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20130306210342Kuliah 2a - Learning Theoies Piaget, Bruner, Vygosky

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Learning theories and psychology in mathematics education PROF. MADYA DR. NOOR SHAH SAAD JABATAN PENGAJIAN PENDIDIKAN FAKULTI PENDIDIKAN & PEMBANGUNAN MANUSIA 
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Learning theories and psychology inmathematics education

PROF. MADYA DR. NOOR SHAH SAADJABATAN PENGAJIAN PENDIDIKAN

FAKULTI PENDIDIKAN & PEMBANGUNAN MANUSIA 

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Learning theories and psychology inmathematics education are concerned with

the intellectual development of the learnersand their applications in the teaching andlearning mathematics.

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The effective mathematics teachers should not only havean excellent grasp of the subject content but should also

have the knowledge on:

how mathematics should be learned,

theories of children’s development,

understanding how learners learn,

theories of mathematical learning and instruction,

instructional method and strategy, and

problem solving in mathematics.

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Our focus:the psychologists’ theory related to theteaching and learning of mathematics forearly childhood ( 0 to 12 years) 

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 - Most influential contemprorary 

theoriest in the area of cognitive

development

- Intellectual Development Theory 

JEAN PIAGET (1896 -

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The theory is about knowledge and how the

knowledge develops in the humanorganism.

There are two theories:

Theory of learning process

Cognitive development theory.

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Theory of learning process

Piaget stress that:

The basis of all learning is the children’s self activities when interacting with environment (physically or socially).

Children’s mental activity is arrange in the mentalstructure (different mental structure can be groupedtogether as schema or a behavioral pattern).

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Mental activities is an adaptation process.

•   Adaptation is a process through which theperson seeks an equilibrium or balance between

 what he or she presently perceives, knows, andunderstands, and what he or she sees in any newphenomenon, experience, or problem.

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 Adaptation includes two processes (inter-connected):

 Assimilation

Combines new experience into an existingschema (cognitive structures)

Interpret the new experience base on previousexperience in the schema (cognitivestructures)

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 Accommodation

Permanent modification of the mentalstructure to fulfill the need of new experience.

Modification can be in qualitative andquantitative in nature.

Frequently happened in learning.

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 Assimilation, accommodation andequilibration

Three important terms in teaching mathematics problemsolving

 Assimilation Accommodation

Equilibration

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Two adaptation process (inter-connected):

 AssimilationCombines new experience into an existingschema (preexisting knowledge).

Interpret the new experience base on previousexperience in the schema.

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  How are these two adaptation processes occur in

teaching?

Example: Teaching addition of numbers:

4+ 5

9

1 2+ 35

4 7

2 5+ 3 8

5 13

 Why thishappened?

This is assimilation.How to overcome the problems?

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Could they overcome the problem by explaining?

Do you have any better ideas?

 Just explaining might be not working.

Most importantly, make them aware of their own mistake.

Make them aware of cognitive conflict.

How?

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 AccommodationPermanent modification of the mentalstructure to fulfill the need of new experience.

Modification can be in qualitative and

quantitative in nature.Frequently happened in learning.

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See this way:

2 6+ 4 7

613

4 6+ 5 3

9 9

Letcompare

each of the values

involved

This is accommodation.

Post questions and make them thingand aware of their mistake

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Equilibration ~ between assimilation &

accommodation

Learning is a process of accumulating new knowledge.

So, use math problems to challenge students and give

opportunity to learn new things.

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Cognitive development theory 

The children’s cognitive development is deferent from oneto another

Changes occur according to the age of the children.

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Cognitive development occur in fourstages:

Sensory-motor stage (0-2 years old)

Pre-operational stage (2-7 years old)

Preconceptual 2 – 4 years

Intuitive 4 – 7 years

Concrete operational stage (7-12 years old)

Formal operational stage (12 years and 18 years)

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a. Sensory-motor stage:

First stage intellectual development occur from 0to 2 years old.

The baby uses sensory-motor to interact and

comprehend the surrounding.They seek stimulation by light and sound

The baby learn to connect the object in the

environment.Eg – recognize the knock on the door as the moment hisfather return home.

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1. Sensory-motor stage:

Children use trial and error to gain mastery overthe environment

Has ability to carry out reflex activity, walk and

finally talk at the end of the stage.

Having fully developed the cognitive structures of the period, the child is ready to move on to the

next stage.

