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UNIVERSITY OF LAGOS
SCHOOL OF POST-GRADUATE STUDIES
FACULTY OF EDUCATION
BIOLOGY EDUCATION
GROUP 2
PIAGET’S AND PAVLOV’S
PSYCHOLOGICAL THEORIES OF
LEARNING
GROUP MEMBERS:
KAZEEM BOLAJI 100310050
OKEKWUO ESTHER 130310023
ONAYEMI TEMILADE 140310522
AISHA ADIGUN 199037011
ARANSIOLA DAVID 199037006
OKOH PRECIOUS 199037007
2
JEAN PIAGET
THE THEORIST
Jean Piaget was a Swiss psychologist and genetic epistemologist. He is most famously known for
his theory of cognitive development that looked at how children develop intellectually
throughout the course of childhood. Prior to Piaget's theory, children were often thought of
simply as mini-adults. Instead, Piaget suggested that the way children think is fundamentally
different from the way that adults think. Piaget provided support for the idea that children think
differently than adults and his research identified several important milestones in the mental
development of children. His work also generated interest in cognitive and developmental
psychology. Piaget's theories are widely studied today by students of both psychology and
education.
His theory had a tremendous influence on the emergence of developmental psychology as a
distinctive subfield within psychology and contributed greatly to the field of education. He is
also credited as a pioneer of the constructivist theory, which suggests that people actively
construct their knowledge of the world based on the interactions between their ideas and their
experiences. Piaget was ranked as the second most influential psychologist of the twentieth
century in one 2002 survey. Piaget later developed an interest in psychoanalysis and spent a year
working at a boys' institution created by Alfred Binet. Binet is known as the developer of the
world's first intelligence test and Piaget took part in scoring these assessments.
While his early career consisted of work in the natural sciences, it was during the 1920s that he
began to move toward work as a psychologist. He married Valentine Châtenay in 1923 and the
couple went on to have three children. It was Piaget's observations of his own children that
served as the basis for many of his later theories.
BACKGROUND AND EARLY LIFE
Jean Piaget was born on August 9, 1896, in Neuchâtel, Switzerland, the son of a historian. He
was his parents‘ first child. Piaget‘s mother, Rebecca Jackson, attributed his intense early interest
in the sciences to his own neurotic tendencies. Yet his father, a medieval literature professor
named Arthur, modeled a passionate dedication to his studies—a trait that Piaget began to
emulate from an early age. Much of Piaget's childhood was influenced by what he saw in his
3
father, a man intensely dedicated to his studies and work. Because of this, at an early age Piaget
began passing up recreation for studying, particularly the study of the natural sciences.
At just ten years old, Piaget‘s fascination with mollusks (shellfish) drew him to the local museum
of natural history, where he stared at specimens for hours on end. When he was eleven, attending
Neuchâtel Latin High School Piaget wrote a short scientific paper on the albino sparrow. His
notes on a rare part-albino (having extremely pale or light skin) sparrow were published, the first
of hundreds of articles and over fifty books. By the time he was a teen, his papers on mollusks
were being widely published. Piaget‘s readers were unaware of his age and considered him an
expert on the topic because several times, when submitting his works to be published in various
magazines, Piaget was forced to keep his young age a secret. Many editors felt that a young
author had very little credibility.
One article, written when he was fifteen, led to a job offer at a natural history museum in
Geneva, Switzerland; he declined in order to continue his education. After high school, Piaget
went on to study zoology at the University of Neuchâtel. At Neuchâtel University he finished
natural science studies in 1916 and earned a doctoral degree, (PhD), for research on mollusks in
1918. That same year Piaget spent a semester studying psychology under Carl Jung and Paul
Eugen Bleuler at the University of Zürich, where Piaget developed a deeper interest in
psychoanalysis. Over the course of the next year, he studied abnormal psychology at the
Sorbonne in Paris.
THE THEORY ITSELF
JEAN PIAGET’S CONSTRUCTIVISM THEORY
Jean Piaget, was becoming an expert on the study of molluks by his teen years becoming a
philosopher in Switzerland, in the early 1900s and spent his time working with children, and
trying to better understand how children learn. The psychological roots of constructivism began
with the developmental work of Jean Piaget (1896-1980), who developed a theory (the theory of
genetic epistemology) that analogized the development of the mind to evolutionary biological
development and highlighted the adaptive function of cognition. Over the course of his later
4
career in child psychology, he identified four stages of mental development that chronicled
young people's journeys from basic object identification to highly abstract thought.
Cognition refers to thinking and memory processes, and cognitive development refers to long-
term changes in these processes. One of the most widely known perspectives about cognitive
development is the cognitive stage theory of Jean Piaget.
Piaget created and studied an account of how children and youth gradually become able to think
logically and scientifically. Piaget was also a psychological constructivist. In his view, learning
proceeded by the interplay of assimilation (adjusting new experiences to fit prior concepts) and
accommodation (adjusting concepts to fit new experiences). The to-and-fro of these two
processes leads not only to short term learning, but also to long-term developmental change. The
long-term developments are really the main focus of Piaget‘s cognitive theory.
After observing children closely, Piaget proposed that cognition developed through distinct
stages from birth through the end of adolescence. By stages he meant a sequence of thinking
patterns with four key features:
1. They always happen in the same order.
2. No stage is ever skipped.
3. Each stage is a significant transformation of the stage before it.
4. Each later stage incorporated the earlier stages into itself.
Basically this is the ―staircase‖ model of development mentioned at the beginning of this
chapter. Piaget proposed four major stages of cognitive development, and called them:
(1) Sensorimotor intelligence
(2) Preoperational thinking
(3) Concrete operational thinking, and
(4) Formal operational thinking.
Each stage is correlated with an age period of childhood, but only approximately.
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THE SENSORIMOTOR STAGE: BIRTH TO AGE 2
In Piaget‘s theory, the sensorimotor stage is first, and is defined as the period when infants
―think‖ by means of their senses and motor actions. The first stage of development lasts from
birth to approximately age two. At this point in development, children know the world
primarily through their senses and motor movements. As every new parent will attest, infants
continually touch, manipulate, look, listen to, and even bite and chew objects. According to
Piaget, these actions allow them to learn about the world and are crucial to their early cognitive
development.
The infant‘s actions allow the child to represent (or construct simple concepts of) objects and
events. A toy animal may be just a confusing array of sensations at first, but by looking, feeling,
and manipulating it repeatedly, the child gradually organizes her sensations and actions into a
stable concept, toy animal. The representation acquires a permanence lacking in the individual
experiences of the object, which are constantly changing. Because the representation is stable,
the child ―knows,‖ or at least believes, that toy animal exists even if the actual toy animal is
temporarily out of sight. Piaget called this sense of stability object permanence, a belief that
objects exist whether or not they are actually present. It is a major achievement of sensorimotor
development, and marks a qualitative transformation in how older infants (24 months) think
about experience compared to younger infants (6 months).
During much of infancy, of course, a child can only barely talk, so sensorimotor development
initially happens without the support of language. It might therefore seem hard to know what
infants are thinking, but Piaget devised several simple, but clever experiments to get around their
lack of language, and that suggest that infants do indeed represent objects even without being
able to talk (Piaget, 1952). In one, for example, he simply hid an object (like a toy animal) under
a blanket. He found that doing so consistently prompts older infants (18–24 months) to search for
the object, but fails to prompt younger infants (less than six months) to do so. (You can try this
experiment yourself if you happen to have access to young infant.) ―Something‖ motivates the
search by the older infant even without the benefit of much language, and the ―something‖ is
presumed to be a permanent concept or representation of the object..
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THE PREOPERATIONAL STAGE: AGE 2 TO 7
In the preoperational stage, children use their new ability to represent objects in a wide variety of
activities, but they do not yet do it in ways that are organized or fully logical. The second stage
of development lasts from the ages of two to seven and is characterized by the development of
language and the emergence of symbolic play. One of the most obvious examples of this kind of
cognition is dramatic play, the improvised make-believe of preschool children. If you have ever
had responsibility for children of this age, you have likely witnessed such play. Ashley holds a
plastic banana to her ear and says: ―Hello, Mom? Can you be sure to bring me my baby doll?
OK!‖ Then she hangs up the banana and pours tea for Jeremy into an invisible cup. Jeremy
giggles at the sight of all of this and exclaims: ―Rinnng! Oh Ashley, the phone is ringing again!
You better answer it.‖ And on it goes.
In a way, children immersed in make-believe seem ―mentally insane,‖ in that they do not think
realistically. But they are not truly insane because they have not really taken leave of their
senses. At some level, Ashley and Jeremy always know that the banana is still a banana and
not really a telephone; they are merely representing it as a telephone. They are thinking on two
levels at once—one imaginative and the other realistic. This dual processing of experience makes
dramatic play an early example of metacognition, or reflecting on and monitoring of thinking
itself. Metacognition is a highly desirable skill for success in school, one that teachers often
encourage (Bredekamp & Copple, 1997; Paley, 2005). Partly for this reason, teachers of young
children (preschool, kindergarten, and even first or second grade) often make time and space in
their classrooms for dramatic play, and sometimes even participate in it themselves to help
develop the play further.
THE CONCRETE OPERATIONAL STAGE: AGE 7 TO 11
The third stage of cognitive development lasts from the ages of seven to approximately age 11.
At this point, logical thought emerges but children still struggle with abstract and theoretical
thinking. As children continue into elementary school, they become able to represent ideas and
events more flexibly and logically. Their rules of thinking still seem very basic by adult
standards and usually operate unconsciously, but they allow children to solve problems more
7
systematically than before, and therefore to be successful with many academic tasks. In the
concrete operational stage, for example, a child may unconsciously follow the rule: ―If nothing is
added or taken away, then the amount of something stays the same.‖ This simple principle helps
children to understand certain arithmetic tasks, such as in adding or subtracting zero from a
number, as well as to do certain classroom science experiments, such as ones involving
judgments of the amounts of liquids when mixed. Piaget called this period the concrete
operational stage because children mentally ―operate‖ on concrete objects and events. They are
not yet able, however, to operate (or think) systematically about representations of objects or
events. Manipulating representations is a more abstract skill that develops later, during
adolescence.
