Thinking in Symbols: The
Development of Representation (Ch 5)
Dr. Jamie Drover
SN-3094, 864-8383
e-mail -- [email protected]
Winter Semester, 2013
Learning to Use Symbols
• Symbols: external referents for objects
and events.
• Representational Insight: Knowledge
that an entity can stand for something
other than itself.
Young Children’s Interpretation of Pictures
and Models
• DeLoache (1987) had 2- and 3-year-old children
search for a toy hidden in a room.
• Earlier, they are shown a model room that
illustrates where the toy is.
• They then have to find the toy in the room.
• Then have to find the model toy in the model
Young Children’s Interpretation of Pictures
and Models
3-year-olds possess
representational insight.
2.5-year-olds do not
Young Children’s Interpretation of Pictures
and Models
• If a picture is used instead of a scale model, 2.5year-olds show representational insight,
whereas 2-year-olds do not (DeLoache 1987).
• These findings may reflect difficulty with dualrepresentation.
• A model is its own item, worthy of its own
• When models are made less interesting,
performance changes.
Young Children’s Interpretation of Pictures
and Models
• When models were viewed through a window,
2.5 year-olds’ performance was better than on
the model task.
• When 3-year-olds were allowed to play with the
model beforehand, performance decreased.
• DeLoache et al. (1997) designed a task that did
not require dual representation.
Young Children’s Interpretation of Pictures
and Models
• “credible shrinking room studies” -- 2.5 yr olds
can succeed
– “shrinking machine” can shrink room
– shown “Terry the Troll”
– machine “shrinks” (then enlarges) Terry
Young Children’s Interpretation of Pictures
and Models
Young Children’s Interpretation of Pictures
and Models
• Standard model task – hide Terry in large room
– Room was “shrunk”
– 2.5 yr can find Terry in small room
• No need for representational link between model
and the room, instead -- large and small room
believed to be the same thing
– no dual representation needed
Young Children’s Interpretation of Pictures
and Models
• Even an 18 month-old will show basic symbolic
• But this is not necessarily dual representation.
• DeLoache et al. (1998) presented pictures to 9
to 19 month-old children from the US and the
Ivory Coast.
• The youngest children treated them as objects.
Young Children’s Interpretation of Pictures
and Models
• By 19 months of age, they realized the picture
represented something else.
The Appearance/Reality Distinction
• The knowledge that the appearance of an object
does not necessarily correspond to its reality.
The Appearance/Reality Distinction
• De Vries (1969) studied qualitative identity
– Children were familiarized with a trained cat.
– The cat was then fitted with a dog mask.
– 3-year-olds believed the mask changed the identity of
the cat.
• Flavell (1986) poured white milk into a red glass
while young children were watching.
• Showed children a sponge that looked like a
The Appearance/Reality Distinction
• They were asked what does it look like to your
eyes right now?
• Asked, what is it, really and truly?
• Made two kinds of errors.
• Phenomenism errors: said milk was really and
truly red.
• Intellectual realism: Said the fake rock looked
like a sponge.
The Appearance/Reality Distinction
• Young children’s poor performance on
appearance/reality distinction tasks is
surprisingly pervasive.
• Might stem from problems with dual encoding.
• They have trouble representing an object in
more than one form at a time.
Jean Piaget
• A Swiss philosopher/psychologist
first trained as a biologist.
• Has had the greatest impact on
developmental psychology.
• Emphasized the role of children in
• Children are not incomplete
– Think differently, qualitative
Assumptions of Piaget’s Theory
• We develop in discrete stages.
• Cognitive development is through a series of
– But underlying functions are continuous.
• Mechanisms of cognitive development are
domain-general (homogeneity of function).
Assumptions of Piaget’s Theory
• Children are not passive creatures, they are
intrinsically active and possess an innate
curiosity and seek stimulation.
– The motivation for development is within the child.
– They are primarily responsible for their own
Assumptions of Piaget’s Theory
• Cognition is a constructive process.
• We interpret the world through our own personal
perspective, ie, through what we already know.
– Constructivism
• Children at different levels construct different
The Constructive Nature of Cognition
• They come to know objects by acting on them –
action schemes.
• Scheme: the basic unit of knowledge.
• These action schemes become internalized –
operations or operational schemes.
Functional Invariants
• Processes that characterize
all biological systems
(including intelligence) and
operate throughout the
• Organization: Through
organization, every
intellectual operation is
related to all other acts of
– Structures/schemes are not
independent, but are
– Domain general
Functional Invariants
• Adaptation: the organism’s ability to adjust its
structures to environmental demands.
