Thursday, 6 February 2014

The birth of an idea Of Dr. Ambedkar

Portrait of Dr. Ambedkar at the Tamil Nadu Legislative Assembly chamber in Madras on September 9, 1980. Photo: The Hindu Archives

Features » Sunday Magazine

Updated: July 27, 2013 18:28 IST

The birth of an idea

Raja Sekhar Vundru
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  • The Hindu Portrait of Dr. Ambedkar at the Tamil Nadu Legislative Assembly chamber in Madras on September 9, 1980. Photo: The Hindu Archives

English as second language

Communication: Students from rural backgrounds tend to stick to minority
language groups. Photo: S.S. Kumar

Features » Education Plus

Updated: July 28, 2013 18:34 IST

English as second language

Tuesday, 4 February 2014

Metacognitive Skills

Metacognitive Skills

Metacognition refers to learners' automatic awareness of their own knowledge and their ability to understand, control, and manipulate their own cognitive processes.2 Metacognitive skills are important not only in school, but throughout life. For example, Mumford (1986) says that it is essential that an effective manager be a person who has learned to learn. He describes this person as one who knows the stages in the process of learning and understands his or her own preferred approaches to it - a person who can identify and overcome blocks to learning and can bring learning from off-the-job learning to on-the-job situations.
As you read this section, do not worry about distinguishing between metacognitive skills and some of the other terms in this chapter. Metacognition overlaps heavily with some of these other terms. The terminology simply supplies an additional useful way to look at thought processes.

Metacognition: An Overview

Metacognition: An Overview

Jennifer A. Livingston

© 1997 by Jennifer A. Livingston 



"Metacognition" is one of the latest buzz words in educational psychology, but what exactly is metacognition? The length and abstract nature of the word makes it sound intimidating, yet its not as daunting a concept as it might seem. We engage in metacognitive activities everyday. Metacognition enables us to be successful learners, and has been associated with intelligence (e.g., Borkowski, Carr, & Pressley, 1987; Sternberg, 1984, 1986a, 1986b). Metacognition refers to higher order thinking which involves active control over the cognitive processes engaged in learning. Activities such as planning how to approach a given learning task, monitoring comprehension, and evaluating progress toward the completion of a task are metacognitive in nature. Because metacognition plays a critical role in successful learning, it is important to study metacognitive activity and development to determine how students can be taught to better apply their cognitive resources through metacognitive control.

Developing Metacognition

Developing Metacognition

By 
Updated on Dec 16, 2008

Metacognition is thinking about thinking, knowing "what we know" and "what we don't know." Just as an executive's job is management of an organization, a thinker's job is management of thinking. The basic metacognitive strategies are:
  1. Connecting new information to former knowledge.
  2. Selecting thinking strategies deliberately.
  3. Planning, monitoring, and evaluating thinking processes. (Dirkes, 1985)
A thinking person is in charge of her behavior. She determines when it is necessary to use metacognitive strategies. She selects strategies to define a problem situation and researches alternative solutions. She tailors this search for information to constraints of time and energy. She monitors, controls and judges her thinking. She evaluates and decides when a problem is solved to a satisfactory degree or when the demands of daily living take a temporary or permanent higher priority.

Saturday, 1 February 2014

What is constructivism?



What is constructivism?
Constructivism concept to classroom
Source:  http://www.thirteen.org/edonline/concept2class/constructivism/exploration.html 
Constructivism is basically a theory -- based on observation and scientific study -- about how people learn. It says that people construct their own understanding and knowledge of the world, through experiencing things and reflecting on those experiences. When we encounter something new, we have to reconcile it with our previous ideas and experience, maybe changing what we believe, or maybe discarding the new information as irrelevant. In any case, we are active creators of our own knowledge. To do this, we must ask questions, explore, and assess what we know.

In the classroom, the constructivist view of learning can point towards a number of different teaching practices. In the most general sense, it usually means encouraging students to use active techniques (experiments, real-world problem solving) to create more knowledge and then to reflect on and talk about what they are doing and how their understanding is changing. The teacher makes sure she understands the students' preexisting conceptions, and guides the activity to address them and then build on them.



Constructivist teachers encourage students to constantly assess how the activity is helping them gain understanding. By questioning themselves and their strategies, students in the constructivist classroom ideally become "expert learners." This gives them ever-broadening tools to keep learning. With a well-planned classroom environment, the students learn HOW TO LEARN.
You might look at it as a spiral. When they continuously reflect on their experiences, students find their ideas gaining in complexity and power, and they develop increasingly strong abilities to integrate new information. One of the teacher's main roles becomes to encourage this learning and reflection process.