Concrete operational thinking differs from preoperational thinking in two ways, each of which
renders children more skilled as students. One difference is reversibility, or the ability to think
about the steps of a process in any order. Imagine a simple science experiment, for example,
such as one that explores why objects sink or float by having a child place an assortment of
objects in a basin of water. Both the preoperational and concrete operational child can recall and
describe the steps in this experiment, but only the concrete operational child can recall them in
any order. This skill is very helpful on any task involving multiple steps—a common feature of
tasks in the classroom. In teaching new vocabulary from a story, for another example, a teacher
might tell students: ―First make a list of words in the story that you do not know, then find and
write down their definitions, and finally get a friend to test you on your list.‖ These directions
involve repeatedly remembering to move back and forth between a second step and a first—a
task that concrete operational students—and most adults—find easy, but that preoperational
children often forget to do or find confusing. If the younger children are to do this task reliably,
they may need external prompts, such as having the teacher remind them periodically to go back
to the story to look for more unknown words
The other new feature of thinking during the concrete operational stage is the child‘s ability
to decenter, or focus on more than one feature of a problem at a time. There are hints of
decentration in preschool children‘s dramatic play, which requires being aware on two levels at
once—knowing that a banana can be both a banana and a ―telephone.‖ But the decentration of
the concrete operational stage is more deliberate and conscious than preschoolers‘ make-believe.
8
Now the child can attend to two things at once quite purposely. Suppose you give students a
sheet with an assortment of subtraction problems on it, and ask them to do this: ―Find all of the
problems that involve two-digit subtraction and that involve borrowing from the next column.
Circle and solve only those problems.‖ Following these instructions is quite possible for a
concrete operational student (as long as they have been listening!) because the student can attend
to the two subtasks simultaneously—finding the two-digit problems and identifying which
actually involve borrowing. (Whether the student actually knows how to ―borrow‖ however, is a
separate question.)
In real classroom tasks, reversibility and decentration often happen together. A well-known
example of joint presence is Piaget‘s experiments with conservation, the belief that an amount or
quantity stays the same even if it changes apparent size or shape (Piaget, 2001; Matthews, 1998).
Imagine two identical balls made of clay. Any child, whether preoperational or concrete
operational, will agree that the two indeed have the same amount of clay in them simply because
they look the same. But if you now squish one ball into a long, thin ―hot dog,‖ the preoperational
child is likely to say that the amount of that ball has changed—either because it is longer or
because it is thinner, but at any rate because it now looks different. The concrete operational
child will not make this mistake, thanks to new cognitive skills of reversibility and decentration:
for him or her, the amount is the same because ―you could squish it back into a ball again‖
(reversibility) and because ―it may be longer, but it is also thinner‖ (decentration). Piaget would
say the concrete operational child ―has conservation of quantity.‖
The classroom examples described above also involve reversibility and decentration. As already
mentioned, the vocabulary activity described earlier requires reversibility (going back and forth
between identifying words and looking up their meanings); but it can also be construed as an
example of decentration (keeping in mind two tasks at once—word identification and dictionary
search). And as mentioned, the arithmetic activity requires decentration (looking for problems
that meet two criteria and also solving them), but it can also be construed as an example of
reversibility (going back and forth between subtasks, as with the vocabulary activity). Either
way, the development of concrete operational skills support students in doing many basic
academic tasks; in a sense they make ordinary schoolwork possible.
9
THE FORMAL OPERATIONAL STAGE: AGE 11 AND BEYOND
In the last of the Piagetian stages, the child becomes able to reason not only about tangible
objects and events, but also about hypothetical or abstract ones. In the fourth and final stage of
cognitive development, lasting from age 12 and into adulthood, children become much more
adept and abstract thought and deductive reasoning. Hence it has the name formal operational
stage—the period when the individual can ―operate‖ on ―forms‖ or representations. With
students at this level, the teacher can pose hypothetical (or contrary-to-fact) problems:
―What if the world had never discovered oil?‖ or ―What if the first European explorers had
settled first in California instead of on the East Coast of the United States?‖ To answer such
questions, students must use hypothetical reasoning, meaning that they must manipulate ideas
that vary in several ways at once, and do so entirely in their minds. The hypothetical reasoning
that concerned Piaget primarily involved scientific problems. His studies of formal operational
thinking therefore often look like problems that middle or high school teachers pose in science
classes. In one problem, for example, a young person is presented with a simple pendulum, to
which different amounts of weight can be hung (Inhelder & Piaget, 1958). The experimenter
asks: ―What determines how fast the pendulum swings: the length of the string holding it, the
weight attached to it, or the distance that it is pulled to the side?‖ The young person is not
allowed to solve this problem by trial-and-error with the materials themselves, but must reason a
way to the solution mentally. To do so systematically, he or she must imagine varying each
factor separately, while also imagining the other factors that are held constant. This kind of
thinking requires facility at manipulating mental representations of the relevant objects and
actions—precisely the skill that defines formal operations.
As you might suspect, students with an ability to think hypothetically have an advantage in many
kinds of school work: by definition, they require relatively few ―props‖ to solve problems. In this
sense they can in principle be more self-directed than students who rely only on concrete
operations—certainly a desirable quality in the opinion of most teachers. Note, though, that
formal operational thinking is desirable but not sufficient for school success, and that it is far
from being the only way that students achieve educational success. Formal thinking skills do not
insure that a student is motivated or well-behaved, for example, nor does it guarantee other
desirable skills, such as ability at sports, music, or art. The fourth stage in Piaget‘s theory is
10
really about a particular kind of formal thinking, the kind needed to solve scientific problems and
devise scientific experiments. Since many people do not normally deal with such problems in the
normal course of their lives, it should be no surprise that research finds that many people never
achieve or use formal thinking fully or consistently, or that they use it only in selected areas with
which they are very familiar (Case & Okomato, 1996). For teachers, the limitations of Piaget‘s
ideas suggest a need for additional theories about development—ones that focus more directly on
the social and interpersonal issues of childhood and adolescence. The next sections describe
some of these.
IMPORTANT CONCEPTS
To better understand some of the things that happen during cognitive development, it is
important first to examine a few of the important ideas and concepts introduced by Piaget. The
following are some of the factors that influence how children learn and grow.
Schemas: A schema describes both the mental and physical actions involved in understanding
and knowing. Schemas are categories of knowledge that help us to interpret and understand the
world. In Piaget's view, a schema includes both a category of knowledge and the process of
obtaining that knowledge. As experiences happen, this new information is used to modify, add
to, or change previously existing schemas.
For example, a child may have a schema about a type of animal, such as a dog. If the child's sole
experience has been with small dogs, a child might believe that all dogs are small, furry, and
have four legs. Suppose then that the child encounters an enormous dog. The child will take in
this new information, modifying the previously existing schema to include these new
observations.
Assimilation: The process of taking in new information into our already existing schemas is
known as assimilation. The process is somewhat subjective because we tend to modify
experiences and information slightly to fit in with our preexisting beliefs. In the example above,
seeing a dog and labeling it "dog" is a case of assimilating the animal into the child's dog
schema.
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Accommodation: Another part of adaptation involves changing or altering our existing schemas
in light of new information, a process known as accommodation. Accommodation involves
modifying existing schemas, or ideas, as a result of new information or new experiences.5
New
schemas may also be developed during this process.
Equilibration: Piaget believed that all children try to strike a balance between assimilation and
accommodation, which is achieved through a mechanism Piaget called equilibration. As children
progress through the stages of cognitive development, it is important to maintain a balance
between applying previous knowledge (assimilation) and changing behavior to account for new
knowledge (accommodation). Equilibration helps explain how children can move from one stage
of thought to the next.
IMPLICATION OF THE THEORY TO SCIENCE EDUCTION
Implications of constructivism for teaching and learning
1. Teachers act as facilitators, supports, guides and models of learning. • Learning concerns
adjusting our mental models to accommodate new experiences
2. Learning concerns making connections between information.
3. Instruction should be built around more complex problems, not problems with clear,
correct answers.
4. Context and personal knowledge have high significance
5. Students should help establish the criteria on which their work is assessed
6. Teachers know more and shouldn‘t let students muddle around
7. Student learning depends on background knowledge – that‘s why teaching facts is so
necessary (reversed).
8. Student interest and effort are more important than textbook content.
9. It is sometimes better for teachers, not students, to decide what activities are to be done.
12
10. Sense making and thinking are most important, not knowing content.
11. Experimentation replaces rote learning
12. Teaching utilizes both skill-based and open-ended approaches
13. Motivation to learn is intrinsic rather than extrinsic (done for its own sake rather than for
grades, test scores or rewards)
14. Learners often produce unique and personal knowledge.
15. Naïve beliefs are used as the starting point for further discussion, exploration and
evaluation for development, rather than being discounted as ‗wrong‘
16. Learning for transfer is important.
17. Learners learn best through finding and generating their own knowledge. • Discovery and
guided discovery learning are important. • Exploration and active learning are important.
18. Learning is collaborative and cooperative, not just individual.
19. Higher order thinking is significant.
20. Classrooms become multidimensional, with different activities at different levels taking
place simultaneously.
Piaget's theory of constructivism impacts learning curriculum because teachers have to make a
curriculum plan which enhances their students' logical and conceptual growth. Teacher must put
emphasis on the significant role that experiences-or connections with the adjoining atmosphere-
play in student education. For example, teachers must bear in mind the role those fundamental
concepts, such as the permanence of objects, plays when it comes to establishing cognitive
structures.
