1. Cognitive Development Jean Piaget
Lori Hamilton October 6, 2004

2. Objectives Jean Piaget Bio Piaget’s Genetic Epistemology
The Stages of Development
The Process of Development
Criticisms of Genetic Epistemology
Alternative Perspectives on Cognitive Development
Implications for Instruction
Discussion/Q&A

3. Jean Piaget Born in Switzerland on August 9, 1896.
Published his first “paper” when he was ten.
Dedicated himself to finding a “biological explanation of knowledge”
University of Neuchâtel. 
In 1921, his first article on the psychology of intelligence was published.
Jean Piaget was born in, Switzerland, on August 9, 1896. 
His father, Arthur Piaget, was a professor of medieval literature with an interest in local history. 
His mother, Rebecca Jackson, was intelligent and energetic, but Jean found her a bit neurotic -- an impression that he said led to his interest in psychology, but away from pathology! 
As the oldest child, he was quite independent and took an early interest in nature, especially the collecting of shells. 
He published his first “paper” when he was ten -- a one page account of his sighting of an albino sparrow.
As a teen, he was encouraged by his mother to attend religious instruction, he found religious argument childish. 
Studying various philosophers and the application of logic, he dedicated himself to finding a “biological explanation of knowledge.” 
Ultimately, philosophy failed to assist him in his search, so he turned to psychology.
After high school, he went on to the University of Neuchâtel. 
In 1921, his first article on the psychology of intelligence was published in the Journal de Psychologie. 
In the same year, he accepted a position at the Institute J. J. Rousseau in Geneva. 
Where he began with his students to research the reasoning of elementary school children. 
This research became his first five books on child psychology. 
Although he considered this work highly preliminary, he was surprised by the strong positive public reaction to his work.

4. Jean Piaget
In 1923, he married one of his student coworkers, Valentine Châtenay. 
Together they had three children which assisted him in his research.
In 1955, he created the International Center for Genetic Epistemology 
Died in Geneva, September 16, 1980
In 1923, he married one of his student coworkers, Valentine Châtenay. 
They had three children, two daughters and a son.
(In 1925, their first daughter was born; in 1927, their second daughter was born; and in 1931, their only son was born.)
They immediately became the focus of intense observation by Piaget and his wife.  This research turned into three more books!
In 1955, he created the International Center for Genetic Epistemology, of which he served as director the rest of his life. 
By the end of his career, he had written over 60 books and many hundreds of articles. 
He died in Geneva, September 16, 1980

5. Conserving Numbers Piagetian assessment for number conservation.
Do I have any children in this room? Can each child introduce themselves and say how old they are?
Call on Nancy.
Two rows lined up together:
Experimenter questions the child…
E: Do both these rows have the same number of balls, or does one have more than the other?
Child: They are the same
E: How do you know?
Child: Because I counted them.
The experimenter rearranges the balls so the first row extends past the second row:
E: Do these rows now have the same number of balls or does one have more than the other?
Child: The top one has more.
Child: Because it sticks out more.
E: Count the blocks for me, would you?
Child: Count 1-4 twice
E: So are there the same number of blocks in each row?
Child: No, that one has more.

6. Is it Alive? Button Table Plants Flowers Animals
For humans, cognitive development is the transformation of the child’s undifferentiated unspecialized cognitive abilities into the adult’s conceptual competence and problem solving skill.
Between ages 4 and 10 children’s understanding of many concepts can change dramatically.
Where is my 5 year old?
Is this item Alive?
Jeremy___ who is 5 years old – says button because it holds my shirt together and a table because you can see it
Where is my 6 year old?
Wanda___ who is 6 years old – didn’t think a table is alive, but a plant isn’t alive either
Can a flower starve?
Wanda___ replies, nah, that’s silly. Only people can starve.
Is there a 10 year old in the class?
Cheryl___ who is 10 years old, judged animals and plants to be alive but not inanimate objects.
How can we account for the differences in behavior among the children described in the two scenarios?
Take Nancy in the numbers, she knows how to count and the evidence of her senses should be enough to convince her that there are the same number of balls in each row. Yet she insists they are different when one appears longer than the other.
Similarly in Is it Alive? Jeremy believes buttons are alive and Wanda believes plants are not alive.
Where did they get these beliefs?
For many psychologists, cognitive development provides these answers. “The idea of development entails the existence of an end point: the child moves, steadily or erratically, toward a goal.” (Kaplan, 1967, cited in Kessen, 1984)
For development to be understood, Sternberg suggested that two fundamental questions must be answered.
1. What are the psychologoical states that children pass through at different points in their development?
2. What are the mechanisms by which they pass from one state to another?
Siegler offered another question
1. How do changes in children’s thinking occur?
click to bring in next statement
For humans, cognitive development is the transformation of the child’s undifferentiated unspecialized cognitive abilities into the adult’s conceptual competence and problem solving skill. Jean Piaget’s theory of cognitive development remains the most complete and widely accepted view.