What does constructivism have to do with my classroom?

What does constructivism have to do with my classroom?

As is the case with many of the current/popular paradigms, you're probably already using the constructivist approach to some degree. Constructivist teachers pose questions and problems, then guide students to help them find their own answers. They use many techniques in the teaching process. For example, they may:

  • prompt students to formulate their own questions (inquiry)
  • allow multiple interpretations and expressions of learning (multiple intelligences)
  • encourage group work and the use of peers as resources (collaborative learning)
More information on the above processes is covered in other workshops in this series. For now, it's important to realize that the constructivist approach borrows from many other practices in the pursuit of its primary goal: helping students learn HOW TO LEARN.
In a constructivist classroom, learning is . . .


Piaget theory:Development of thinking

Development of thinking 

Introduction to Piaget theory and  Piaget's Stages Piaget: General Evaluation with Applying Piaget to Education

           Background and introduction: Piaget is a towering figure in psychology and widely respected by all, including those who have criticised or adopted his theories.   Contrary to popular belief Piaget was not French (despite being called Jean), he was in fact Swiss.  Nor was he a psychologist (not at the outset anyway) but a zoologist (which should really be spelt zooologist surely!).  He had his first publication on molluscs when he was still at High School!

Vygotsky's Theory Applying to Education

Lev Vygotsky  
(“the Mozart of Psychology”)

Vygotsky's Theory and Evaluation of Vygotsky with Applying Vygotsky to Education


For most of his adult life Vygotsky lived in Communist Russia, as a result his work shows definite Marxist
influences emphasising the role of social interaction and culture.  Vygotsky died of tuberculosis at the age of 37, as a result his theory never went through the later developments that Piaget’s and others were afforded.  Vygotsky is regarded by many to have been a genius and well ahead of his time. 
Vygotsky believed that a child's cognitive development cannot be seen as occurring in a social vacuum.  In Vygotsky's view, our ability to think and reason by ourselves and for ourselves (what he terms inner speech or verbal thought) is the result of a fundamentally social process.  At birth, we are social beings who are capable of interacting with others, but able to do little either practically or intellectually by or for ourselves.  Gradually, however, we move towards self-sufficiency and independence, and by participating in social activities, our capabilities become transformed.  For Vygotsky, cognitive development involves an active internalisation of problem-solving processes that takes place as a result of mutual interaction between children and those with whom they have regular social contact (initially the parents, but later friends and classmates).
Vygotsky's process of internalisation is the reverse of how Piaget (at least initially) saw things.  As Rogoff (1990) has noted, Piaget's idea of 'the child as a scientist' is replaced by the idea of 'the child as an apprentice', who acquires the knowledge and skills of a culture through graded collaboration with those who already possess such knowledge and skills.  According to Vygotsky (1981):  
'Any function in the child's cultural development appears twice, or on two planes.  First it appears on the social plane, and then on the psychological plane.'

Bruner's Theory with Applying Bruner to education

Jerome Bruner and Bruner's Theory with Applying Bruner to education 


 Bruner's Theory with Applying Bruner to education Bruner's Theory with Applying Bruner to education

Jerome Bruner
Background
Bruner’s early work on child development came at a time when thinking in the area was dominated by the behaviourists.  Behaviourism had developed as a means of producing an objective and measurable way of explaining the learning process, based, as it was, on scientific rigour.  Bruner was to apply similar techniques to the study of the internal mental processes involved in learning and was therefore an early pioneer of the cognitive approach to psychology.  Bruner was heavily influenced by the work of jean Piaget and later by the work of Lev Vygotsky.  His eventual theory shows the influence of both.

The child
According to Bruner, the child’s cognitive structures mature with age as a result of which the child can think and organize material in increasingly complex ways.  Here we see influence of Piaget again, but also of the information processing model.  Children are also seen as naturally inquisitive, thirsty for knowledge and understanding.  The child naturally adapts to its environment and abstract thinking develops through action. 