Piaget's theory of constructivism argues that people produce knowledge and form meaning based
upon their experiences. Piaget's theory covered learning theories, teaching methods, and
education reform. Two of the key components which create the construction of an individual's
new knowledge are accommodation and assimilation. Assimilating causes an individual to
incorporate new experiences into the old experiences. This causes the individual to develop new
13
outlooks, rethink what were once misunderstandings, and evaluate what is important, ultimately
altering their perceptions. Accommodation, on the other hand, is reframing the world and new
experiences into the mental capacity already present. Individuals conceive a particular fashion in
which the world operates. When things do not operate within that context, they must
accommodate and reframing the expectations with the outcomes.
Apart from learning theories, Piaget's theory of constructivism addresses how learning actually
occurs, not focusing on what influences learning. The role of teachers is very important. Instead
of giving a lecture the teachers in this theory function as facilitators whose role is to aid the
student when it comes to their own understanding. This takes away focus from the teacher and
lecture and puts it upon the student and their learning. The resources and lesson plans that must
be initiated for this learning theory take a very different approach toward traditional learning as
well. Instead of telling, the teacher must begin asking. Instead of answering questions that only
align with their curriculum, the facilitator in this case must make it so that the student comes to
the conclusions on their own instead of being told. Also, teachers are continually in conversation
with the students, creating the learning experience that is open to new directions depending upon
the needs of the student as the learning progresses. Teachers following Piaget's theory of
constructivism must challenge the student by making them effective critical thinkers and not
being merely a "teacher" but also a mentor, a consultant, and a coach.
Piaget's theories and works are significant to people who work with children, as it enables them
to understand that children's development is based on stages. The construction of identity and
knowledge as one predicated upon the development of stages helps to explain the intellectual
growth of children of all ages. Piaget's ideas have helped to construct the notion of learning as
not something linear and depository, but rather as an element that must be understood in
accordance to the cognitive stage of the child. it is through this that Piaget's work becomes
invaluable to educators and those who work with children for it allows one to understand why
children learn at the rate they do. This is essential for those who work with children as it helps to
explain some of the most fundamental issues behind why children learn and how to proceed with
instruction of children.
14
 The influence of Piaget‘s ideas in developmental psychology has been enormous. He
changed how people viewed the child‘s world and their methods of studying children.
He was an inspiration to many who came after and took up his ideas. Piaget's ideas have
generated a huge amount of research which has increased our understanding of cognitive
development.
 His ideas have been of practical use in understanding and communicating with children,
particularly in the field of education (re: Discovery Learning).
AWARDS AND LEGACY
Piaget received honorary degrees from Oxford and Harvard universities and made many
impressive guest appearances at conferences concerning childhood development and learning.
Piaget was the recipient of an array of honorary degrees and accolades, including the prestigious
Erasmus (1972) and Balzan (1979) prizes He remained a quiet figure, though, preferring to avoid
the spotlight. This kind of lifestyle allowed him to further develop his theories. The author of
more than 50 books and hundreds of papers, Piaget summed up his passion for the ongoing
pursuit of scientific knowledge with these words: "The current state of knowledge is a moment in
history, changing just as rapidly as the state of knowledge in the past has ever changed and, in
many instances, more rapidly."
Piaget kept himself to a strict personal schedule that filled his entire day. He awoke every
morning at four and wrote at least four publishable pages before teaching classes or attending
meetings. After lunch he would take walks and ponder on his interests. "I always like to think on
a problem before reading about it," he said. He read extensively in the evening before going to
bed. Every summer he vacationed in the Alpine Mountains of Europe and wrote many works.
DEATH
Jean Piaget died of unknown causes on September 16, 1980, in Geneva, Switzerland. He was 84
years old. His body rests at the Cimetière des Plainpalais.
15
THE INFLUENCE ON BIOLOGY
His theory of cognitive development suggests that children move through four different stages of
mental development, which helps to make teaching a student easy. Piaget believed that children's
understanding through at least the first three stages differ from those of adults and are based on
actively exploring the environment (surroundings) rather than on language understanding. This
theory has a great impact on the teaching and learning process as a biology teacher.
With it, a teacher can relate a child‘s age and the possible error he or she can make. It can help
design a curriculum to help children explore the world in their own way as he believes they think
different from adults. Piaget believed that the process of thinking and the intellectual
development could be regarded as an extension of the biological process which has also two on-
going processes: assimilation and accommodation.
To test his theory, Piaget observed the habits in his own children.
As a biology teacher ,the teacher is made to understand the various stages of development of a
child- What he or she can assimilate at that age. With this stage of development, a teacher is able
to understand the learning differences among child of same age group. Those who are fast or
slow learners. At this early stage of development a teacher can as well know the temperament
which each child‘s fall under.
16
REFERENCES
Bringuier, J.C. (1980). Conversations with Jean Piaget. Chicago: University of Chicago Press.
Edwards, L., Hopgood, J., Rosenberg, K., & Rush, K. (2000). Mental Development and
Education. Retrieved April 25, 2009, from Flinders University Web site:
http://ehlt.flinders.edu.au/education/DLiT/2000/Piaget/begin.htm
Huitt, W. & Hummel, J. (1998). Cognitive development. Retrieved April 25, 2009 from the
World Wide Web: http://chiron.valdosta.edu/whuitt/col/cogsys/piaget.html
Lefrancois, G.R. (2006). Theories of Human Learning. Belmont, CA: Thomson Higher
Education.
Evans, R. (1973). Jean Piaget, the Man and His Ideas. New York: Dutton.
Piaget, J. (1952). Autobiography. In E. Boring (ed). History of psychology in autobiography.
Vol. 4. Worcester, MA: Clark University Press
Piaget, J. (1936) Origins of intelligence in the child. London: Routledge & Kegan Paul.
Piaget, J. (1945) Play, dreams and imitation in childhood. London: Heinemann.
Piaget, J. (1970) Main trends in psychology. London: George Allen & Unwin.
Piaget, J. (1970). Genetic epistemology. New York: W.W. Norton & Company.
Piaget, J. (1973). Memory and intelligence. New York: BasicBooks
(2009). Piaget's stages of cognitive development. Retrieved April 30, 2009, from About.com:
Psychology Web site: http://psychology.about.com/library/quiz/bl_piaget_quiz.htm
Plucker, J. (2007). Human Intelligence . Retrieved May 1, 2009, from Indiana University Web
site: http://www.indiana.edu/~intell/piaget.shtml
Slavin, R.E. (2005). Educational psychology: theory and practice. Needham Heights, MA: Allyn
and Bacon.
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Smith, L. (2000). A brief biography of jean piaget. Retrieved April 25, 2009, from Jean Piaget
Society Web site: http://www.piaget.org/aboutPiaget.html
Wadsworth, B.J. (1996). Piaget's theory of cognitive and affective development: White Plains,
NY: Longman.
Wood, K.C. (2008). Piaget's Stages. Retrieved April 25, 2009, from Department of Educational
Psychology and Instrutional Technology, University of Georgia Web site:
http://projects.coe.uga.edu/eplt /index.php?title=Piaget%27s_Stages#Educational_Implications
18
JEROME BRUNER
THE THEORIST
Jerome Bruner was a cognitive psychologist who felt that the goal of education should be
intellectual development, as opposed to rote memorization of facts. Bruner held the following
beliefs regarding learning and education:
 He believed curriculum should foster the development of problem-solving skills through
the processes of inquiry and discovery.
 He believed that subject matter should be represented in terms of the child's way of
viewing the world.
 That curriculum should be designed so that the mastery of skills leads to the mastery of
still more powerful ones.
 He also advocated teaching by organizing concepts and learning by discovery.
 Finally, he believed culture should shape notions through which people organize their
views of themselves and others and the world in which they live.
BACKGROUND AND EARLY LIFE
Bruner was born blind (due to cataracts) on October 1, 1915, in New York City, to Herman and
Rose Bruner, who were Polish Jewish immigrants. An operation at age two restored his vision.
He received a bachelor's of arts degree in Psychology in 1937 from Duke University, and went
on to earn a master's degree in Psychology in 1939 and then a doctorate in Psychology in 1941
from Harvard University. In 1939, Bruner published his first psychological article on the effect
of thymus extract on the sexual behavior of the female rat. During World War II, Bruner served
on the Psychological Warfare Division of the Supreme Headquarters Allied Expeditionary Force
committee under General Dwight D. Eisenhower, researching social psychological phenomena.
In 1945, Bruner returned to Harvard as a psychology professor and was heavily involved in
research relating to cognitive psychology and educational psychology. In 1970, Bruner left
Harvard to teach at the University of Oxford in the United Kingdom. He returned to the United
19
States in 1980, to continue his research in developmental psychology. In 1991, Bruner joined the
faculty at New York University (NYU), where he taught primarily in the School of Law,
THE THEORY ITSELF
The intellectual development includes three stages:
i. Enactive stage (learning through action)
ii. Iconic stage (learners‘ use of pictures or models)
iii. Symbolic stage(Development of the ability to think in abstract term).
Enactive (0 - 1 years)
This is the first kind of memory. This mode is used within the first year of life (corresponding
with Piaget‘s sensorimotor stage). Thinking is based entirely on physical actions, and infants
learn by doing, rather than by internal representation (or thinking). It involves encoding physical
action based information and storing it in our memory. For example, in the form of movement as
a muscle memory, a baby might remember the action of shaking a rattle.
Iconic (1 - 6 years)
Information is stored as sensory images (icons), usually visual ones, like pictures in the mind.
For some, this is conscious; others say they don‘t experience it. This may explain why, when we
are learning a new subject, it is often helpful to have diagrams or illustrations to accompany the
verbal information. Thinking is also based on the use other mental images (icons), such as
hearing, smell or touch.
