been paved for us, in development, we typically forge our own unique paths as we walk See also: 23093; 23082; 23083; 23064; 23094; 23098; 23137; 23071; 23024; 25003; 24058; 25007; 23122; 61107; 92013; 61134; 92016 Bibliography Andrews, G., Halford, G.S., 2002 A cognitive complexity metric applied to cognitive development Cognitive Psychology 45, 153–219 Baddeley, A., 2012 Working memory: theories, models, and controversies Annual Review of Psychology 63, 1–29 Bryant, P.E., Trabasso, T., 1971 Transitive inference and memory in young children Nature 232, 456–458 Case, R., 1985 Intellectual Development: Birth to Adulthood Academic Press, New York Case, R., 1992 The Mind’s Staircase: Exploring the Conceptual Underpinnings of Children’s Thought and Knowledge Erlbaum, Hillsdale, NJ Case, R., Okamoto, Y., Griffin, S., McKeough, A., Bleiker, C., Henderson, B., Stephenson, K.M., 1996 The role of central conceptual structures in the development of children’s thought Monographs of the Society for Research in Child Development 61, 1–2 Serial No 246 Commons, M., Trudeau, E., Stein, S., Richards, F., Krause, S.R., 1998 Hierarchical complexity of tasks shows the existence of developmental stages Developmental Review 18, 237–278 Demetriou, A., Mouyi, A., 2011 Processing efficiency, representational capacity, and reasoning: modeling their dynamic interactions In: Barrouillet, P., Gaillard, V (Eds.), Cognitive Development and Working Memory: A Dialogue between NeoPiagetian Theories and Cognitive Approaches Psychology Press, New York, NY, US, pp 69–103 Demetriou, A., Spanoudis, G., Mouyi, A., 2010 The development of mental processing In: Overton, W.F., Lerner, R.M (Eds.), The Handbook of Life-span Development, Cognition, biology, and methods, vol John Wiley & Sons, Hoboken, NJ, pp 306–345 Fischer, K.W., 1980 A theory of cognitive development: the control and construction of hierarchies of skills Psychological Review 87, 477–531 Fischer, K.W., Bidell, T.R., 2006 Dynamic development of psychological structures in action and thought In: Lerner, R (Ed.), Damon, W (Series Ed.), Handbook of Child Psychology, fifth ed vol Theoretical Models of Human Development, Wiley, New York Fischer, K.W., Shaver, P.R., Carnochan, P., 1990 How emotions develop and how they organise development Cognition and Emotion 4, 81–127 Gelman, R., Baillargeon, R., 1983 A review of some Piagetian concepts In: Flavell, J.H., Markman, E (Eds.), Cognitive Development, Handbook of Child Development, vol John Wiley, New York, pp 167–230 To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter TNQ Books and Journals Pvt Ltd It is not allowed to publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 10 Neo-Piagetian Theories of Cognitive Development van Geert, P., 2000 The dynamics of general developmental mechanisms: from Piaget and Vygotsky to dynamic systems models Current Directions in Psychological Science 9, 64–68 Halford, G.S., 1993 Children’s Understanding: The Development of Mental Models Erlbaum, New York Halford, G.S., Andrews, G., 2006 Reasoning and problem solving In: Kuhn, D., Siegler, R (Eds.), Handbook of Child Psychology: Cognitive, Language and Perceptual Development, sixth ed., vol John Wiley & Sons, Hoboken, New Jersey, pp 557–608 Halford, G.S., Andrews, G., Wilson, W.H., Phillips, S., 2012 Computational models of relational processes in cognitive development Cognitive Development 27, 481–499 Klahr, D., Wallace, J.G., 1976 Cognitive Development: An Information-Processing View Lawrence Erlbaum, Oxford England Mascolo, M.F., 2013 Developing through relationships: a coactive systems framework In: Lerner, R., Benson, J (Eds.), Embodiment and Epigenesis: Theoretical and Methodological Issues in Understanding the Role of Biology within the Relational Developmental System Elsevier, New York Mascolo, M.F., 2005 Change processes in development: the concept of coactive scaffolding New Ideas in Psychology 23, 185–196 Mascolo, M.F., Fischer, K.W Dynamic development of structures of thinking, feeling and acting, In: Overton, W., Molennar, P (Eds.), Handbook of Child Psychology and Developmental Science vol Theory and Method, John Wiley, New York, in press Matusov, E., Hayes, R., 2000 Sociocultural critique of Piaget and Vygotsky New Ideas in Psychology 18, 215–239 Pascual-Leone, J., 1970 A mathematical model for the transition rule in Piaget’s developmental stages Acta Psychologica 32, 301–345 Pascual-Leone, J., Johnson, J., 1991 The psychological unit and its role in task analysis A reinterpretation of object permanence In: Chandler, M., Chapman, M (Eds.), Criteria for Competence: Controversies in the Assessment of Children’s Abilities Eribaum, Hillsdale, NJ, pp 153–187 Saxe, G.B., 1991 Culture and Cognitive Development: Studies in Mathematical Understanding Erlbaum, Hillsdale, NJ Vygotsky, L.S., 1978 Mind in Society Harvard University Press, Cambridge, MA AU13 ... bib12 bib22 s0020 Neo- Piagetian Models of Development p0040 Neo- Piagetian models of development preserve three core aspects of Piaget’s theory: (1) knowing involves the invocation of schemes or psychological... proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo- Piagetian Theories of Cognitive Development remained close to the original Piagetian. .. publish this proof online or in print This proof copy is the copyright property of the publisher and is confidential until formal publication ISB2 23097 Neo- Piagetian Theories of Cognitive Development