Constructivist theory of cognitive development
Like Piaget and Vygotsky, Bruner believes the child has to learn for itself by making sense of its own environment.  In fact Bruner could be seen as an ‘extreme constructivist’ since he believes the World we experience is a product of our mind.  What we perceive and think of as our World is constructed through our mind as a product of symbolic processes. 
Bruner rejected the idea of stages as popularized by Piaget and to a lesser extent Vygotsky.  Rather than looking at the ages of developmental changes Bruner concentrates more on how knowledge is represented and organized as the child develops. 

Modes of representation
This looks as though its stages but it isn’t!  With stages the child would progress from one to the next and then, crucially, leave the old way of thinking or operating behind.  For Bruner, the earlier ways of thinking are still used later in life where they can be very useful for some tasks.
Modes of representation are the ways (or format) in which the child manipulates information.

1. Enactive (First year)
This is similar to the first half of Piaget’s sensori-motor stage of development.  The child has little in the way of mental faculties so ‘thinking is a physical action.’  Knowledge is what the child can manipulate or do with movements, for example tying knots, pointing etc.  In later life the enactive mode will allow riding a bike, swimming, driving a car and so on.  These are automatic patterns of activity that have been ‘hard wired’ into our muscles.  Thinking about how we do them or trying to explain to others in words how to tie shoe laces or ride a bike is practically impossible because they are enactive.  As for Piaget, the gaining of object permanence is a major qualitative change in the child’s thinking.

2. Iconic (Second year)
This is similar to the second half of Piaget’s sensori-motor and preoperational stages of development.  For the first time the child has mental images that allow it to retain pictures after the stimulus has gone.  Drawing is now possible.  These icons or images are built up from past experience and based on a number of exposures to similar objects and events.  Our image of a cup isn’t based soley on seeing one cup but on seeing many.  However, at present the child lacks the ability to solve problems.
3. Symbolic (six or seven years onwards)
This is similar to Piaget’s concrete operational stage of development.  For Bruner, symbols include words (language), music, numbers and so an.  Anything we use to symbolize something else.  The precise timing of this one depends on the child, particularly its language ability.  For the first time the child can categorise, think logically and solve problems.

Bruner’s main interest was in the child’s transition from iconic to symbolic modes.
A major implication of Bruner’s theory is that cognitive development can be speeded up by training children in the use of symbols.  Some of the studies that follow (e.g. Frank) suggest that this is the case.  Clearly this runs counter to Piaget who believed progress through his stages was biologically determined. 

Culture provides the ‘instructions’ about how humans should develop and these are passed on from one generation to the next.  Bruner clearly disagrees with Piaget’s view of the child as isolated and learning on its own.  The child works with others to develop its framework for thinking and this framework is culture-dependent. Again we see the influence of Vygotsky J
Bruner and Kenney (1966)
Aims- what age children start to use symbolic mode of representation.
Method- children aged 3-7 shown a board divided into 9 squares. On each square was a plastic beaker. Beakers of different sizes & widths, tallest at back & widest on left, each child had to look at the beakers. There was a reproduction test were the beakers were mixed up and the child was asked to put them back how they were.
Transposition test removed beakers and asked them to put them back in a mirror image of the original arrangement
Results
Reproduction task
Transposition task
Age 5
60%
O%
Age 6
70%
27%
Age 7
80%
80%
Most 5 year olds correctly completed the reproduction test however few under 7 could complete the transposition task, most over 7 could complete both tasks.
The reproduction task was designed to use iconic representation, as the child forms a mental picture and copies it however the transposition task could not be done as it doesn’t look like original arrangement.
Conclusion
The study supports the view that children on average begin to acquire the symbolic mode at around 6 or 7 years of age. The task required the ability to mentally transform the visual information and was dependent on statements such as ‘it gets fatter going one way and taller going in another’ etc.  The children were using language (symbolic mode) to guide their thinking.





Brief biography
Was born in New York in 1915 and at time of writing is still going strong (well still going) at the ripe old age of 94!  Bruner had a difficult childhood with early operations to correct his vision and his father dying when he was only twelve.  The rest of his education was then interrupted by frequent changes of school.  Despite this however, Bruner studied at Duke University and went on to get his PhD in psychology from Harvard University in 1941.  Whilst there he met and worked under Gordon Allport, one of the leading psychologists of his time. 