Symbolic (7 years onwards)
This develops last. This is where information is stored in the form of a code or symbol, such as
language. This mode is acquired around six to seven years-old (corresponding to Piaget‘s
concrete operational stage). In the symbolic stage, knowledge is stored primarily as words,
mathematical symbols, or in other symbol systems, such as music. Symbols are flexible in that
they can be manipulated, ordered, classified etc., so the user isn‘t constrained by actions or
images (which have a fixed relation to that which they represent).
20
IMPLICATION OF BRUNER’S THEORY OF LEARNING TO SCIENCE EDUCATION
Burner‘s theory of learning in education aims at creating autonomous learners (learning to learn).
The purpose of education is not to impact knowledge, but instead to facilitate a child‘s thinking
and problem-solving which can then be transferred to a range of situations. Learning is an active
process. Learners select and transform information. Learners make appropriate decisions and
postulate hypotheses and test their effectiveness.
Learners use prior experience to fit new information into the pre-existing structures. Scaffolding
is the process through which able peers or adult offers supports for learning. This assistance
becomes gradually less frequent as it becomes unnecessary.
Educational Implications
The aim of education should be to create autonomous learners (i.e., learning to learn). For Bruner
(1961), the purpose of education is not to impart knowledge, but instead to facilitate a child's
thinking and problem-solving skills which can then be transferred to a range of situations.
Specifically, education should also develop symbolic thinking in children.
In 1960 Bruner's text, The Process of Education was published. The main premise of Bruner's
text was that students are active learners who construct their own knowledge.
 Readiness
Bruner (1960) opposed Piaget's notion of readiness. He argued that schools waste time trying to
match the complexity of subject material to a child's cognitive stage of development. This means
students are held back by teachers as certain topics are deemed too difficult to understand and
must be taught when the teacher believes the child has reached the appropriate state of cognitive
maturity.
 The Spiral Curriculum
Bruner (1960) adopts a different view and believes a child (of any age) is capable of
understanding complex information: 'We begin with the hypothesis that any subject can be
taught effectively in some intellectually honest form to any child at any stage of development.'
(p. 33) Bruner (1960) explained how this was possible through the concept of the spiral
curriculum. This involved information being structured so that complex ideas can be taught at a
21
simplified level first, and then re-visited at more complex levels later on.Therefore, subjects
would be taught at levels of gradually increasing difficultly (hence the spiral analogy). Ideally,
teaching his way should lead to children being able to solve problems by themselves.
 Discovery Learning
Bruner (1961) proposes that learners‘ construct their own knowledge and do this by organizing
and categorizing information using a coding system. Bruner believed that the most effective way
to develop a coding system is to discover it rather than being told it by the teacher. The concept
of discovery learning implies that students construct their own knowledge for themselves (also
known as a constructivist approach). The role of the teacher should not be to teach information
by rote learning, but instead to facilitate the learning process. This means that a good teacher will
design lessons that help students discover the relationship between bits of information. To do this
a teacher must give students the information they need, but without organizing for them. The use
of the spiral curriculum can aid the process of discovery learning.
Bruner and Vygotsky
Both Bruner and Vygotsky emphasize a child's environment, especially the social environment,
more than Piaget did. Both agree that adults should play an active role in assisting the child's
learning. Bruner, like Vygotsky, emphasized the social nature of learning, citing that other
people should help a child develop skills through the process of scaffolding.
Scaffolding refers to the steps taken to reduce the degrees of freedom in carrying out some task
so that the child can concentrate on the difficult skill she is in the process of acquiring' (Bruner,
1978, p. 19). He was especially interested in the characteristics of people whom he considered to
have achieved their potential as individuals.
The term scaffolding first appeared in the literature when Wood, Bruner, and Ross described
how tutors' interacted with a pre-schooler to help them solve a block reconstruction problem
(Wood et al., 1976). The concept of scaffolding is very similar to Vygotsky's notion of the zone
of proximal development, and it's not uncommon for the terms to be used interchangeably.
22
Scaffolding involves helpful, structured interaction between an adult and a child with the aim of
helping the child achieve a specific goal. The purpose of the support is to allow the child to
achieve higher levels of development by:
 Simplifying the task or idea.
 Motivating and encouraging the child.
 Highlighting important task elements or errors.
 Giving models that can be imitated.
Bruner and Piaget agree that
Children are innately pre-adapted to learning
Children have a natural curiosity
Children‘s cognitive structures develop over time
Children are active participants in the learning process
Cognitive development entails the acquisition of symbols
They Disagree that
Social factors, particularly language, were important for cognitive growth. These underpin the
concept of ‗scaffolding‘.
The development of language is a cause not a consequence of cognitive development you can
speed-up cognitive development. you don‘t have to wait for the child to be ready the
involvement of adults and more knowledgeable peers makes a big difference.
AWARDS
As an adjunct professor at NYU School of Law, Bruner studied how psychology affects legal
practice. During his career, Bruner was awarded honorary doctorates from Yale University,
Columbia University, The New School, the Sorbonne, the ISPA Instituto Universitário, as well
as colleges and universities in such locations as Berlin and Rome, and was a Fellow of the
American Academy of Arts and Sciences.
DEATH
He turned 100 in October 2015 and died on June 5, 2016.
23
INFLUENCEOF THE THEORY ON BIOLOGY
As a biology teacher, concepts should be taught from simple to complex. The use of pictures,
charts and models can never be overemphasized. Bruner states that what determines the level of
intellectual development is the extent to which the child has been given appropriate instruction
together with practice or experience.
So, the right way of presentation and the right explanation will enable a child to grasp a concept
usually only understood by an adult. His theory stresses the role of education and the adult.
Although Bruner proposes stages of cognitive development, he doesn‘t see them as representing
different separate modes of thought at different points of development (like Piaget). Instead, he
sees a gradual development of cognitive skills and techniques into more integrated ―adult‖
cognitive techniques.
Bruner views symbolic representation as crucial for cognitive development, and since language
is our primary means of symbolizing the world, he attaches great importance to language in
determining cognitive development.
The teachers must revisit material to enhance knowledge. Building on pre-taught ideas to grasp
the full formal concept is of paramount importance according to Bruner. Feel free to re-introduce
vocabulary, grammar points, and other topics now and then in order to push the students to a
deeper comprehension and longer retention.
Material must be presented in a sequence giving the learners the opportunity to:
1) acquire and construct knowledge,
2) transform and transfer his learning.
 Students should be involved in using their prior experiences and structures to learn new
knowledge.
 Help students to categorize new information in order to able to see similarities and
differences between items.
 Teachers should assist learners in building their knowledge. This assistance should fade
away as it becomes unnecessary.
24
 Teachers should provide feedback that is directed towards intrinsic motivation. Grades
and competition are not helpful in the learning process. Bruner states that learners must
―experience success and failure not as reward and punishment, but as information‖
25
REFERENCES
Anderson, J. R. (1990). Cognitive psychology and its implications(3rd ed.). New York:
Bruner, J. S. (1957). Going beyond the information given. New York: Norton.
Bruner, J. S. (1960). The Process of education. Cambridge, Mass.: Harvard University Press.
Bruner, J. S. (1961). The act of discovery. Harvard Educational Review, 31, 21-32.
Bruner, J. S. (1966). Toward a theory of instruction, Cambridge, Mass.: Belkapp Press.
Bruner, J. S. (1973). The relevance of education. New York: Norton.
Bruner, J. S. (1978). The role of dialogue in language acquisition. In A. Sinclair, R., J. Jarvelle,
and W. J.M. Levelt (eds.) The Child's Concept of Language. New York: Springer-Verlag.
Freeman.Berk, L. E. (1997). Child development (4th ed.).
Needham Heights, MA: Allyn & Bacon.Burns, M., & Silbey, R. (2000). So you have to teach
math? Sound advice for K-6 teachers. Sausalito, CA: Math Solutions Publications.
Eggen, P. D., & Kauchak, D. P. (2000). Educational psychology: Windows on classrooms (5th
ed.). Upper Saddle River, NJ: Prentice
Hall.Fuson, K. C. (1988). Children‘s counting and concepts of numbers. New York:
Springer.Gelman, R., Meck, E., & Merkin, S. (1986). Young children‘s numerical competence.
Cognitive Development, 1, 1–29.
Johnson-Laird, P. N. (1999). Deductive reasoning. Annual Review of Psychology, 50, 109–135.
Kamii, C. (1982). Number in preschool and kindergarten: Educational implications of Piaget‘s
theory. Washington, DC: National Association for the Education ofYoung Children.
26
Martin, D. J. (2000). Elementary science methods:A constructivist approach (2nd ed.). Belmont,
CA: Wadsworth.
McLeod, S. A. (2019, July 11). Bruner. Simply psychology:
https://www.simplypsychology.org/bruner.html
McNallyWeinert, F. E., & Helmke, A. (1998). The neglected role of individual differences in
theoretical models of cognitive development. Learning and Instruction, 8, 309–324.
Papila, D. E., & Olds, S. W. (1996). A child‘s world: Infancy through adolescence (7th ed.). New
York: McGraw-Hill.
Piaget, J. (1970). Science of education and the psychology of the child. New York: Viking.
Piaget, J. (1977). Epistemology and psychology of functions. Dordrecht, Netherlands: D. Reidel
Publishing Company.Thompson, C. S. (1990). Place value and larger numbers. In J. N.
Payne (Ed.), Mathematics for young children (pp. 89–108). Reston, VA: National Council of
Teachers of Mathematics.
Thurstone, L. L. (1970). Attitudes can be measured. In G. F. Summers (Ed.), Attitude
measurement (pp. 127–141). Chicago: Rand.
Wise, S. L. (1985). The development and validity of a scale measuring attitudes toward statistics.