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2. Pre-Operational Stage (2-7 years)

This stage marks the emergence of symbolic functions and theuse of language as a means of representing environmental eventsand objects.

Two substages: preconceptual and Intuitive

Pre-conceptual stage – is a transition period largely characterizedby exploration and investigation.

The more activity children experience, the more they questionand explore

They are interested in the why and how of events.

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2. Pre-Operational Stage (2-7 years)

Start to use simple language and symbol to visualize concepts.

The average two-year-old understand : between 200 – 300 words

The average five-year-old understand: about 2000 wordsBy the age of six: average child has a vocabulary of 16,000 words

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 They are not conscious of the categories they are usingin cognitive functioning;

 Judgment are fragmentary and inconsistent;

Example: Two rows of dimes

Intuitive Stage -

The child will say that the longer row hasmore of dimes in it. WHY 

 

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Three Characteristics:

①   Children’s understanding of concepts is based largely on whatthey see, surface appearances and vivid or dominant characteristics dominate their perception.

The child is fooled by appearances, thelonger row looks like more.

 

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Three Characteristics:

② Comprehension of a situation, event, or object is based ona single perceptual aspect, the most dominant andnoticeable from a perceptual standpoint.

The child only focus on the length of the row

③ Thought is irreversible – the child cannot return to thestarting point of a mental sequence.

The child cannot mentally picture the starting point of the problem.

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2. Pre-Operational Stage (2-7 years)

Cognitive Development – principle of Conservation.

Conservation is the idea that the amount of something stays the same regardless of changes inshape or the number of pieces into which it isdivided.

Piaget studies the conservation of mass, weight, volume, continuous quantity, number.

figure 3.1 (pages 59)

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The children are said to be egocentric.

Egocentric student sees the world only from his or her own

point of view and is unaware of other perspectives and of his or her own limitations.

 Able to think transductively: from one specific example toanother specific example only.

Difficulty:neither deductive or inductive.Do not have capability to compare process.Difficult to differentiate the concept of quantity, volume,space and area.Unable to observe reversal process.

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 3. Concrete operational stage (7-12 ys old)

From 7 until around 12, 13 or 14 years old.

The children’s level of egocentric start to decreasegradually.

 Able to identify certain characteristic of an object.

 Able to classify object into set and subset according tospecific characteristic.

 Acquire the concept of transformation and reversalprocess.

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Reversibility of thought is perfected.

example: 2+3 = 5 then 5 – 3 = 2

If water is frozen into ice, then ice can be meltedinto water.

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 Able to think inductively and deductively.

Not able to think abstractly.

Logical thinking limited to concrete matter only.

Less capability in solving word problem; might resortto unsystematic methods.

Incapable of making generalization:

example: 3+4 = 4+3;

7+12 = 12+7;

thus a+b = b+a.

Less capable of learning more then one concept at thesame time.

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4. Formal operational stage (12 years oldand above)

From 12 to around 16, 17 or 18 yrs old.

Capable in thinking abstract manner and solve complexproblem.

They could think inductively and deductively in order to provemath theorem and roles, and making generalisation andconclusion.

 Able to use math symbol to present abstract idea, relate a certainconcept to another concept, apply logic to solve the problem,

and could argue an implication like “if x, then y”. 

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 Able to carry out scientific thinking and math reasoningex- making hypothesis, test hypothesis and making aconclusion.

 Able to identify all relevance factors related to a problem orsituation.

End of the stage, able to comprehend and apply complexconcept, ex – permutation, combination, proportionality,correlation and probability.

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Math learning and instruction

Needs to understand the children’s ability andreadiness.

But aware, some students in the lower secondary school still in the concrete operational stage.

Needs to examine and identify the intellectualdevelopment characteristics that the studentspossess before teaching.

The teacher should realize that secondary schoolat concrete operational stage need to learn withconcrete materials, especially new topics.

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Ex: Teaching geometry:

Even though students at the concrete operational stage areable to explain and describe certain concept correctly, they might face difficulties in explaining the same concept usingmath symbol and statement (because logical thinkinglimited to concrete matter only).

 Also, not be able to solve word problems; and might usedunsystematic or inaccurate method.

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 Jerome Bruner

Bruner describe: – 

Learning theory (or intellectual developmenttheory) as descriptive:

as mental activities performs by the students at certainstage.

Explains event that has occurred and expected to occur.

Instructional theory (or intellectual developmenttheory) as prescriptive:

The procedure and objective of instruction.

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Bruner’s Learning Theory  

The cognitive development stage.