Evidence for the modes
Frank (reported by Bruner 1964)
An ingenious reworking of the classic Piaget water conservation study:
Frank selected a group of 4 to 6 year olds that had been unable to successfully complete the original Piaget test. 
  1. They are shown the two measuring cylinders with equal amounts of water and the empty beaker.
  2. A screen is placed in front of the apparatus and a line drawn on the screen indicating the water level in the two taller cylinders.
  3. Water is poured from one of the cylinders into the beaker (all is still hidden behind the screen)
  4. The child is now asked ‘which has more to drink or are they both the same?’
Results of this part of the test:
Results of unscreened test
Results of screened test
4 year olds
0%
50%
5 year olds
20%
90%
6 year olds
50%
100%
  1. The screen is then removed and the child is again asked about which has the most water, the tall thin cylinder or the smaller but wider beaker
Results of this second test
4 year olds: revert back to their original (incorrect answer) that the tall cylinder has more water
5 and 6 year olds generally stick to the correct answer given when the beakers were hidden.
Explanation of findings
In the Piaget original, children can see the whole procedure and so rely on their iconic mode to solve the task.  By screening the procedure Frank was preventing iconic mode and by asking them to describe what was happening was encouraging their symbolic mode.  This more advanced mode of thinking was capable of conservation whereas the lower, iconic was not.
Later, when tested without the screen, the older children were now able to conserve. However, the younger children generally failed, even if they had been able to do the task when it was screened.  This suggests that lessons had not been learned by this group and they had returned to iconic thinking.  Four year olds, it would seem, are mostly unable to acquire symbolic thinking.  This last finding appears to support Piaget’s idea of preparedness.  Regardless of methods used, some children are just too young to progress further
Sonstroem et al (1966)
In a similar reworking of a Piagetian conservation task, children were asked to roll out a ball of plasticine (enactive mode) so it was longer and thinner.   They were asked to watch their own actions (iconic mode) and to describe what they were doing (symbolic mode).  By using all three modes together, the children were far more successful in conserving amount. 
But: Although the above researchers (and Bruner) put this improved performance down to the use of language, other research Furth (1966) on deaf children, seems to suggest that although language helps it isn’t essential for the development of abstract thinking
Language
Here we have a major difference with Piaget but clear influence from Vygotsky.
Let’s consider the transition from iconic mode to symbolic mode.  For Bruner this comes about through the mastering of language.  Like Vygotsky, Bruner thinks language accommodates cognitive development and the two then become inextricably intertwined and over time develop side by side each helping the development of the other.  For Piaget language is merely a tool that develops as a result of cognitive development. 
Language is needed for communication with adults and older peers who can facilitate learning.  Similarly it is essential for the scaffolding process. 
Language of course is also essential for thought!
Bruner suggests language training as a way of speeding up the cognitive development of the child, the concept of which would be totally alien to Piaget.
Evaluation
The ability to acquire language is common across all human cultures.  This has led to the nativist theory of language acquisition, basically that the rules for acquiring grammar are hard wired into the human brain.  Linguist, philosopher, political activist and all-round brain box, Noam Chomsky suggested that humans possess a LAD (Language Acquisition Device) that allows us to learn the rules of grammar when we are exposed to human speech.
Bruner however, believes we possess a LASS* (Language Acquisition Social System).  Simply listening to language is not sufficient.  The child needs to be exposed to the mutual eye gazing and turn taking that are needed for conversation.  Language, according to Bruner, needs to take place in a social context. 
Evidence for this is provided by the case of Jim (and other deprived children e.g. Genie).
Jim was born to parents that were both deaf and dumb.  Until the age of three, Jim’s only exposure to language was through the television.  Although he learned speech it was noticeably odd, with him developing his own, unique grammatical characteristics and poor articulation (Sachs et al 1981).  Bruner suggests that this was due to lack of social interaction in the learning of speech. 
However, social interaction doesn’t explain all the complexities of acquisition.  The language we hear is often incorrect, poorly defined, incomplete and full of hesitations, mispronounciations and other errors, yet despite this we still learn to talk!  It also takes place at a very early stage in human development, when other cognitive skills are barely beginning and when complex thought doesn’t exist. 
Culture
According to Bruner our culture determines the sort of person we become.  There ‘cannot be a self independent of one’s culture.’