Educational and Psychological Measurement, 45, 401–405.
Wood, D. J., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of
Child Psychiatry and Psychology, 17(2), 89-100.
Zimmerman, B. J., & Whitehurst, G. J. (1979). Structure and function: A comparison of two
views of the development of language and cognition. In G. J. Whitehurst and B. J.
Zimmerman (Eds.), The functions of language and cognition(pp. 1–22). New York: Academy
https://www.simplypsychology.org/bruner.html
27

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PIAGET’S AND PAVLOV’S PSYCHOLOGICAL THEORIES OF LEARNING

  • 1. UNIVERSITY OF LAGOS SCHOOL OF POST-GRADUATE STUDIES FACULTY OF EDUCATION BIOLOGY EDUCATION GROUP 2 PIAGET’S AND PAVLOV’S PSYCHOLOGICAL THEORIES OF LEARNING GROUP MEMBERS: KAZEEM BOLAJI 100310050 OKEKWUO ESTHER 130310023 ONAYEMI TEMILADE 140310522 AISHA ADIGUN 199037011 ARANSIOLA DAVID 199037006 OKOH PRECIOUS 199037007
  • 2. 2 JEAN PIAGET THE THEORIST Jean Piaget was a Swiss psychologist and genetic epistemologist. He is most famously known for his theory of cognitive development that looked at how children develop intellectually throughout the course of childhood. Prior to Piaget's theory, children were often thought of simply as mini-adults. Instead, Piaget suggested that the way children think is fundamentally different from the way that adults think. Piaget provided support for the idea that children think differently than adults and his research identified several important milestones in the mental development of children. His work also generated interest in cognitive and developmental psychology. Piaget's theories are widely studied today by students of both psychology and education. His theory had a tremendous influence on the emergence of developmental psychology as a distinctive subfield within psychology and contributed greatly to the field of education. He is also credited as a pioneer of the constructivist theory, which suggests that people actively construct their knowledge of the world based on the interactions between their ideas and their experiences. Piaget was ranked as the second most influential psychologist of the twentieth century in one 2002 survey. Piaget later developed an interest in psychoanalysis and spent a year working at a boys' institution created by Alfred Binet. Binet is known as the developer of the world's first intelligence test and Piaget took part in scoring these assessments. While his early career consisted of work in the natural sciences, it was during the 1920s that he began to move toward work as a psychologist. He married Valentine Châtenay in 1923 and the couple went on to have three children. It was Piaget's observations of his own children that served as the basis for many of his later theories. BACKGROUND AND EARLY LIFE Jean Piaget was born on August 9, 1896, in Neuchâtel, Switzerland, the son of a historian. He was his parents‘ first child. Piaget‘s mother, Rebecca Jackson, attributed his intense early interest in the sciences to his own neurotic tendencies. Yet his father, a medieval literature professor named Arthur, modeled a passionate dedication to his studies—a trait that Piaget began to emulate from an early age. Much of Piaget's childhood was influenced by what he saw in his
  • 3. 3 father, a man intensely dedicated to his studies and work. Because of this, at an early age Piaget began passing up recreation for studying, particularly the study of the natural sciences. At just ten years old, Piaget‘s fascination with mollusks (shellfish) drew him to the local museum of natural history, where he stared at specimens for hours on end. When he was eleven, attending Neuchâtel Latin High School Piaget wrote a short scientific paper on the albino sparrow. His notes on a rare part-albino (having extremely pale or light skin) sparrow were published, the first of hundreds of articles and over fifty books. By the time he was a teen, his papers on mollusks were being widely published. Piaget‘s readers were unaware of his age and considered him an expert on the topic because several times, when submitting his works to be published in various magazines, Piaget was forced to keep his young age a secret. Many editors felt that a young author had very little credibility. One article, written when he was fifteen, led to a job offer at a natural history museum in Geneva, Switzerland; he declined in order to continue his education. After high school, Piaget went on to study zoology at the University of Neuchâtel. At Neuchâtel University he finished natural science studies in 1916 and earned a doctoral degree, (PhD), for research on mollusks in 1918. That same year Piaget spent a semester studying psychology under Carl Jung and Paul Eugen Bleuler at the University of Zürich, where Piaget developed a deeper interest in psychoanalysis. Over the course of the next year, he studied abnormal psychology at the Sorbonne in Paris. THE THEORY ITSELF JEAN PIAGET’S CONSTRUCTIVISM THEORY Jean Piaget, was becoming an expert on the study of molluks by his teen years becoming a philosopher in Switzerland, in the early 1900s and spent his time working with children, and trying to better understand how children learn. The psychological roots of constructivism began with the developmental work of Jean Piaget (1896-1980), who developed a theory (the theory of genetic epistemology) that analogized the development of the mind to evolutionary biological development and highlighted the adaptive function of cognition. Over the course of his later
  • 4. 4 career in child psychology, he identified four stages of mental development that chronicled young people's journeys from basic object identification to highly abstract thought. Cognition refers to thinking and memory processes, and cognitive development refers to long- term changes in these processes. One of the most widely known perspectives about cognitive development is the cognitive stage theory of Jean Piaget. Piaget created and studied an account of how children and youth gradually become able to think logically and scientifically. Piaget was also a psychological constructivist. In his view, learning proceeded by the interplay of assimilation (adjusting new experiences to fit prior concepts) and accommodation (adjusting concepts to fit new experiences). The to-and-fro of these two processes leads not only to short term learning, but also to long-term developmental change. The long-term developments are really the main focus of Piaget‘s cognitive theory. After observing children closely, Piaget proposed that cognition developed through distinct stages from birth through the end of adolescence. By stages he meant a sequence of thinking patterns with four key features: 1. They always happen in the same order. 2. No stage is ever skipped. 3. Each stage is a significant transformation of the stage before it. 4. Each later stage incorporated the earlier stages into itself. Basically this is the ―staircase‖ model of development mentioned at the beginning of this chapter. Piaget proposed four major stages of cognitive development, and called them: (1) Sensorimotor intelligence (2) Preoperational thinking (3) Concrete operational thinking, and (4) Formal operational thinking. Each stage is correlated with an age period of childhood, but only approximately.
  • 5. 5 THE SENSORIMOTOR STAGE: BIRTH TO AGE 2 In Piaget‘s theory, the sensorimotor stage is first, and is defined as the period when infants ―think‖ by means of their senses and motor actions. The first stage of development lasts from birth to approximately age two. At this point in development, children know the world primarily through their senses and motor movements. As every new parent will attest, infants continually touch, manipulate, look, listen to, and even bite and chew objects. According to Piaget, these actions allow them to learn about the world and are crucial to their early cognitive development. The infant‘s actions allow the child to represent (or construct simple concepts of) objects and events. A toy animal may be just a confusing array of sensations at first, but by looking, feeling, and manipulating it repeatedly, the child gradually organizes her sensations and actions into a stable concept, toy animal. The representation acquires a permanence lacking in the individual experiences of the object, which are constantly changing. Because the representation is stable, the child ―knows,‖ or at least believes, that toy animal exists even if the actual toy animal is temporarily out of sight. Piaget called this sense of stability object permanence, a belief that objects exist whether or not they are actually present. It is a major achievement of sensorimotor development, and marks a qualitative transformation in how older infants (24 months) think about experience compared to younger infants (6 months). During much of infancy, of course, a child can only barely talk, so sensorimotor development initially happens without the support of language. It might therefore seem hard to know what infants are thinking, but Piaget devised several simple, but clever experiments to get around their lack of language, and that suggest that infants do indeed represent objects even without being able to talk (Piaget, 1952). In one, for example, he simply hid an object (like a toy animal) under a blanket. He found that doing so consistently prompts older infants (18–24 months) to search for the object, but fails to prompt younger infants (less than six months) to do so. (You can try this experiment yourself if you happen to have access to young infant.) ―Something‖ motivates the search by the older infant even without the benefit of much language, and the ―something‖ is presumed to be a permanent concept or representation of the object..