Enactive Stage (from birth to about age 3)Learning through doing/the children’s own body movements.

Iconic Stage (from about age 3 to about age 8)Learning through body movement and the use of brainsto think and visualize the image in their minds.

Symbolic Stage (from about age 8 upwards)

 Able to think by using appropriate language. Acquire new concepts and use them while command of language improve.

 Able to manipulate symbols.

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Knowledge is represented in the form of informationTable below display example of material that could beused:

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Type of 

material

Enactive

(action)

Iconic (image) Symbolic

(symbol)Manipulative Actual object,

Model of object

Pictorial chip Number cards,

Symbol cards

Printed - Textbooks,Postal,

Photographic picture

Textbooks,Poster

Screen Transparencies,Films

Transparencies,Films, Slides

Transparencies,Films, Slides

Interactive Computersoftware

Computer software Computersoftware

Types of Material and Modes of Representation

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Ex:

 A set of base 10 block consists of a cube measure 1cm by 1cm, a rod measuring 10cm by 1cm, and a block measuring10cm by 10cm by 1cm.

unit Rod Block 

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Ex: Addition: 4 + 5

 Answer: 359

+

=

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Ex: Addition: 124 + 235

 Answer: 359

+

=

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Conclusion - Bruner:

First stage (Anactive – concrete) – learning counting(number or algebra) using block base 10 (DIENES BLOCK).

Second stage (iconic - pictorial) – using pencil to represent

/ concretize situation (ex: 234+335).Third stage (Symbolic/abstract) – ex: no 3 does not haveany meaning unless associate with object.

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 VYGOTSKY 

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Vygotsky

Percaya bahawa perkembangan kognitif berlaku dalampersekitaran sosiobudaya

Kebanyakan daripada kemahiran kognitif kanak-kanak

terhasil daripada interaksi sosial kanak-kanak dengan ibubapa, orang dewasa lain, rakan sebaya dan guru

Kemahiran kognitif kanak-kanak diperoleh melaluibimbingan orang yang lebih dewasa yang menjadi model

dan menstrukturkan pengalaman pembelajaran kanak-kanak

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Proses bimbingan ini dikenali sebagai scalffolding. Konsep“scaffolding”. Scaffolding : sokongan sementara padabinaan. Pelajar beransur-ansur menerima tanggungjawabdari sedikit kepada sepenuhnya ke atas pembelajaran

Pembelajaran ini berlaku dalam zone of proximal development (ZPD) 

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Konsep Zon Perkembangan Proksimal 

Menurut beliau, faktor-faktor yang berpengaruh dalam pembentukanbagaimana seseorang individu berfikir adalah berdasarkan sejarahmasyarakatnya dan pengalamannya dalam masyarakat itu.

 Zone of Proximal Development ('ZPD') - Vygotsky referred to the distance

between the abilities displayed independently and with social support asthe ZPD; his thesis being that this "zone" was created by learning.

ie. ZPD as cite directly from Vygotsky "the distance between the actuallevel of development as determined by independent problem solving[without guided instruction] and the level of potential development asdetermined by problem solving under adult guidance or in collaboration

 with more capable peers". Measurement would thus be achieved by comparing the student's performance on both tasks.

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Penyelesaian masalah

dengan bimbingandaripada orang yang berkebolehan

Tahap Perkembangan Potensi

ZPD ZON OF PROXIMAL DEVELOPMENT

Tahap Perkembangan Sebenar

Penyelesaian masalahsecara bersendirian

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ZPD menjelaskan bahawa kebolehan pelajar akan

meningkat apabila berada dalam pengaruh sosial ataurakan-rakan berbanding dengan pembelajaran secaraindividu.

http://www healthofchildren co

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http://www.healthofchildren.com/C/Cognitive-

Development.htmlInfancy 

 As soon as they are born, infants begin learning to use their senses to explore the world around them. Most newborns can focus on andfollow moving objects, distinguish the pitch and volume of sound, see all colors and distinguish their hue and brightness, and startanticipating events, such as sucking at the sight of a nipple. By three months old, infants can recognize faces; imitate the facial expressions of others, such as smiling and frowning; and respond to familiar sounds.

 At six months of age, babies are just beginning to understand how the world around them works. They imitate sounds, enjoy hearing theirown voice, recognize parents, fear strangers, distinguish between animate and inanimate objects, and base distance on the size of an object.They also realize that if they drop an object, they can pick it up again. At four to seven months, babies can recognize their names.