• Assimilation: the incorporation of new
information in already existing schemes.
• Accommodation: a current scheme is changed
to incorporate new information.
Assimilation and Accommodation
• Knowledge is constructed by these processes.
• Every act of intelligence involves both.
– One may predominate over the other.
– Play, imitation
• The organism’s attempt to keep its cognitive
structures in balance.
• When information does not match current
schemes, disequilibrium results.
• Achieved through alteration of cognitive
structures (e.g., accommodation).
• The child may also assimilate.
Stages of Development
• The order of the stages are invariant and
culturally universal.
• Development is epigenetic
– Based on bidirectional interactions between structure
and function.
– Later development is based on earlier development.
– New structure is a transformation of an earlier one.
The Sensorimotor Stage
• Birth to 2 years.
• Intelligence is limited to one’s own actions on the
• Do not form mental representations.
– Understand only what is physically present.
• Knowledge progresses from sensorimotor to
representational thinking.
The Sensorimotor Stage
• There is a change in personal perspective.
– Learn to differentiate themselves from the external
There are six substages
1) the use of reflexes: Birth to 1 month
Use reflexes to interpret the world
They apply reflexes to objects and assimilate
them to their schemes.
The Sensorimotor Stage
Highly restricted in what they can know.
They do not behave intentionally, but can adapt.
2) Primary circular reactions: 1 to 4 months
Reflexes are extended, new patterns of behavior
are acquired.
• Can modify reflex schemes.
The Sensorimotor Stage
• Primary Circular
Reactions: the first
class of acquired
repetitive behaviors.
• Based on hereditary
• Show primitive signs
of intentionality.
The Sensorimotor Stage
• 3) Secondary Circular Reactions: 4 to 8 months.
• Not based on reflexes, but represent the first
acquired new behaviors.
• These behaviors first appear by chance.
• 4) Coordination of secondary circular reactions:
8 to 12 months.
• Show goal-directed behavior and cause and
The Sensorimotor Stage
• Coordinates secondary circular reactions.
• 5) Tertiary Circular Reactions: 12 to 18 months.
• Characterized by clear means/end
• Can alter existing schemes directly related to
obtaining a solution.
• Show increasing locomotive abilities.
• Show a peak in curiosity.
The Sensorimotor Stage
• Still cannot form mental representations.
• Solve problems through trial and error.
• 6) Invention of new means through mental
• Symbolic functioning is first seen.
• New means are invented through mental
The Sensorimotor Stage
• Show symbolic function through language,
deferred imitation, gestures, and mental
The Development of Operations
• In the three stages following the sensorimotor
stage, children can form mental representations.
• Preoperations: 2-7
• Concrete Operations: 7-11
• Formal Operations: Begins at 11
The Development of Operations
• Operations: Cognitive schemes that
describe ways in which children act on
their world.
• Mental; require the use of symbols
• Derive from action. They are internalized
• Exist within an organized system.
– All cognitive operations are integrated.
The Development of Operations
• Operations are logical and follow rules.
• Reversibility – knowledge that an operation can be
reversed. Two types:
– negation – an operation can be negated, or inverted
• (5+2 = 7; 7-2 = 5)
– compensation -- change in one dimension offset by
changes in another -- a tall thin man and a short fat
man can weigh the same
The Transition from Preoperational to
Concrete Operational Thought
• Thinking in the preoperations stage is intuitive,
lacking logic.
• More concerned with appearance than logic
• The realization that an entity stays the same
despite changes in its form.
• This is the sign that one has achieved concrete
The Transition from Preoperational to
Concrete Operational Thought
• E.g. conservation of liquid (volume).
• 5-year-olds cannot solve this problem. 8-yearolds can solve the problem and explain why.
The Transition from Preoperational to
Concrete Operational Thought
• The pre-operational child thinks intuitively.
• If the liquid is poured back into the original
container, preoperational children claim
the amounts are equal.
• This does not produce contradiction
(disequilibrium) in the preoperational child.
– But it does in older children. They will soon
The Transition from Preoperational to
Concrete Operational Thought
• Conservation does not develop simultaneously
for all properties of materials.
• Number before mass before weight before
– Note that there is heterogeneity here.
Conservation of Number
The Transition from Preoperational to
Concrete Operational Thought
• Preoperational children can not apply negation
or compensation to conservation problems.