  • 6. 6 THE PREOPERATIONAL STAGE: AGE 2 TO 7 In the preoperational stage, children use their new ability to represent objects in a wide variety of activities, but they do not yet do it in ways that are organized or fully logical. The second stage of development lasts from the ages of two to seven and is characterized by the development of language and the emergence of symbolic play. One of the most obvious examples of this kind of cognition is dramatic play, the improvised make-believe of preschool children. If you have ever had responsibility for children of this age, you have likely witnessed such play. Ashley holds a plastic banana to her ear and says: ―Hello, Mom? Can you be sure to bring me my baby doll? OK!‖ Then she hangs up the banana and pours tea for Jeremy into an invisible cup. Jeremy giggles at the sight of all of this and exclaims: ―Rinnng! Oh Ashley, the phone is ringing again! You better answer it.‖ And on it goes. In a way, children immersed in make-believe seem ―mentally insane,‖ in that they do not think realistically. But they are not truly insane because they have not really taken leave of their senses. At some level, Ashley and Jeremy always know that the banana is still a banana and not really a telephone; they are merely representing it as a telephone. They are thinking on two levels at once—one imaginative and the other realistic. This dual processing of experience makes dramatic play an early example of metacognition, or reflecting on and monitoring of thinking itself. Metacognition is a highly desirable skill for success in school, one that teachers often encourage (Bredekamp & Copple, 1997; Paley, 2005). Partly for this reason, teachers of young children (preschool, kindergarten, and even first or second grade) often make time and space in their classrooms for dramatic play, and sometimes even participate in it themselves to help develop the play further. THE CONCRETE OPERATIONAL STAGE: AGE 7 TO 11 The third stage of cognitive development lasts from the ages of seven to approximately age 11. At this point, logical thought emerges but children still struggle with abstract and theoretical thinking. As children continue into elementary school, they become able to represent ideas and events more flexibly and logically. Their rules of thinking still seem very basic by adult standards and usually operate unconsciously, but they allow children to solve problems more
  • 7. 7 systematically than before, and therefore to be successful with many academic tasks. In the concrete operational stage, for example, a child may unconsciously follow the rule: ―If nothing is added or taken away, then the amount of something stays the same.‖ This simple principle helps children to understand certain arithmetic tasks, such as in adding or subtracting zero from a number, as well as to do certain classroom science experiments, such as ones involving judgments of the amounts of liquids when mixed. Piaget called this period the concrete operational stage because children mentally ―operate‖ on concrete objects and events. They are not yet able, however, to operate (or think) systematically about representations of objects or events. Manipulating representations is a more abstract skill that develops later, during adolescence. Concrete operational thinking differs from preoperational thinking in two ways, each of which renders children more skilled as students. One difference is reversibility, or the ability to think about the steps of a process in any order. Imagine a simple science experiment, for example, such as one that explores why objects sink or float by having a child place an assortment of objects in a basin of water. Both the preoperational and concrete operational child can recall and describe the steps in this experiment, but only the concrete operational child can recall them in any order. This skill is very helpful on any task involving multiple steps—a common feature of tasks in the classroom. In teaching new vocabulary from a story, for another example, a teacher might tell students: ―First make a list of words in the story that you do not know, then find and write down their definitions, and finally get a friend to test you on your list.‖ These directions involve repeatedly remembering to move back and forth between a second step and a first—a task that concrete operational students—and most adults—find easy, but that preoperational children often forget to do or find confusing. If the younger children are to do this task reliably, they may need external prompts, such as having the teacher remind them periodically to go back to the story to look for more unknown words The other new feature of thinking during the concrete operational stage is the child‘s ability to decenter, or focus on more than one feature of a problem at a time. There are hints of decentration in preschool children‘s dramatic play, which requires being aware on two levels at once—knowing that a banana can be both a banana and a ―telephone.‖ But the decentration of the concrete operational stage is more deliberate and conscious than preschoolers‘ make-believe.
  • 8. 8 Now the child can attend to two things at once quite purposely. Suppose you give students a sheet with an assortment of subtraction problems on it, and ask them to do this: ―Find all of the problems that involve two-digit subtraction and that involve borrowing from the next column. Circle and solve only those problems.‖ Following these instructions is quite possible for a concrete operational student (as long as they have been listening!) because the student can attend to the two subtasks simultaneously—finding the two-digit problems and identifying which actually involve borrowing. (Whether the student actually knows how to ―borrow‖ however, is a separate question.) In real classroom tasks, reversibility and decentration often happen together. A well-known example of joint presence is Piaget‘s experiments with conservation, the belief that an amount or quantity stays the same even if it changes apparent size or shape (Piaget, 2001; Matthews, 1998). Imagine two identical balls made of clay. Any child, whether preoperational or concrete operational, will agree that the two indeed have the same amount of clay in them simply because they look the same. But if you now squish one ball into a long, thin ―hot dog,‖ the preoperational child is likely to say that the amount of that ball has changed—either because it is longer or because it is thinner, but at any rate because it now looks different. The concrete operational child will not make this mistake, thanks to new cognitive skills of reversibility and decentration: for him or her, the amount is the same because ―you could squish it back into a ball again‖ (reversibility) and because ―it may be longer, but it is also thinner‖ (decentration). Piaget would say the concrete operational child ―has conservation of quantity.‖ The classroom examples described above also involve reversibility and decentration. As already mentioned, the vocabulary activity described earlier requires reversibility (going back and forth between identifying words and looking up their meanings); but it can also be construed as an example of decentration (keeping in mind two tasks at once—word identification and dictionary search). And as mentioned, the arithmetic activity requires decentration (looking for problems that meet two criteria and also solving them), but it can also be construed as an example of reversibility (going back and forth between subtasks, as with the vocabulary activity). Either way, the development of concrete operational skills support students in doing many basic academic tasks; in a sense they make ordinary schoolwork possible.
  • 9. 9 THE FORMAL OPERATIONAL STAGE: AGE 11 AND BEYOND In the last of the Piagetian stages, the child becomes able to reason not only about tangible objects and events, but also about hypothetical or abstract ones. In the fourth and final stage of cognitive development, lasting from age 12 and into adulthood, children become much more adept and abstract thought and deductive reasoning. Hence it has the name formal operational stage—the period when the individual can ―operate‖ on ―forms‖ or representations. With students at this level, the teacher can pose hypothetical (or contrary-to-fact) problems: ―What if the world had never discovered oil?‖ or ―What if the first European explorers had settled first in California instead of on the East Coast of the United States?‖ To answer such questions, students must use hypothetical reasoning, meaning that they must manipulate ideas that vary in several ways at once, and do so entirely in their minds. The hypothetical reasoning that concerned Piaget primarily involved scientific problems. His studies of formal operational thinking therefore often look like problems that middle or high school teachers pose in science classes. In one problem, for example, a young person is presented with a simple pendulum, to which different amounts of weight can be hung (Inhelder & Piaget, 1958). The experimenter asks: ―What determines how fast the pendulum swings: the length of the string holding it, the weight attached to it, or the distance that it is pulled to the side?‖ The young person is not allowed to solve this problem by trial-and-error with the materials themselves, but must reason a way to the solution mentally. To do so systematically, he or she must imagine varying each factor separately, while also imagining the other factors that are held constant. This kind of thinking requires facility at manipulating mental representations of the relevant objects and actions—precisely the skill that defines formal operations. As you might suspect, students with an ability to think hypothetically have an advantage in many kinds of school work: by definition, they require relatively few ―props‖ to solve problems. In this sense they can in principle be more self-directed than students who rely only on concrete operations—certainly a desirable quality in the opinion of most teachers. Note, though, that formal operational thinking is desirable but not sufficient for school success, and that it is far from being the only way that students achieve educational success. Formal thinking skills do not insure that a student is motivated or well-behaved, for example, nor does it guarantee other desirable skills, such as ability at sports, music, or art. The fourth stage in Piaget‘s theory is
  • 10. 10 really about a particular kind of formal thinking, the kind needed to solve scientific problems and devise scientific experiments. Since many people do not normally deal with such problems in the normal course of their lives, it should be no surprise that research finds that many people never achieve or use formal thinking fully or consistently, or that they use it only in selected areas with which they are very familiar (Case & Okomato, 1996). For teachers, the limitations of Piaget‘s ideas suggest a need for additional theories about development—ones that focus more directly on the social and interpersonal issues of childhood and adolescence. The next sections describe some of these. IMPORTANT CONCEPTS To better understand some of the things that happen during cognitive development, it is important first to examine a few of the important ideas and concepts introduced by Piaget. The following are some of the factors that influence how children learn and grow. Schemas: A schema describes both the mental and physical actions involved in understanding and knowing. Schemas are categories of knowledge that help us to interpret and understand the world. In Piaget's view, a schema includes both a category of knowledge and the process of obtaining that knowledge. As experiences happen, this new information is used to modify, add to, or change previously existing schemas. For example, a child may have a schema about a type of animal, such as a dog. If the child's sole experience has been with small dogs, a child might believe that all dogs are small, furry, and have four legs. Suppose then that the child encounters an enormous dog. The child will take in this new information, modifying the previously existing schema to include these new observations. Assimilation: The process of taking in new information into our already existing schemas is known as assimilation. The process is somewhat subjective because we tend to modify experiences and information slightly to fit in with our preexisting beliefs. In the example above, seeing a dog and labeling it "dog" is a case of assimilating the animal into the child's dog schema.
  • 11. 11 Accommodation: Another part of adaptation involves changing or altering our existing schemas in light of new information, a process known as accommodation. Accommodation involves modifying existing schemas, or ideas, as a result of new information or new experiences.5 New schemas may also be developed during this process. Equilibration: Piaget believed that all children try to strike a balance between assimilation and accommodation, which is achieved through a mechanism Piaget called equilibration. As children progress through the stages of cognitive development, it is important to maintain a balance between applying previous knowledge (assimilation) and changing behavior to account for new knowledge (accommodation). Equilibration helps explain how children can move from one stage of thought to the next. IMPLICATION OF THE THEORY TO SCIENCE EDUCTION Implications of constructivism for teaching and learning 1. Teachers act as facilitators, supports, guides and models of learning. • Learning concerns adjusting our mental models to accommodate new experiences 2. Learning concerns making connections between information. 3. Instruction should be built around more complex problems, not problems with clear, correct answers. 4. Context and personal knowledge have high significance 5. Students should help establish the criteria on which their work is assessed 6. Teachers know more and shouldn‘t let students muddle around 7. Student learning depends on background knowledge – that‘s why teaching facts is so necessary (reversed). 8. Student interest and effort are more important than textbook content. 9. It is sometimes better for teachers, not students, to decide what activities are to be done.