Introduction to Piaget & Development of thinking with stages

Development of thinking 
Background and introduction
Piaget is a towering figure in psychology and widely respected by all, including those who have criticised or adopted his theories.   Contrary to popular belief Piaget was not French (despite being called Jean), he was in fact Swiss.  Nor was he a psychologist (not at the outset anyway) but a zoologist (which should really be spelt zooologist surely!).  He had his first publication on molluscs when he was still at High School!
Whilst working with Binet (who was French) and an early pioneer of IQ tests, he became fascinated by child development and spent the next 50 some years of his life studying the subject.  As a result Piaget was a true expert in his field, which as we shall see later, also covered moral development.
Piaget’s theory is sometimes described as ‘genetic epistemology.’  ‘Genetic’ because he believed that the stages we progress through and the structures and processes we use, are inbuilt and true for all of us regardless of culture.  ‘Epistemology’ (not a word to be uttered when in the state suggested by the word) actually means the study of knowledge.  Basically Piaget believed that the way in which we learn about and adapt to our World is constant across all cultures and races, and proceeds as a set sequence in all.
Central to Piaget's theory is how the child adapts to an ever-changing World.  Piaget noticed that even the youngest of children are inquisitive and actively explore their world.  Piaget is most famous for his stages but any description of his theory must also include a discussion of the structures that underlie these stages.  It is tempting in an essay on Piaget to write exclusively about his stages, since you will know them backwards in great detail by the time the exam comes round.  However, it is essential that the other aspects of his theory are covered too.  His processes (or ‘functional invariants’ as he lovingly referred to them) are constant (as their name suggests) throughout all stages, working to make sense of our environment.  Schemas (strictly speaking the plural should be ‘schemata’) are the internal representations that we hang our understanding on.  Schemata were mentioned in AS memory and will crop up in other topics later in the year.  Enough waffle… lets get on with it.
Above: photo of Piaget in later life.  He died in 1980 at the age of 84 (despite being a ‘sickly’ as a child).


I got so excited telling you about the great man that I neglected to mention the structure of this first topic.  It covers the way our thinking develops over time, and how as we mature we become capable of more complex methods of thinking.  A number of theories have developed (that word again) to try and explain how this happens.  The syllabus currently specifies three: Piaget, Vygotsky and Bruner.  As of 2011-12 series however, Bruner will be dropped. 
You may also come across ‘Information Processing’ which does appear later, but which you cannot be specifically tested on.
Schemas and associated concepts
Schema:  an internal representation of the world.  This acts as a framework on which the child bases its knowledge of its environment.  According to Piaget we are born with some schemata including sucking and grasping.  In the first year of life many other simple schemata develop, for example the schema for mum very quickly develops as the child learns to distinguish her from others as a source of food and comfort.  Later the schemata become more complex and include concepts such as density, grammar, love, nature-nurture debate etc.   Schemata are crucial as they enable us to interpret and predict events. 
Helen Bee (2000) believes that schemata are not so much the categories themselves but the action of categorising.
Equilibrium and disequilibrium:  the child requires a stable internal world.  If new experience does not match existing schema then a state of disequilibrium (or inbalance) is produced.  The child needs to accommodate to restore the balance, i.e. alter its perception of how things work.  Piaget saw this desire for equilibrium as innate and believed that it drives or motivates us to learn.   Simple examples would be having a schema for dog and misinterpreting a cat as a dog.  On being told the mistake this causes temporary confusion and the child needs to alter its schemata to allow for this. 
Disequilibrium is essential for learning!!!!
Adaptation: refers to how a child changes over time as it makes sense of the World in which it lives.  Adaptation comes about through the processes of assimilation and accommodation:
·       Assimilation:  new information or experiences can be fitted into the child's existing schema or current understanding of the world.  It sees a poodle and is able to fit this into the same schema as the family’s bull mastiff!
·       Accommodation:  new information or experiences cannot be fitted into the child's current understanding so it either has to alter existing schema or create a whole new schema;  for example cat doesn’t fit in with its schema for dog or George W Bush doesn’t tie in with its concept of intelligent life form!  In these cases new schemata need to be constructed or changes made to existing schemata.  So the child develops a schema for cat and one for nepotism in World Politics!
Operations
Not always mentioned specifically in texts but nevertheless crucial, by definition, to the stages.  Operations are mental transformations or manipulations that occur in the mind.  Piaget believed that it was operations that provided the rules by which the child is able to understand the world.  While schemas develop with experience operations only develop as the child’s brain develops.  So children in the first two stages do not possess operations, hence ‘preoperational.’  As the brain matures the child is capable of ever more complex understanding.
Stages
Sensori-motor (0-2 years)
The child lacks internal schemas or representations.  The child's understanding of its world is directly through its senses from moment to moment.  It is so called because it senses its environment and carries out movement (motor) to react to it.  At this stage that is all the child can do!
Features:
Egocentricism. The child has no concept of 'self' so is unable to distinguish itself from its environment.  Unlike some of the other concepts Piaget believed that egocentricism gradually reduces as the child gets older. 
Research evidence
See three mountains task in preoperational stage.
Lacks object permanence.  Child assumes that objects no longer exist if they’re not visible. 
Research evidence
Piaget carried out research on his own children.  They would be shown an attractive object that would then be hidden from view.  Children up to the age of 8 months don’t bother to look for it assuming it to no longer exist.  After 8 months children will continue to search for hidden objects.
Evidence against
Bower & Wishart (1972) showed objects to children between the ages of 1 and 4 months.  Lights were switched off so that the objects were no longer visible but the child could be seen, by infrared camera, continuing to search for the object.
Baillargeon and DeVos (1991) employed an ingenious experiment using long and short carrots.  It relies on the concept that children will spend longer looking at events that they consider to be impossible.  In this case, even though the carrots were not visible for a crucial stage of the experiment children as young as three months old realised that they still existed and spent longer puzzling over the ‘impossible situation.’ 
Young children glance at this one but seem to realise there's nothing unusual about it.
However, they spend significantly longer looking at this one, suggesting that they realise its impossible.  That is they realise that the carrot should still be visible in the space.
Clearly this casts doubt on Piaget’s assertion that children didn’t develop object permanence until 8 months of age!
 