7. Piaget’s Genetic Epistemology
Piaget’s view was named constructivism because he firmly believed that knowledge acquisition is a process of continuous self-construction.
Knowledge is invented and reinvented as the child develops and interacts with the world surrounding him/her.
If we remember from previous weeks, what is?
*Empiricists argue that knowledge results from an accumulation of experience
*Nativists believe that the organism is born with innate set of ideas that form the basis for knowledge.
*Interpretists some of whom are also nativists, assume that all knowledge is actively constructed within the organism, rather than being received passively from the environment.
Piaget evolved a view consistent with interpretivism, that suggested a compromise between nativism and empiricism.
He labeled this view interactionism, since cognition was assumed to be an interaction between heredity and environment.
He also called his view constructivism because he firmly believed that knowledge acquisition is a process of continuous self-construction.
Knowledge is invented and reinvented as the child develops and interacts with the world surrounding him/her.
Piaget believed that children actively approach their environments and acquire knowledge through their actions.
Ex: Young infants know to suck on objects placed in their mouths, and mouth words as they learn to talk
Piaget called these goal-directed behaviors schemes and contended that schemes evolve as children develop.

8. Piaget’s Genetic Epistemology Types of Knowledge
Defined
Knowledge about the physical properties of objects
Abstract Knowledge
Knowledge made by people
How acquired
Discovered by actions of objects; objects are the source
Invented from actions on objects; actions are the source
Obtained from actions on and interactions with others; people are the source
Reinforcer
Objects
People
Examples of areas of knowledge
Size, color, texture, thickness, taste, sound, flexibility
Number, mass, area, volume, length, class, order, time
Language, moral, rules, values, culture
Logical-Mathematical Knowledge
Physical Knowledge
Social Knowledge
Physical knowledge also called empirical knowledge has to do with knowledge about objects in the world which can be gained through their perceptual properties.
In conserving numbers, Nancy knows that the balls are solid, can come in different colors and sizes.
These inherent properties of balls and children acquire knowledge of these properties by seeing and handling the balls.
Objects themselves and child’s physical actions on objects are the source of physical knowledge.
Logical-Mathematical Knowledge is abstract and must be invented, but through actions on objects that are fundamentally different from these actions enabling physical knowledge.
Ex. To acquire physical knowledge a child may pick up balls and feel it, taste it, hit another object with it, or bounce it.
But to understand two rows of balls are in some way the same when they look physically different requires a different kind of action scheme.
Physical knowledge of balls can be extended only to other balls, but conservation of number applies to balls, pennies, people or anything else. The cognitive result, of schemes enabling the invention of logical-mathematical knowledge is a coherent set of mental operations.
Social Knowledge is a culture-specific and can be learned only from other people within one’s cultural group.
Actions again hold the key to the acquisition of this kind of knowledge, action, interactions with other people.

9. Criteria for the Stages of Development
Each stage must represent a qualitative change in children’s cognition.
2. Children progress through the stages in a culturally invariant sequence.
3. Each stage includes the cognitive structures and abilities of the preceding stage.
Piaget believed children go through 4 stages.
These are the criteria for defining true developmental stages
Each stage must represent a qualitative change in children’s cognition.
ex. Children must demonstrate qualitative leaps as well, as qualitative improvements with age, which imply that changes have occurred in the underlying logical structures of cognition.
2. Children progress through the stages in a culturally invariant sequence.
This means every child passes through the stages in exactly the same order of necessity. Once a higher stage has been entered, regression to a lower stage is not possible, and all normal children reach the last stage.
3. Each stage includes the cognitive structures and abilities of the preceding stage.
The more primitive structures of early stages are not lost as a child progresses to a later stage. Each stage is more adaptive, more adequate than the one preceding it.
4. At each stage, the child’s schemes and operations form an integrated whole.
The schemes a child employs to explore her world depends upon her stage of development.
This is why one child will think a button is alive and an older child believes a plant is alive.
4. At each stage, the child’s schemes and operations form an integrated whole.