  • 12. 12 10. Sense making and thinking are most important, not knowing content. 11. Experimentation replaces rote learning 12. Teaching utilizes both skill-based and open-ended approaches 13. Motivation to learn is intrinsic rather than extrinsic (done for its own sake rather than for grades, test scores or rewards) 14. Learners often produce unique and personal knowledge. 15. Naïve beliefs are used as the starting point for further discussion, exploration and evaluation for development, rather than being discounted as ‗wrong‘ 16. Learning for transfer is important. 17. Learners learn best through finding and generating their own knowledge. • Discovery and guided discovery learning are important. • Exploration and active learning are important. 18. Learning is collaborative and cooperative, not just individual. 19. Higher order thinking is significant. 20. Classrooms become multidimensional, with different activities at different levels taking place simultaneously. Piaget's theory of constructivism impacts learning curriculum because teachers have to make a curriculum plan which enhances their students' logical and conceptual growth. Teacher must put emphasis on the significant role that experiences-or connections with the adjoining atmosphere- play in student education. For example, teachers must bear in mind the role those fundamental concepts, such as the permanence of objects, plays when it comes to establishing cognitive structures. Piaget's theory of constructivism argues that people produce knowledge and form meaning based upon their experiences. Piaget's theory covered learning theories, teaching methods, and education reform. Two of the key components which create the construction of an individual's new knowledge are accommodation and assimilation. Assimilating causes an individual to incorporate new experiences into the old experiences. This causes the individual to develop new
  • 13. 13 outlooks, rethink what were once misunderstandings, and evaluate what is important, ultimately altering their perceptions. Accommodation, on the other hand, is reframing the world and new experiences into the mental capacity already present. Individuals conceive a particular fashion in which the world operates. When things do not operate within that context, they must accommodate and reframing the expectations with the outcomes. Apart from learning theories, Piaget's theory of constructivism addresses how learning actually occurs, not focusing on what influences learning. The role of teachers is very important. Instead of giving a lecture the teachers in this theory function as facilitators whose role is to aid the student when it comes to their own understanding. This takes away focus from the teacher and lecture and puts it upon the student and their learning. The resources and lesson plans that must be initiated for this learning theory take a very different approach toward traditional learning as well. Instead of telling, the teacher must begin asking. Instead of answering questions that only align with their curriculum, the facilitator in this case must make it so that the student comes to the conclusions on their own instead of being told. Also, teachers are continually in conversation with the students, creating the learning experience that is open to new directions depending upon the needs of the student as the learning progresses. Teachers following Piaget's theory of constructivism must challenge the student by making them effective critical thinkers and not being merely a "teacher" but also a mentor, a consultant, and a coach. Piaget's theories and works are significant to people who work with children, as it enables them to understand that children's development is based on stages. The construction of identity and knowledge as one predicated upon the development of stages helps to explain the intellectual growth of children of all ages. Piaget's ideas have helped to construct the notion of learning as not something linear and depository, but rather as an element that must be understood in accordance to the cognitive stage of the child. it is through this that Piaget's work becomes invaluable to educators and those who work with children for it allows one to understand why children learn at the rate they do. This is essential for those who work with children as it helps to explain some of the most fundamental issues behind why children learn and how to proceed with instruction of children.
  • 14. 14  The influence of Piaget‘s ideas in developmental psychology has been enormous. He changed how people viewed the child‘s world and their methods of studying children. He was an inspiration to many who came after and took up his ideas. Piaget's ideas have generated a huge amount of research which has increased our understanding of cognitive development.  His ideas have been of practical use in understanding and communicating with children, particularly in the field of education (re: Discovery Learning). AWARDS AND LEGACY Piaget received honorary degrees from Oxford and Harvard universities and made many impressive guest appearances at conferences concerning childhood development and learning. Piaget was the recipient of an array of honorary degrees and accolades, including the prestigious Erasmus (1972) and Balzan (1979) prizes He remained a quiet figure, though, preferring to avoid the spotlight. This kind of lifestyle allowed him to further develop his theories. The author of more than 50 books and hundreds of papers, Piaget summed up his passion for the ongoing pursuit of scientific knowledge with these words: "The current state of knowledge is a moment in history, changing just as rapidly as the state of knowledge in the past has ever changed and, in many instances, more rapidly." Piaget kept himself to a strict personal schedule that filled his entire day. He awoke every morning at four and wrote at least four publishable pages before teaching classes or attending meetings. After lunch he would take walks and ponder on his interests. "I always like to think on a problem before reading about it," he said. He read extensively in the evening before going to bed. Every summer he vacationed in the Alpine Mountains of Europe and wrote many works. DEATH Jean Piaget died of unknown causes on September 16, 1980, in Geneva, Switzerland. He was 84 years old. His body rests at the Cimetière des Plainpalais.
  • 15. 15 THE INFLUENCE ON BIOLOGY His theory of cognitive development suggests that children move through four different stages of mental development, which helps to make teaching a student easy. Piaget believed that children's understanding through at least the first three stages differ from those of adults and are based on actively exploring the environment (surroundings) rather than on language understanding. This theory has a great impact on the teaching and learning process as a biology teacher. With it, a teacher can relate a child‘s age and the possible error he or she can make. It can help design a curriculum to help children explore the world in their own way as he believes they think different from adults. Piaget believed that the process of thinking and the intellectual development could be regarded as an extension of the biological process which has also two on- going processes: assimilation and accommodation. To test his theory, Piaget observed the habits in his own children. As a biology teacher ,the teacher is made to understand the various stages of development of a child- What he or she can assimilate at that age. With this stage of development, a teacher is able to understand the learning differences among child of same age group. Those who are fast or slow learners. At this early stage of development a teacher can as well know the temperament which each child‘s fall under.
  • 16. 16 REFERENCES Bringuier, J.C. (1980). Conversations with Jean Piaget. Chicago: University of Chicago Press. Edwards, L., Hopgood, J., Rosenberg, K., & Rush, K. (2000). Mental Development and Education. Retrieved April 25, 2009, from Flinders University Web site: http://ehlt.flinders.edu.au/education/DLiT/2000/Piaget/begin.htm Huitt, W. & Hummel, J. (1998). Cognitive development. Retrieved April 25, 2009 from the World Wide Web: http://chiron.valdosta.edu/whuitt/col/cogsys/piaget.html Lefrancois, G.R. (2006). Theories of Human Learning. Belmont, CA: Thomson Higher Education. Evans, R. (1973). Jean Piaget, the Man and His Ideas. New York: Dutton. Piaget, J. (1952). Autobiography. In E. Boring (ed). History of psychology in autobiography. Vol. 4. Worcester, MA: Clark University Press Piaget, J. (1936) Origins of intelligence in the child. London: Routledge & Kegan Paul. Piaget, J. (1945) Play, dreams and imitation in childhood. London: Heinemann. Piaget, J. (1970) Main trends in psychology. London: George Allen & Unwin. Piaget, J. (1970). Genetic epistemology. New York: W.W. Norton & Company. Piaget, J. (1973). Memory and intelligence. New York: BasicBooks (2009). Piaget's stages of cognitive development. Retrieved April 30, 2009, from About.com: Psychology Web site: http://psychology.about.com/library/quiz/bl_piaget_quiz.htm Plucker, J. (2007). Human Intelligence . Retrieved May 1, 2009, from Indiana University Web site: http://www.indiana.edu/~intell/piaget.shtml Slavin, R.E. (2005). Educational psychology: theory and practice. Needham Heights, MA: Allyn and Bacon.
  • 17. 17 Smith, L. (2000). A brief biography of jean piaget. Retrieved April 25, 2009, from Jean Piaget Society Web site: http://www.piaget.org/aboutPiaget.html Wadsworth, B.J. (1996). Piaget's theory of cognitive and affective development: White Plains, NY: Longman. Wood, K.C. (2008). Piaget's Stages. Retrieved April 25, 2009, from Department of Educational Psychology and Instrutional Technology, University of Georgia Web site: http://projects.coe.uga.edu/eplt /index.php?title=Piaget%27s_Stages#Educational_Implications
  • 18. 18 JEROME BRUNER THE THEORIST Jerome Bruner was a cognitive psychologist who felt that the goal of education should be intellectual development, as opposed to rote memorization of facts. Bruner held the following beliefs regarding learning and education:  He believed curriculum should foster the development of problem-solving skills through the processes of inquiry and discovery.  He believed that subject matter should be represented in terms of the child's way of viewing the world.  That curriculum should be designed so that the mastery of skills leads to the mastery of still more powerful ones.  He also advocated teaching by organizing concepts and learning by discovery.  Finally, he believed culture should shape notions through which people organize their views of themselves and others and the world in which they live. BACKGROUND AND EARLY LIFE Bruner was born blind (due to cataracts) on October 1, 1915, in New York City, to Herman and Rose Bruner, who were Polish Jewish immigrants. An operation at age two restored his vision. He received a bachelor's of arts degree in Psychology in 1937 from Duke University, and went on to earn a master's degree in Psychology in 1939 and then a doctorate in Psychology in 1941 from Harvard University. In 1939, Bruner published his first psychological article on the effect of thymus extract on the sexual behavior of the female rat. During World War II, Bruner served on the Psychological Warfare Division of the Supreme Headquarters Allied Expeditionary Force committee under General Dwight D. Eisenhower, researching social psychological phenomena. In 1945, Bruner returned to Harvard as a psychology professor and was heavily involved in research relating to cognitive psychology and educational psychology. In 1970, Bruner left Harvard to teach at the University of Oxford in the United Kingdom. He returned to the United
  • 19. 19 States in 1980, to continue his research in developmental psychology. In 1991, Bruner joined the faculty at New York University (NYU), where he taught primarily in the School of Law, THE THEORY ITSELF The intellectual development includes three stages: i. Enactive stage (learning through action) ii. Iconic stage (learners‘ use of pictures or models) iii. Symbolic stage(Development of the ability to think in abstract term). Enactive (0 - 1 years) This is the first kind of memory. This mode is used within the first year of life (corresponding with Piaget‘s sensorimotor stage). Thinking is based entirely on physical actions, and infants learn by doing, rather than by internal representation (or thinking). It involves encoding physical action based information and storing it in our memory. For example, in the form of movement as a muscle memory, a baby might remember the action of shaking a rattle. Iconic (1 - 6 years) Information is stored as sensory images (icons), usually visual ones, like pictures in the mind. For some, this is conscious; others say they don‘t experience it. This may explain why, when we are learning a new subject, it is often helpful to have diagrams or illustrations to accompany the verbal information. Thinking is also based on the use other mental images (icons), such as hearing, smell or touch. Symbolic (7 years onwards) This develops last. This is where information is stored in the form of a code or symbol, such as language. This mode is acquired around six to seven years-old (corresponding to Piaget‘s concrete operational stage). In the symbolic stage, knowledge is stored primarily as words, mathematical symbols, or in other symbol systems, such as music. Symbols are flexible in that they can be manipulated, ordered, classified etc., so the user isn‘t constrained by actions or images (which have a fixed relation to that which they represent).