 
Pre-Operational Stage (2 to 7 years)
Child is still dominated by the external world, rather than it's own thoughts.  However, it now forms some simple internal representations of its world (schemas) through its increasing ability to use language.  The stage is called 'pre-operational' since the child is unable to perform operations (such as heart by-passes and key hole surgery; well you know what I mean!).  An 'operation' according to Piaget, is a mental rule for manipulating objects or ideas into new forms, and then, crucially, being able to manipulate them back again.  Since preoperational children are unable to reverse things mentally they are unable to do this. 
Features:
Egocentricism
Child remains egocentric but this now refers more to its inability to see things from other people's perspectives, as famously demonstrated by the 'Three Mountains' task.
 

Research evidence
Piaget & Inhelder’s ‘Three Mountains Task.’  Children would be seated at a table with a 3D model of three mountains in front of them.  A doll would be placed in various positions around the table and the child shown photos of various views.  They would be asked to choose the picture that best fitted the view as seen from the doll.  To complete this task successfully children would have to imagine the view as seen by the doll.  The researchers found that children below the age of 7 had problems completing the task, tending to choose the photo that showed their view of the mountains.  Think of the young girl in the video explaining her new toy to her grandfather on the phone and assuming that because she could see it so could her granddad.
Evidence to contradict Piaget
Hughes (1975) repeated the three mountains task using a situation he thought would be more familiar to the child, i.e. the naughty boy hiding from the policeman.  Hughes found that 90% of children aged 3 to 5 could complete the task successfully, concluding that it was lack of understanding rather than egocentricism that was causing the problems for Piaget's participants. 
Animism
This is related to egocentricism and is the tendency to attribute feelings to inanimate objects so for example the child may apologise for hurting its teddy bear or decide to punish one of its toys for being naughty. I’ll restrain from any adult humour here!
Realism
Believing that psychological events, such as dreams, are real.
Lack of Conservation
The inability to realise that some things remain unchanged despite looking different.  Piaget concentrated on conservation of number and volume.  Piaget put this down to the child's inability to pay attention to more than one characteristic of a situation at a time and to its inability to reverse operations in its head (e.g. to visualise the water being poured back into the original container). 
Piaget believed that conservation of number develops first.  He demonstrated this by the use of counters.  Children are shown 2 rows each with the same number of counters and realise the 2 rows contain the same number.  If the researcher rearranges one of the rows by spacing the counters out the child believes there are more.
Conservation of volume, as demonstrated by pouring liquid from small wide beakers into tall thin measuring cylinders, develops later, at the very end of the preoperational stage.
 