10. The Stages of Development
Typical Characteristics
Sensorimotor (birth to approx. age 2)
Modifies reflexes to make them more adaptive.
Becomes goal-directed in behavior, with goals moving from concrete to abstract.
Begins to mentally represent objects and events
Preoperational (2 to 7 years)
Acquires the semiotic function; engages in symbolic play and languages games.
Has difficulty seeing another person’s point of view, thought and communication are egocentric.
Reasons from a focus on one perceptual dimension of problems
Concrete Operational (7 to 11 years)
Performs true mental operations (conservation, reversibility) and solves concrete problems in a logical fashion.
Has difficulty thinking hypothetically and systematically considering all aspects of a problem
Formal Operational (11 years onward)
Solves abstract problems in systematic and logical fashion.
Reasons hypothetically and often develops concerns over social issues.
Sensorimotor (birth to approx. age 2)
Modifies reflexes to make them more adaptive.
Becomes goal-directed in behavior, with goals moving from concrete to abstract.
Begins to mentally represent objects and events
Characteristics of infants intelligence were physical coordination such as alertness, ability to recognize people and objects.
Babies actions are generally focused on their own bodies, sucking fingers or feet etc.
Towards the end of this phase children begin to mentally represent objects and events. They are using simple motor indicators as symbols for other events.
Ex. Piaget’s child wanted hand watch to be opened wider so she opened her mouth wider to show she wanted this.
Preoperational (2 to 7 years)
Acquires the semiotic function; engages in symbolic play and languages games.
Has difficulty seeing another person’s point of view, thought and communication are egocentric.
Reasons from a focus on one perceptual dimension of problems
Ex: Can’t see someone else’s point of view.
Two children have individual conversations when talking to each other.
Back to the balls, Nancy is unable to see past the idea that one row was longer than the other, even though there is the same number of balls which makes them the same.
Concrete Operational (7 to 11 years)
Performs true mental operations (conservation, reversibility) and solves concrete problems in a logical fashion.
Has difficulty thinking hypothetically and systematically considering all aspects of a problem
Ex: They have difficulty thinking about and discussing possible answers to questions such as, Will you be happy in the future?
Formal Operational (11 years onward)
Solves abstract problems in systematic and logical fashion.
Reasons hypothetically and often develops concerns over social issues.
Ex: When given a chemistry problem of pouring chemicals together, kids at this age mix two or all four liquids at once but do not consider using three liquids at a time. They also keep records about their tests and make hypothesis about the results.
Some kids begin thinking about nature of existence, truth, justice and morality.

11. The Process of Development
Assimilation
Occurs when a child perceives new objects or events in terms of existing schemes or operations.
Accommodation
When existing schemes or operations must be modified to account for a new experience, accommodation has occurred.
Equilibration
Characterizes the child’s transition from one stage of development to the next.
Piaget’s description of stages answers the question of psychological states children pass through in development.
What mechanism did he propose as responsible for children’s progression from one stage to the next?
Piaget considered three processes as being critical to development: assimilation, accommodation and equilibration.
Assimilation
Occurs when a child perceives new objects or events in terms of existing schemes or operations.
ex: The scheme is the action of throwing, shaking and are means of assimilating information about the object.
Accommodation
When existing schemes or operations must be modified to account for a new experience, accommodation has occurred.
ex: Jeremy will eventually change his thinking, from a button is not alive to the belief that a plant is alive.
Equilibration
Master development process, encompassing both assimilation and accommodation.
Characterizes the child’s transition from one stage of development to the next.
Ex: When Wanda hears plants being referred to alive, she will experience disequilibrium. She is then likely to be unsure of what it means to be alive. She later will find out that plans to grow and reproduce like animals do and will gain a new equilibrium at a more sophisticated level of thought.