By nine months, infants can imitate gestures and actions, experiment with the physical properties of objects, understand simple words suchas "no," and understand that an object still exists even when they cannot see it. They also begin to test parental responses to their behavior,such as throwing food on the floor. They remember the reaction and test the parents again to see if they get the same reaction.

 At 12 months of age, babies can follow a fast moving object; can speak two to fours words, including "mama" and "papa"; imitate animalsounds; associate names with objects; develop attachments to objects, such as a toy or blanket; and experience separation anxiety  whenaway from their parents. By 18 months of age, babies are able to understand about 10–50 words; identify body parts; feel a sense of o wnershipby using the word "my" with certain people or objects; and can follow directions that involve two different tasks, such as picking up toys andputting them in a box.

Read more: Cognitive Development - stages, meaning, average, Definition, Description, Common problems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18sr6CHOI 

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Toddlerhood

Between 18 months to three years of age, toddlers have reached the "sensorimotor" stage of Piaget's theory of cognitive development that involves rudimentary thought. For instance, they understand the permanence of objects and people, visually follow the displacement of objects, and begin to use instruments and tools.Toddlers start to strive for more independence, which can present challenges to parents concerned for theirsafety . They also understand discipline and what behavior is appropriate and inappropriate, and they understand the concepts of words like "please" and "thank you."

Two-year-olds should be able to understand 100 to 150 words and start adding about ten new words per day.Toddlers also have a better understanding of emotions, such as love, trust, and fear. They begin to understandsome of the ordinary aspects of everyday life, such as shopping for food, telling time, and being read to.

Read more: Cognitive Development - stages, meaning, average, Definition, Description, Common problems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18srOrXf1 

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Preschool

Preschoolers, ages three to six, should be at the "preoperational" stage of Piaget's cognitivedevelopment theory, meaning they are using their imagery and memory skills. They should beconditioned to learning and memorizing, and their view of the world is normally very self-centered. Preschoolers usually have also developed their social interaction skills, such asplaying and cooperating with other children their own age. It is normal for preschoolers to test

the limits of their cognitive abilities, and they learn negative concepts and actions, such astalking back to adults, lying , and bullying. Other cognitive development in preschoolers aredeveloping an increased attention span, learning to read, and developing structured routines,such as doing household chores.

Read more: Cognitive Development - stages, meaning, average, Definition, Description,Common problems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18srazYL7 

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School age

 Younger school-age children, six to 12 years old, should be at the "concrete operations" stage of Piaget's cognitive developmenttheory, characterized by the ability to use logical and coherent actions in thinking and solving problems. They understand theconcepts of permanence and conservation by learning that volume, weight, and numbers may remain constant despite changesin outward appearance. These children should be able to build on past experiences, using them to explain why some thingshappen. Their attention span should increase with age, from being able to focus on a task for about 15 minutes at age six to anhour by age nine.

 Adolescents, ages 12 through 18, should be at the "formal operations" stage of Piaget's cognitive development theory. It ischaracterized by an increased independence for thinking through problems and situations. Adolescents should be able tounderstand pure abstractions, such as philosophy and higher math concepts. During this age, children should be able to learnand apply general information needed to adapt to specific situations. They should also be able to learn specific information andskills necessary for an occupation. A major component of the passage through adolescence is a cognitive transition. Comparedto children, adolescents think in ways that are more advanced, more efficient, and generally more complex. This ability can beseen in five ways.

Read more: Cognitive Development - stages, meaning, average, Definition, Description, Common problems 

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 Vygotsky's Theory of Cognitive Development

Lev Vygotsky differed from Piaget in that the role of social context and culture inchildren's cognition was a central part of his theory (Rowe and Wertsch 2002).Rather than seeing the development of knowledge as transcending culture andcontext, Vygotsky argued that an understanding of how knowledge developsrequires an understanding of the social and historical origins of knowledge and of changes in that knowledge. He also proposed a central role for language in cognitivedevelopment. Vygotsky argued that human knowledge originates in socially meaningful activity and is shaped by language.