  • 20. 20 IMPLICATION OF BRUNER’S THEORY OF LEARNING TO SCIENCE EDUCATION Burner‘s theory of learning in education aims at creating autonomous learners (learning to learn). The purpose of education is not to impact knowledge, but instead to facilitate a child‘s thinking and problem-solving which can then be transferred to a range of situations. Learning is an active process. Learners select and transform information. Learners make appropriate decisions and postulate hypotheses and test their effectiveness. Learners use prior experience to fit new information into the pre-existing structures. Scaffolding is the process through which able peers or adult offers supports for learning. This assistance becomes gradually less frequent as it becomes unnecessary. Educational Implications The aim of education should be to create autonomous learners (i.e., learning to learn). For Bruner (1961), the purpose of education is not to impart knowledge, but instead to facilitate a child's thinking and problem-solving skills which can then be transferred to a range of situations. Specifically, education should also develop symbolic thinking in children. In 1960 Bruner's text, The Process of Education was published. The main premise of Bruner's text was that students are active learners who construct their own knowledge.  Readiness Bruner (1960) opposed Piaget's notion of readiness. He argued that schools waste time trying to match the complexity of subject material to a child's cognitive stage of development. This means students are held back by teachers as certain topics are deemed too difficult to understand and must be taught when the teacher believes the child has reached the appropriate state of cognitive maturity.  The Spiral Curriculum Bruner (1960) adopts a different view and believes a child (of any age) is capable of understanding complex information: 'We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any stage of development.' (p. 33) Bruner (1960) explained how this was possible through the concept of the spiral curriculum. This involved information being structured so that complex ideas can be taught at a
  • 21. 21 simplified level first, and then re-visited at more complex levels later on.Therefore, subjects would be taught at levels of gradually increasing difficultly (hence the spiral analogy). Ideally, teaching his way should lead to children being able to solve problems by themselves.  Discovery Learning Bruner (1961) proposes that learners‘ construct their own knowledge and do this by organizing and categorizing information using a coding system. Bruner believed that the most effective way to develop a coding system is to discover it rather than being told it by the teacher. The concept of discovery learning implies that students construct their own knowledge for themselves (also known as a constructivist approach). The role of the teacher should not be to teach information by rote learning, but instead to facilitate the learning process. This means that a good teacher will design lessons that help students discover the relationship between bits of information. To do this a teacher must give students the information they need, but without organizing for them. The use of the spiral curriculum can aid the process of discovery learning. Bruner and Vygotsky Both Bruner and Vygotsky emphasize a child's environment, especially the social environment, more than Piaget did. Both agree that adults should play an active role in assisting the child's learning. Bruner, like Vygotsky, emphasized the social nature of learning, citing that other people should help a child develop skills through the process of scaffolding. Scaffolding refers to the steps taken to reduce the degrees of freedom in carrying out some task so that the child can concentrate on the difficult skill she is in the process of acquiring' (Bruner, 1978, p. 19). He was especially interested in the characteristics of people whom he considered to have achieved their potential as individuals. The term scaffolding first appeared in the literature when Wood, Bruner, and Ross described how tutors' interacted with a pre-schooler to help them solve a block reconstruction problem (Wood et al., 1976). The concept of scaffolding is very similar to Vygotsky's notion of the zone of proximal development, and it's not uncommon for the terms to be used interchangeably.
  • 22. 22 Scaffolding involves helpful, structured interaction between an adult and a child with the aim of helping the child achieve a specific goal. The purpose of the support is to allow the child to achieve higher levels of development by:  Simplifying the task or idea.  Motivating and encouraging the child.  Highlighting important task elements or errors.  Giving models that can be imitated. Bruner and Piaget agree that Children are innately pre-adapted to learning Children have a natural curiosity Children‘s cognitive structures develop over time Children are active participants in the learning process Cognitive development entails the acquisition of symbols They Disagree that Social factors, particularly language, were important for cognitive growth. These underpin the concept of ‗scaffolding‘. The development of language is a cause not a consequence of cognitive development you can speed-up cognitive development. you don‘t have to wait for the child to be ready the involvement of adults and more knowledgeable peers makes a big difference. AWARDS As an adjunct professor at NYU School of Law, Bruner studied how psychology affects legal practice. During his career, Bruner was awarded honorary doctorates from Yale University, Columbia University, The New School, the Sorbonne, the ISPA Instituto Universitário, as well as colleges and universities in such locations as Berlin and Rome, and was a Fellow of the American Academy of Arts and Sciences. DEATH He turned 100 in October 2015 and died on June 5, 2016.
  • 23. 23 INFLUENCEOF THE THEORY ON BIOLOGY As a biology teacher, concepts should be taught from simple to complex. The use of pictures, charts and models can never be overemphasized. Bruner states that what determines the level of intellectual development is the extent to which the child has been given appropriate instruction together with practice or experience. So, the right way of presentation and the right explanation will enable a child to grasp a concept usually only understood by an adult. His theory stresses the role of education and the adult. Although Bruner proposes stages of cognitive development, he doesn‘t see them as representing different separate modes of thought at different points of development (like Piaget). Instead, he sees a gradual development of cognitive skills and techniques into more integrated ―adult‖ cognitive techniques. Bruner views symbolic representation as crucial for cognitive development, and since language is our primary means of symbolizing the world, he attaches great importance to language in determining cognitive development. The teachers must revisit material to enhance knowledge. Building on pre-taught ideas to grasp the full formal concept is of paramount importance according to Bruner. Feel free to re-introduce vocabulary, grammar points, and other topics now and then in order to push the students to a deeper comprehension and longer retention. Material must be presented in a sequence giving the learners the opportunity to: 1) acquire and construct knowledge, 2) transform and transfer his learning.  Students should be involved in using their prior experiences and structures to learn new knowledge.  Help students to categorize new information in order to able to see similarities and differences between items.  Teachers should assist learners in building their knowledge. This assistance should fade away as it becomes unnecessary.
  • 24. 24  Teachers should provide feedback that is directed towards intrinsic motivation. Grades and competition are not helpful in the learning process. Bruner states that learners must ―experience success and failure not as reward and punishment, but as information‖
  • 25. 25 REFERENCES Anderson, J. R. (1990). Cognitive psychology and its implications(3rd ed.). New York: Bruner, J. S. (1957). Going beyond the information given. New York: Norton. Bruner, J. S. (1960). The Process of education. Cambridge, Mass.: Harvard University Press. Bruner, J. S. (1961). The act of discovery. Harvard Educational Review, 31, 21-32. Bruner, J. S. (1966). Toward a theory of instruction, Cambridge, Mass.: Belkapp Press. Bruner, J. S. (1973). The relevance of education. New York: Norton. Bruner, J. S. (1978). The role of dialogue in language acquisition. In A. Sinclair, R., J. Jarvelle, and W. J.M. Levelt (eds.) The Child's Concept of Language. New York: Springer-Verlag. Freeman.Berk, L. E. (1997). Child development (4th ed.). Needham Heights, MA: Allyn & Bacon.Burns, M., & Silbey, R. (2000). So you have to teach math? Sound advice for K-6 teachers. Sausalito, CA: Math Solutions Publications. Eggen, P. D., & Kauchak, D. P. (2000). Educational psychology: Windows on classrooms (5th ed.). Upper Saddle River, NJ: Prentice Hall.Fuson, K. C. (1988). Children‘s counting and concepts of numbers. New York: Springer.Gelman, R., Meck, E., & Merkin, S. (1986). Young children‘s numerical competence. Cognitive Development, 1, 1–29. Johnson-Laird, P. N. (1999). Deductive reasoning. Annual Review of Psychology, 50, 109–135. Kamii, C. (1982). Number in preschool and kindergarten: Educational implications of Piaget‘s theory. Washington, DC: National Association for the Education ofYoung Children.
  • 26. 26 Martin, D. J. (2000). Elementary science methods:A constructivist approach (2nd ed.). Belmont, CA: Wadsworth. McLeod, S. A. (2019, July 11). Bruner. Simply psychology: https://www.simplypsychology.org/bruner.html McNallyWeinert, F. E., & Helmke, A. (1998). The neglected role of individual differences in theoretical models of cognitive development. Learning and Instruction, 8, 309–324. Papila, D. E., & Olds, S. W. (1996). A child‘s world: Infancy through adolescence (7th ed.). New York: McGraw-Hill. Piaget, J. (1970). Science of education and the psychology of the child. New York: Viking. Piaget, J. (1977). Epistemology and psychology of functions. Dordrecht, Netherlands: D. Reidel Publishing Company.Thompson, C. S. (1990). Place value and larger numbers. In J. N. Payne (Ed.), Mathematics for young children (pp. 89–108). Reston, VA: National Council of Teachers of Mathematics. Thurstone, L. L. (1970). Attitudes can be measured. In G. F. Summers (Ed.), Attitude measurement (pp. 127–141). Chicago: Rand. Wise, S. L. (1985). The development and validity of a scale measuring attitudes toward statistics. Educational and Psychological Measurement, 45, 401–405. Wood, D. J., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychiatry and Psychology, 17(2), 89-100. Zimmerman, B. J., & Whitehurst, G. J. (1979). Structure and function: A comparison of two views of the development of language and cognition. In G. J. Whitehurst and B. J. Zimmerman (Eds.), The functions of language and cognition(pp. 1–22). New York: Academy https://www.simplypsychology.org/bruner.html
  • 27. 27