12. Criticisms of Genetic Epistemology
Piaget’s Claim
Counterevidence
Not all cultures show evidence of formal operations
Even in Western culture people fail to reason at the formal operational level much of the time.
1. The sequence of stages is culturally invariant, with formal operations inevitably reached.
2. There is qualitative change in cognition from stage to stage and consistency of reasoning within a stage.
Children actually learn more at given stages then Piaget thought, and they do not always reason consistently within a stage
Children are sometimes egocentric beyond the preoperational stage.
Preoperational children are not egocentric all the time.
3. Children exhibit the characteristics of each stage, and each stage includes all the competence of the previous stage.
Claim 1: regardless of culture children go through all four stages of sensoimotor to formal operations per Piaget.
it is evident that children of different cultures reach the different stages at different ages.
it has been found there can be temporary regression in the reasoning of early concrete operational children. This may mean cognitive development occurs in steady, incremental changes rather than discontinuous stages.
Counter argument:
Not all cultures show evidence of formal operations
Even in Western culture people fail to reason at the formal operational level much of the time.
Claim 2: carries two implications
1. that development is discontinuous
2. reasoning on different problems is consistent within a given stage.
Ex: a bridge collapsing, the forces that cause a bridge to give away build up over a long period of time. But the collapse itself is sudden. What appear to be the sudden changes in children’s thinking are actually part of a gradual progression.
Counter Argument
Children actually learn more at given stages then Piaget thought, and they do not always reason consistently within a stage
Claim 3: You can examine the traits purported to characterize children’s thinking at each stage and ask whether these traits are an adequate description.
Piaget’s studies suggest that children are egocentric, but the nature of the task rather than the stage of development appears to be the critical factor determining when they are egocentric.
Ex: if you ask a 3 year old to show you their drawings, they hold the side with the artwork toward you. If they were completely egocentric, they would do the opposite since they would assume that what they see you can see too.
Children are sometimes egocentric beyond the preoperational stage.
Preoperational children are not egocentric all the time.
Claim 4: For children to make the transition between stages, cognitive restructuring (accommodation in response to disequilibrium) must occur.
Let’s go back to Cheryl, she knew more about the basic biological functions and bodily processes shared by animals than the younger children.
Counter Argument:
Reasoning appears to be more domain-specific than global.
Piaget asked the right question. What mental processes lead children to think differently from adults and how do they represent what they see?
4. Global restructuring characterizes stage shifting.
Reasoning appears to be more domain-specific than global.

13. Group Project
From what you have studied of learning theory so far, would you design different instruction for children than you would for adults when teaching how to operate a personal computer?
Why or why not?
If you would create different instruction for the two groups, what would these differences entail?
Why would you make those instructional decisions?
Divide class in 3 groups to discuss for 5-10 minutes.

14. Alternative Perspectives
Neo-Piagetian View
Computational Model
Componential Analysis
Framework Theory
New Agenda Based on Variability, Choice and Change
All of these alternative views have two assumptions in common with Piaget’s views
Children think about any particular topic in only one way at most points in development
2. A major goal of developmental theory should be identifying the way of thinking used by children at particular ages.