Read more: Development - Cognitive, Self - EMOTIONAL, MORAL - Symbolic

Interactionism, Gender, Theory, Family, History, Definition, Children, Child, andEmotions http://family.jrank.org/pages/371/Development.html#ixzz18ssr8Zph 

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Processes that originate in the social world are transferred to the inner mental world (inner speech), and shape the development of higher cognitive processes such as problem-solving. A key part of this transfer lies in the child's mastery of the symbolic or artificial stimuli (signs)characteristic of the child's culture, such as language. Part of the development of children'sthinking therefore requires apprenticeship into culturally specific cognitive and socialpractices. According to Vygotsky, cognitive development does not happen just in the head of the child. Rather, it is a process of learning to operate with physical, symbolic, and cognitivetools in ways that in themselves change cognitive processes. The difference between a child'sindividual performance and that child's performance when guided by experts is metaphorically described by Vygotsky's zone of proximal development (ZPD). The ZPD was described by 

 Vygotsky (1978) as "the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined throughproblem solving under adult guidance or in collaboration with more capable peers" (p. 86).This notion of an enhanced level of mental functioning when an expert guides an apprenticehas been inf luential in education and in the study of learning disability.

Read more: Development - Cognitive, Self - EMOTIONAL, MORAL - Symbolic Interactionism,Gender, Theory, Family, History, Definition, Children, Child, and Emotions http://family.jrank.org/pages/371/Development.html#ixzz18st46Ftq  

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Constructivism Perspective

 Jean Piaget (1896-1980) was one of the most influential researchers in the area of developmental psychology during the 20th century.

Piaget originally trained in the areas of biology and philosophy and consideredhimself a "genetic epistemologist." He was mainly interested in the biologicalinfluences on "how we come to know." He believed that what distinguishes humanbeings from other animals is our ability to do "abstract symbolic reasoning."

Piaget's views are often compared with those of Lev Vygotsky (1896-1934), wholooked more to social interaction as the primary source of cognition and behavior.

The writings of Piaget (e.g., 1972, 1990; see Piaget, Gruber, & Voneche) and Vy gotsky  (e.g. V  ygotsky, 1986; Vygotsky & Vy gotsky, 1980), along with the work of  JohnDewey (e.g., Dewey, 1997a, 1997b), Jerome Bruner (e.g., 1966, 1974) and Ulrick

Neisser (1967) form the basis of the constructivist theory of learning andinstruction.

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Infancy 

 As soon as they are born, infants begin learning to use their senses to explorethe world around them. Most newborns can focus on and follow movingobjects, distinguish the pitch and volume of sound, see all colors anddistinguish their hue and brightness, and start anticipating events, such assucking at the sight of a nipple. By three months old, infants can recognize

faces; imitate the facial expressions of others, such as smiling and frowning;and respond to familiar sounds.

 At six months of age, babies are just beginning to understand how the worldaround them works. They imitate sounds, enjoy hearing their own voice,recognize parents, fear strangers, distinguish between animate and inanimate

objects, and base distance on the size of an object. They also realize that if they drop an object, they can pick it up again. At four to seven months, babies canrecognize their names.

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By nine months, infants can imitate gestures and actions, experiment with the physicalproperties of objects, understand simple words such as "no," and understand that anobject still exists even when they cannot see it. They also begin to test parental responsesto their behavior, such as throwing food on the floor. They remember the reaction andtest the parents again to see if they get the same reaction.

 At 12 months of age, babies can follow a fast moving object; can speak two to fours words,including "mama" and "papa"; imitate animal sounds; associate names with objects;

develop attachments to objects, such as a toy or blanket; and experience separationanxiety  when away from their parents. By 18 months of age, babies are able tounderstand about 10–50 words; identify body parts; feel a sense of ownership by usingthe word "my" with certain people or objects; and can follow directions that involve twodifferent tasks, such as picking up toys and putting them in a box.

Read more: Cognitive Development - stages, meaning, average, Definition, Description,Common problems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18sr6CHOI 

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Toddlerhood

Between 18 months to three years of age, toddlers have reached the "sensorimotor" stageof Piaget's theory of cognitive development that involves rudimentary thought. For

instance, they understand the permanence of objects and people, visually follow thedisplacement of objects, and begin to use instruments and tools. Toddlers start to strivefor more independence, which can present challenges to parents concerned for theirsafety . They also understand discipline and what behavior is appropriate andinappropriate, and they understand the concepts of words like "please" and "thank you."

Two-year-olds should be able to understand 100 to 150 words and start adding about ten

new words per day. Toddlers also have a better understanding of emotions, such as love,trust, and fear. They begin to understand some of the ordinary aspects of everyday life,such as shopping for food, telling time, and being read to.