Centration v. Decentration
• Preoperational children’s perception is centered.
• They make judgments based on the most salient
The Transition from Preoperational to
Concrete Operational Thought
• Concrete operational children are decentered.
• Can remove their attention from specific aspects
of the conservation problem and make decision
based on all dimensions.
• Centration is not limited to conservation tasks
but is found in everyday life
– Use height to estimate age
The Transition from Preoperational to
Concrete Operational Thought
• Preoperational children assume that others see
the world as they do.
• This permeates their complete cognitive world.
• Perhaps this egocentricity is adaptive.
Transition from Concrete to Formal
Operational Thought
• In early adolescence, children’s thoughts are no
longer applied to the concrete.
– Not limited to tangible facts or object
Hypothetico-Deductive Reasoning
• The benchmark of formal operations.
• They can generate hypotheses.
• Can think solely on the basis of symbols.
Transition from Concrete to Formal
Operational Thought
• Can generate ideas not yet experienced.
Thinking like a scientist
• Can think inductively.
• Go from specific observations to broad
• Hypotheses are generated then systematically
Transition from Concrete to Formal
Operational Thought
• Pendulum problem
• Given four factors that can affect pendulum speed
– String length, weight of object, height of release, force of
• Must formulate a hypothesis
• Vary a single factor while holding the others constant.
Transition from Concrete to Formal
Operational Thought
• Preoperational children can carry out the first
• Concrete operational children can’t get the right
– Can’t isolate a variable.
• Thinking About Thinking
• Can examine the content of their own thought.
Transition from Concrete to Formal
Operational Thought
• Can acquire new information from internal
• Reflective abstraction: a rearrangement, by
means of thought, of some matter previously
presented to the subject in a rough or immediate
• Adolescents demonstrate centration.
Transition from Concrete to Formal
Operational Thought
• Believe that their abstract ideas are unique to
• Adolescents are extremely self-conscious.
• Playing to an imaginary audience.
• Leads to the personal fable
– Belief in uniqueness and invulnerability.
– May explain reckless behavior
• May be adaptive by ensuring experimentation
and independence.
Transition from Concrete to Formal
Operational Thought
• It’s debatable whether adolescents or even
adults are the logical thinkers Piaget thought
they were.
• Formal operational thought is used by adults in
some contexts, but not in other.
The State of Piaget’s Theory Today
• Piaget’s theory continues to influence us today.
• But is it accurate?
• Contributions
• Founded cognitive development as we know it.
– Became task focused
• Emphasized the active role of the child.
– Constructivism
The State of Piaget’s Theory Today
• Equilibration as an explanation.
• Introduced critical concepts.
– Scheme, object permanence, egocentrism
• Provided an accurate description of
• Influence went beyond cognitive development.
The State of Piaget’s Theory Today
• Piaget’s intent was to measure competence.
• May have underestimated the competence of
– Object permanence, mental representation,
• Children can be trained to think at a higher level.
– Conservation
– May be context specific
The State of Piaget’s Theory Today
• In some cases, Piaget may have
overestimated how adults think.
– See garlic powder example (p 182; Capon &
Kuhn, 1977).
Fuzzy Trace Theory
• Piaget’s theory is not perfect.
• New forms of thinking don’t necessarily replace
older ones.
• Older children and adults can solve problems
• Dual-Processing: There are multiple ways of
knowing, or of solving problems.
Fuzzy Trace Theory
• Based on intuitionism: People think, reason, and
remember by processing inexact “fuzzy” memory
• Cognition is intuitive.
• Memory traces exist on a literal/verbatim –
fuzzy/gistlike continuum.
• People of all ages prefer to use fuzzy traces when
solving problems.
– The extent of this preference changes with age.
• Reduction to essence rule
Fuzzy Trace Theory
• Fuzzy traces are more easily accessed than
verbatim traces.
• Verbatim traces are more susceptible to
• Making responses produces output interference
that hinders performance.
– Scheduling effects: caused by serial nature
– Feedback effects
Developmental Differences
• There are changes in gist extraction.
• Young children are biased toward storing and
retrieving verbatim traces.
• A verbatim to gist shift occurs during the
elementary school years.
• Brainerd and Gordon (1994) have provided
evidence for this (p. 191).
– Preschool children showed better memories for
verbatim questions than for other questions.
Developmental Differences
• Age differences have been found in sensitivity to
output interference.
• Verbatim memory traces are more sensitive to
interference than fuzzy traces.