15. Match the Theory (Alternative Perspective) with the correct Feature
1. Genetic
Epistemology (Piaget)
a. Computer simulations of Piaget’s theory
2. Non-Piagetian View
(Case)
b. Development more or less equivalent to novice becoming expert.
Based on information-processing theory.
3. Computational Model
(Klahr)
c. Variability is characteristic of thinking.
Strategy choice is adaptive.
Children’s thinking is always changing.
4. Componential Analysis
(Sternberg)
d. Stages similar to those of Piaget. Increasingly sophisticated logical structures at each stage. Biological maturation assumed.
5. Framework Theory
Carey
e. Qualitative differences in knowledge states.
Domain-specific development
6. Variability, Choice and Change
(Siegler)
f. Four stages of Development: Sensory-motor, Preoperational, Concrete-Operational, Formal-Operational
Genetic Epistemology-Piaget
Answer is F
Four stages of Development: Sensory-motor, Preoperational, Concrete-Operational, Formal-Operational
Development Process: Accommodation, Assimilation, Equilibration
Neo-Piagetian View – Robert Cast
Answer is D
Stages similar to those of Piaget. Increasingly sophisticated logical structures at each stage. Biological maturation assumed.
Children’s mental structures can best be modeled by using the sorts of concepts developed in the field of information processing and computer similation, rather than those developed in the field of symbolic logic.
Children’s problem solving in terms of short-term memory capacity and the proportion of that capacity devoted to operating space or storage space.
As processing becomes more automatic the requirements for operating space diminish allowing for more storage space.
Computational Model- Computer simulations of Piaget’s theory Answer is A
Klahr and Wallace undertook a research program aimed at uniting Piaget’s theory of development with techniques for simulating human cognition.
Focused on one aspect- quantitative development.
Proposal that humans mentally represent quantity through one of three quantifiers.
Subitizing, counting and estimating.
Subitizing refers to the rapid recognition of collections of four or fewer objects.
Four or fewer people can tell by looking how many there are. When more than four items are present people resort to counting.
Then when the collection grows large enough that counting is impractical, estimating enables a quantity to be represented.
Componential Analysis –Sternberg Answer is B
Development more or less equivalent to novice becoming expert.
Based on information-processing theory.
Differs from other theorists discussed so far in his almost total lack of reference to Piaget’s theory.
Grounds his research squarely within information-processing theory and proposes to account for intellectual development in terms of “changes in the availability, accessibility and ease of execution of a variety of kinds of information-processing components.”
Intelligence is made up of three types of information processing components: metacomponents, performance components, and knowledge acquisition components.
Metacomponents- are executive processes used in planning and decision making in task performance
ex. Decide what problem is and what strategy will be used to solve it.
Performance components- those processes involved in the actual completion of a problem-solving task.
ex. Comparing possible answer options
Knowledge acquisition components- those used for learning new information required to solve a problem at hand.
ex. Selectively encoding relevant information, meaningfully interpreting this information, and integrating it with previous knowledge compose the set of knowledge-acquisition components.
Framework Theory- Carey and others Answer is E
Qualitative differences in knowledge states.
Domain-specific development
Evolved from several lines of research focused on conceptual change.
Novice expert studies drew attention to qualitative differences in how experts and novices represent information and solve problems.
What causes them to change as children grow up? What is the engine of cognitive development?
Role of two heuristic processes in conceptual change-
1. construct mapping across domains, including physical analogies
2. thought experiments, including limited case studies
New Agenda Based on Variability, Choice and Change- Siegler Answer is C
Requires reformulation of basic assumptions about children’s thinking.
Uses a piece of Piaget theory as a starting point then developed a theory utilizing information-processing concepts and analyses.
He focused on how children encode features of a problem and select rules to solve it.
His results showed that performance was related to age on a problem requiring the use and combination of multiples rules to solve.
Ex. Instead of a staircase (thinking at a certain level for prolonged periods followed by moving rapidly upward for a brief period), Siegler proposed overlapping waved as a more accurate picture of development: endlessly variable, endlessly changing, a wave, like children’s thinking never stands still”

16. Match the Theory with the correct Developmental Process
1. Genetic
Epistemology (Piaget)
a. Generalization global restructuring (brought on by local, domain-specific restructuring)
2. Non-Piagetian View
(Case)
b. Feedback (to provide a self-correcting function)
3. Computational Model
(Klahr)
c. Encoding monitoring of task demands, trail and error, learning
4. Componential Analysis
(Sternberg)
d. Automatization (to reduce operation space to STM)
5. Framework Theory
Carey
e. Knowledge restructuring in specific domains
6. Variability, Choice and Change
(Siegler)
f. Accommodation
Assimilation
Equilibration
Genetic Epistemology-Piaget
Answer is F
Neo-Piagetian View – Robert Cast
Answer is D
Computational Model-
Answer is A
Componential Analysis –Sternberg
Answer is B
Framework Theory- Carey and others
Answer is E
New Agenda Based on Variability, Choice and Change- Siegler
Answer is C

17. Implications for Instruction of Development Theory
There are three basic instructional principles on which Piagetian theorists generally agree.
The Learning Environment Should Support the Activity of the Child
Children’s Interactions with their Peers are an Important Source of Cognitive Development.
The Learning Environment Should Support the Activity of the Child
Children acquire knowledge through their actions and thinking is considered to be action-based.
Piaget’s emphasis on activity is the fact that children receive feedback from their own actions.
Experiments where the child conducts it is more meaningful than when a teacher demonstrates it.
Piagetian educators encourage play as a strategy for active self discovery.
2. Children’s Interactions with their Peers are an Important Source of Cognitive Development.
Preoperational children are characteristically egocentric in their thinking and language
Piaget believed that peer interactions are essential in helping children move beyond egocentric thoughts.
3. Adopt Instructional Strategies that Make Children Aware of Conflicts and Inconsistencies in Their Thinking.
This principle derives from Piaget’s master developmental process, equilibration.
Recall that children must experience disequilibrium between their current cognitive structures and new information to be assimilated, in order for them to move to a new stage of development.
When confronted with the inadequacy of their reasoning children learned to adopt more complex and adequate rules.
Brainerd called this confrontation conflict teaching and argued that it serves to induce disequilibrium.
1. The critically of diagnosing what children already know and how they think.
“know your learner”
2. Take into account the order in which concepts spontaneously emerge in cognitive development for conflict instruction. A Piagetian perspective is that concepts are acquired as a function of the logical structures that underlie them.
Adopt Instructional Strategies that Make Children Aware of Conflicts and Inconsistencies in Their Thinking.