Read more: Cognitive Development - stages, meaning, average, Definition, Description,Common problems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18srOrXf1 

7/28/2019 20130306210342Kuliah 2a - Learning Theoies Piaget, Bruner, Vygosky

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Preschool

Preschoolers, ages three to six, should be at the "preoperational" stage of 

Piaget's cognitive development theory, meaning they are using their imagery and memory skills. They should be conditioned to learning and memorizing,and their view of the world is normally very self-centered. Preschoolers usually have also developed their social interaction skills, such as playing andcooperating with other children their own age. It is normal for preschoolers totest the limits of their cognitive abilities, and they learn negative concepts andactions, such as talking back to adults, lying , and bullying. Other cognitive

development in preschoolers are developing an increased attention span,learning to read, and developing structured routines, such as doing householdchores.

Read more: Cognitive Development - stages, meaning, average, Definition,Description, Common problems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18srazYL7 

7/28/2019 20130306210342Kuliah 2a - Learning Theoies Piaget, Bruner, Vygosky

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School age

 Younger school-age children, six to 12 years old, should be at the "concrete operations" stage of 

Piaget's cognitive development theory, characterized by the ability to use logical and coherent actionsin thinking and solving problems. They understand the concepts of permanence and conservation by learning that volume, weight, and numbers may remain constant despite changes in outwardappearance. These children should be able to build on past experiences, using them to explain why some things happen. Their attention span should increase with age, from being able to focus on a taskfor about 15 minutes at age six to an hour by age nine.

 Adolescents, ages 12 through 18, should be at the "formal operations" stage of Piaget's cognitivedevelopment theory. It is characterized by an increased independence for thinking through problemsand situations. Adolescents should be able to understand pure abstractions, such as philosophy andhigher math concepts. During this age, children should be able to learn and apply generalinformation needed to adapt to specific situations. They should also be able to learn specificinformation and skills necessary for an occupation. A major component of the passage throughadolescence is a cognitive transition. Compared to children, adolescents think in ways that are moreadvanced, more efficient, and generally more complex. This ability can be seen in five ways.

Read more: Cognitive Development - stages, meaning, average, Definition, Description, Commonproblems http://www.healthofchildren.com/C/Cognitive-Development.html#ixzz18sroIfrf  

7/28/2019 20130306210342Kuliah 2a - Learning Theoies Piaget, Bruner, Vygosky

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 Vygotsky's Theory of Cognitive Development

Lev Vygotsky differed from Piaget in that the role of social context and culture inchildren's cognition was a central part of his theory (Rowe and Wertsch 2002).Rather than seeing the development of knowledge as transcending culture andcontext, Vygotsky argued that an understanding of how knowledge developsrequires an understanding of the social and historical origins of knowledge and of changes in that knowledge. He also proposed a central role for language in cognitivedevelopment. Vygotsky argued that human knowledge originates in socially meaningful activity and is shaped by language.

Read more: Development - Cognitive, Self - EMOTIONAL, MORAL - Symbolic

Interactionism, Gender, Theory, Family, History, Definition, Children, Child, andEmotions http://family.jrank.org/pages/371/Development.html#ixzz18ssr8Zph 

7/28/2019 20130306210342Kuliah 2a - Learning Theoies Piaget, Bruner, Vygosky

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Processes that originate in the social world are transferred to the inner mental world(inner speech), and shape the development of higher cognitive processes such asproblem-solving. A key part of this transfer lies in the child's mastery of the symbolic orartificial stimuli (signs) characteristic of the child's culture, such as language. Part of thedevelopment of children's thinking therefore requires apprenticeship into culturally 

specific cognitive and social practices.

 According to Vygotsky, cognitive development does not happen just in the head of thechild. Rather, it is a process of learning to operate with physical, symbolic, and cognitivetools in ways that in themselves change cognitive processes. The difference between achild's individual performance and that child's performance when guided by experts ismetaphorically described by Vygotsky's zone of proximal development (ZPD).

The ZPD was described by Vygotsky (1978) as "the distance between the actualdevelopmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance orin collaboration with more capable peers" (p. 86). This notion of an enhanced level of mental functioning when an expert guides an apprentice has been influential ineducation and in the study of learning disability.

Read more: Development - Cognitive, Self - EMOTIONAL, MORAL - Symbolic

Interactionism, Gender, Theory, Family, History, Definition, Children, Child, andEmotions http://family.jrank.org/pages/371/Development.html#ixzz18st46Ftq 

7/28/2019 20130306210342Kuliah 2a - Learning Theoies Piaget, Bruner, Vygosky

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