Evidence against
McGarrigle & Donaldson (1974) showed that children as young as 4 could conserve number if the situation is given meaning.
It is also important to note that Piaget concentrates almost entirely on mathematical skills and logic.  Between the ages of 7 and 11 children acquire a vast number of other new skills that Piaget chose to ignore.
McGarrigle & Donaldson (1974) repeated Piaget’s conservation experiment on 6-year-old children.  The child is shown 2 rows of equal numbers of counters.  The child agrees that the 2 rows are the same.  If the researcher then messes one of the rows up, without altering the number of counters, only 16% believe that the number of counters is still the same.  So far just as Piaget would have predicted. However, when a naughty teddy bear messes up the row of counters 62% of children in this age group are able to conserve!  This shows that children are better able to conserve than Piaget proposed.  M & D assume that in the original condition it appears to the child that the researchers are intending to alter the number of counters, or that they are asking a trick question.  In the teddy condition there is a reason for the counters just to be messed up so the situation has meaning.       
Rose & Black (1974) believed asking the child the same question twice was confusing.  ‘Are there the same number of buttons in each row?’  The buttons would then be rearranged and the question repeated.  Perhaps the children believe this to be a trick question.  Samuel & Bryant (1984) repeated the counters experiment but only asked the question once, after the counters had been rearranged.  This produced more correct answers!
General evaluation points on this stage:
Piaget’s research has generated lots of research into this particular stage, but it has been inconclusive or at odds with Piaget’s original work:
Piaget often under-estimated the age at which children could perform activities.  Wheldall & Poborca (1980) believe that children are unable to perform conservation tasks because they don't understand the question.
Variations in an experimental procedure can produce very different findings.  Some studies conclude that children are still egocentric others that they have out grown this characteristic.
Piaget’s original studies were often poorly thought through and for example were not suited to the age range of the children he was studying.  Instructions may have been confusing or the tasks themselves too complex.  For example ‘Three Mountains’ task which was manageable when re-worked by Hughes in a more familiar format.
 
Concrete Operations Stage (7 to 11 years)
The child is now able to carry out operations on its environment and develops logical thought.  However, it still requires concrete examples, being unable to think in abstract terms.  Less importance is attached to information from our senses as we use thought and imagination more.
Features
Reversibility refers to the ability to mentally picture an action being carried out in reverse.  This is essential for conservation, e.g. imagining the water being poured back into the original beaker.
Conservation made possible by the ability to decentre.  Conservation of number is first (5 to 6 years), followed by conservation of weight (7 to 8 years) and finally conservation of volume by 11 years of age.
Transitivity is only possible with concrete examples.  For example 'Jackie is fairer than Sarah, Jackie is darker than Nicola.  Who is the darkest?'  The concrete operational child would not be able to work this one out mentally, it would require dolls or pictures of the three girls.  Similarly A > B > C.  This would not be possible since it requires abstract thought rather than concrete examples.
Research Evidence
Piaget's own studies demonstrated that children in this age group were able to conserve successfully. 
Other studies have broadly backed Piaget’s findings for this stage, although he has been criticised for failing to consider other cultures.
·        Jahoda (1983) found that children as young as 9 years old in Zimbabwe could understand abstract economic concepts if they’d worked in their parents’ business. 
·        Price-Williams (1969) showed conservation in children as young as 6 years old who had been raised in pottery making factories.

Formal Operational stage (11 years onwards)
Piaget used the term ‘formal’ since children in this stage can concentrate on the form of an argument without being distracted by the content (Jarvis 2001).  For example if x is greater than y but less than z.  The child can now work this out without needing to know what x, y and z refer to.  Smith et al (1998) provide the following example:
‘All green birds have two heads.  I have a green bird called Charlie.  How many heads does Charlie have?’  A child in the earlier stages would be bogged down by the content, i.e. birds have one head.  Formal thinkers can concentrate on the structure (or form) of the question in this context.
Piaget maintained that everyone would reach this stage eventually, even if it took us until 20.  However, there is plenty of evidence to suggest that this is not the case and that certainly it tends to occur later than Piaget predicted.
Bradmetz (1999), in a longitudinal study showed that out of 62 children tested at the age of 15, on a series of Piagetian tasks, only one had reached formal thought!
Features
Abstract thought
The child can now think in abstract terms so no longer requires concrete examples to solve problems. 
Hypothetical thought
The child is able to consider things that it has no experience of and consider imaginary scenarios. 
Hypotheses testing
Faced with a problem the formal thinker will approach it logically, produce a list of possibilities and test each one systematically.  (Think of GCSE science coursework).
Solve syllogisms
These are a form of reasoning in which a conclusion is reached from a number of statements.
For example:
            When B is larger than C, X is smaller than C.  But C is never larger than B. 
            True or false, X is never larger than B?
Other features
This level of thought also allows for an appreciation of values and ideals (necessary for more advanced moral thinking).
Research evidence
Piaget would set children the task of finding what determines the frequency of swing of a pendulum.  Concrete thinkers normally believe that it is the push that the experimenter gives it.  When they test possibilities they fail to control other variables.  The formal thinker on the other hand considers all possible variables such as push, length of string, weight of bob etc.  They carefully isolate variables and control confounding variables.
Evidence against
1.      Some psychologists argue that formal operational thought is not as important to everyday life as Piaget seems to have concluded.  Since most problems we face have no one obvious right answer, logical thought is not always necessary.
2.      It seems many adults never actually reach Piaget’s description of formal thinking.
3.      Gladwin (1970) argues that the tests Piaget used are inappropriate for testing non-western culture.  The Pulawat navigators of Polynesia demonstrate formal thinking when navigating in their canoes but fail western tests designed to test their formal thinking.