18. Implications for Instruction of an Information-Processing View
The Role of Rules in Children’s Thinking
Case recommends that teachers follow a three step procedure:
1. The ways in which children are oversimplifying a given type of problem must be identified.
2. Students should be shown why their strategy will not work to solve the problem and what information they are ignoring.
3. They should be taught and given many opportunities to practice a better strategy incorporating all the rules necessary to solve the problem.
Despite their different perspectives on development, information-processing, theorists have suggested implications for instruction that, in a general way, resemble Piaget’s.
Information processing theorists have attempted to discuss in more detail than Piaget, what activity is beneficial for intellectual growth and how cognitive conflicts can be most effectively induced.
So far the developmental theorists we have discussed have little to say about strategies for peer interaction.
The Role of Rules in Children’s Thinking
Case, Klahr and Wallace, Siegler and Sternberg suggest that rules are a useful means for characterizing children’s thinking.
Case believes that children’s short term memory places limits on the number of operations (or rules) they can manager at one time. This is why children over simplify problems and miss important information.
Case recommends that teachers follow a three step procedure:
1. The ways in which children are oversimplifying a given type of problem must be identified.
2. Students should be shown why their strategy will not work to solve the problem and what information they are ignoring.
3. They should be taught and given many opportunities to practice a better strategy incorporating all the rules necessary to solve the problem.
Remember to reduce memory overload by using small steps and familiar terms and objects. Practice each step a lot in order to remember it.

19. Implications for Instruction of an Information-Processing View
Promoting Conceptual Change
New scientific conceptions emerge when:
There is existing dissatisfaction with the old conception
2. A new conception can be grasped
3. The new conception appears plausible
Promoting Conceptual Change
Like Piaget, theorists from an information-processing perspective firmly believe that conceptual change is an integral part of cognitive development.
Unlike Piaget, they explain this change in terms of domain-specific expertise and changing mental models as opposed to general logical structures.
Posner contended that useful guidelines for instruction can be found in the metaphor of conceptual change as scientific paradigm shift.
New scientific conceptions emerge when
1. there is existing dissatisfaction with the old conception
These consist of experiences or information that cannot be easily assimilated to the existing conception.
ex. Children hear adults say the earth is like a round ball. When in their minds the earth is flat and stationary. Children then think they misunderstood. Because an adult could not be wrong, but they can’t experience the earth being round.
2. a new conception can be grasped
Understanding a new concept can be taught through analogies metaphors, and physical models. This can be done to teach new things or re-teach existing info.
3. the new conception appears plausible
The plausibility of a new conception hinges on its relation to the learner’s experiential beliefs and it’s ability to account for anomalies.
Any new model or theory must account for all previous data as well as the anomalous data that caused its creation in the first place.
4. the new conception opens up new areas of inquiry
Discussing and illustrating implications of the new theory, as well as have students create inventions stemming from a new concept are ways teachers have found to enhance understanding of a new idea.
Teachers should spend a good amount of time diagnosing student misconceptions and guiding them to mental models more consistent with scientific findings.
4. The new conception opens up new areas of inquiry

20. Discussion and Q & A
Next week Brunner and Vygotsky who study cognitive development as well as adult learning and in a cultural context.

21. Sources
Boeree, Dr. C. George, Personality Theories, Driscoll, Marcy P. Psychology of learning for instruction. Allyn and Bacon (2000) Jean Piaget Society, Kearsley, Greg, The Theory Into Practice Database Online BKT, Hour Glass Picture SciNet Science Pictures, Picture of bananas Songs & Musical Notes, Music Picture