General criticisms


Ages and stages

Research mostly suggests that children acquire their skills earlier than Piaget suggested (e.g. Hughes, McGarrigle and Donaldson etc).

Some psychologists believe that only 30% of the population reach formal ops.  This is the one stage were Piaget seems to have over-estimated rather than under-estimated the ability of the child.  Dasen argues that some cultures don’t develop formal operational thought at all. 
Many of the stages overlap (decalage) for example during the concrete stage there is constant development in small sub-stages as the child learns to conserve number then amount and finally liquid.  So rather than a sudden stop-start stage process, development becomes more of a steady progression. 

Cross-cultural evidence
From a cross-cultural perspective the order of the stages seems to be universal, although rate of progression varies. 
Dasen (1984) carried out conservation type tests and tests of spatial relationships on Aboriginal children ages eight to fourteen.
Typically he found that they performed less well than Western children on conservation tasks with this skill not being developed until the age of 13 in some of those tested whereas spatial awareness developed younger than in the west.  In fact when tested for conservation many adults couldn’t complete the task successfully.  Such finding are perhaps not surprising in a group of people that spend so much time on the move and amounts don’t need to be measured accurately.  However, when Aborigines live in western societies and receive a western education their skills develop in line with western norms. 
This would suggest that the stages are not as universal as Piaget believed and also suggests that culture is a major influence on development.  See Vygotsky’s theory for an explanation of this one. 

Performance and ability. 

Piaget measured a child’s performance and assumed that this was a true reflection of its underlying ability.  For whatever reason children do not always perform to the best of their ability, e.g. lack of understanding of the problem, as highlighted by McGarrigle & Donaldson (1974).


Other abilities. 
Piaget tended to focus on logical and mathematical thought development, neglecting other developments such as memory and social abilities etc.  These may account for the wide individual differences between children.
 

Methods.
Hughes and McGarrigle & Donaldson have shown that using different methods, children can achieve stages at an earlier age than was predicted.  They believe Piaget’s experiments were over complex and used language that the child was unable to relate to.
Piaget used the clinical interview technique, which is time consuming.  As a result his sample sizes tended to be small.
When observing behaviour it is usual to use inter-rater reliability (two or more people observing and comparing notes in some way) in order to reduce bias.  Piaget could have used this method but preferred to observe alone making his research less reliable and reducing its validity. 

Demand characteristics

It is believed that children in Piaget’s experiments may have given answers that they thought Piaget wanted to hear rather than the answers that they believed to be right.
 
Unrealistic
As Segall (1999) points out, Piaget portrays a child as an ‘idealised, non-existent individual, completely divorced form the social environment.’  As we’ll see later, Vygotsky helps to redress this balance.
Individual differences
These were largely ignored.  Piaget admitted that he wanted to produce a general (nomothetic) theory of development of intelligence and knowledge.  He wasn’t interested in individual differences. 
 

General Favourable comments

Much of Piaget’s work has received widespread support.  Piaget did adapt his early theories to take account of criticisms.  He also believed that one day it could be integrated with other theories to produce a rounded view of child development.

Productivity
Few Psychologists, if any, have provoked as much follow up research.  Over the years this has added significantly to our understanding of child development.  For example Bruner and the Information Processing theories both take Piaget as a starting point.

Always mention how influential Piaget’s work has been, both in influencing educational policies (although this was not Piaget’s intention) and in stimulating other research.  Schaffer (2004) believes the theory is still the most comprehensive account of how a child comes to understand the World. 

 


 
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