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Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 10-03-2007
:tourist: An open letter to Brian Butterworth
AND ALL HUMANITY.
[COLOR="Red"]every teacher or parent needs to start here
this the best research available
http://www.youtube.com/watch?v=Fcb8nT0QC6o[/COLOR]
Long before the earliest written records, there are drawings that indicate a knowledge of mathematics and of measurement of time based on the stars. For example, paleontologists have discovered ochre rocks in a cave in South Africa adorned with scratched geometric patterns dating back to c. 70,000 BC.[1] Also prehistoric artifacts discovered in Africa and France, dated between 35,000 BC and 20,000 BC,[2] indicate early attempts to quantify time.[3]:
unny: Dear Brian
How simple was it for me to find this on the net, and post it here.
72,000 YEARS and what have we learnt, not very much in comparison to knowledge itself.
Consider my statement
“we do not know what we do not know”
The decimal system is our greatest single asset, without it I very much doubt that I could have found those five lines and clearly identified the concept of time.
Your profession is that of a scientist, your politics indicate that you believe all men are created equal, though obviously in far from equal circumstances.
My thesis is simple improving education at a stroke.
The decimal system is from where the possibility of human equality springs.
THE ANSWEAR IS WITHIN OUR OWN GRASP
Within our two hands and their message and meaning and that ability those two hand bestow on humanity, the direct evolutionary link between the human brain and reality is our salvation .
Is it four million years since we split from the chimpanzee or four million and ten years.
We are capable of thinking and doing, probably we will only ever be the only thinking and doing life form within the entire universe or entirety itself.
Our frail humanity has to share knowledge and part of that knowledge as to be with the possibility and speed of knowledge acquisition, my concentrated thinking relates to the two vital human developments that make a tolerable future for humanity possible, the development of standard formula as simple as the decimal system itself, to build our neurological pathways in order that we humanity shall survive, and prosper.
Our children have the natural right to the best possible education,
only by acquiring perfect arithmetic and adequate reading ability as early and as quickly as possible, will it ever be possible.
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 10-03-2007
unny: I am extremely concerned with the concept of universal education, I believe that we can simplify universal education, by perfecting first of all mathematics, and then of course teaching every child in the world to read adequately.
Once we have a child with perfect arithmetic and adequate reading ability, we have given that child the very basic knowledge that it needs to help itself, if are we then to create situations not unlike our British institutions of public libraries but even more complicated and more complex than that, free for all “computer and learning centersâ€,
manned by volunteers and educational enthusiasts, universal in concept and application.
Simply because computer education and computer directed education can teach us about virtually everything we do, alongside every possible interrelated concept the human brain is capable of with the exception of teaching us, to become as perfect in mental arithmetic as it is possible for any human to be, and of course ensuring we have adequate reading ability to manage the computer given guidance.
So for every child in every country all they would ever need is,
The occasional use of a computer some decent books and the association of educationally minded people which would allow any child anywhere to develop an educational ability to a level they personally find acceptable for themselves.
It is totally irrefutable that the computer will take over the major part of mainstream education over the entire world.
Education as we know it today is not in the Stone Age it is locked into a political and habitual dark age, all natural ability was available to human beings in the Stone Age as we are human beings developed by evolution. Evolution provided us with adequate training, we simply learnt to do what we had to do to live, copying speech and every possible physical skill needed to live.
Maria Montessori was the first teacher with an adequate grasp of the human brain, also having the personality and ability to develop a teaching system which related to human evolutionary characteristics, why the political leaders of today choose to ignore the lessons that she learnt and proved over one hundred years ago is beyond my personal comprehension.
Having researched educational behavior for over ten years, I clearly see that it is a situation which will have change thrust upon it, there are two things (in our western world) which are obviously essential to modernise, the provision of adequate education available at the press of a button, and the simplification of building a home, many of today's children would be better employed building their own house on a piece of ground provided for them by the government, then they are in classrooms which most of them should have left years before.
I mentally see three divisions in (schools) education, leaving the first four years of a child’s life entirely to its parents, virtually every child at four years old is adequately equipped to start meeting other children and adults in educational life, allowing them to be introduced to many new people, to have conversations with children of different ages, to become fully acquainted with mathematics, to be taught to read properly and acquaint themselves with many matters about the world, to spend four years in a situation where they are completely safe, to spend four years in a situation where they are absolutely happy, to spend four years in a situation where they develop their personal abilities, where they are four years perfecting their neurological capabilities that are the possession and right of every child, our perfect child is becoming ready for the world of computers, is becoming ready for the world of television, is becoming ready for the second stage of its education, the stage where we stop actively trying to develop the brain's capabilities, not that we can stop the brain naturally developing its capabilities, but we turn to a situation, where from eight to twelve years of age the child has to learn a great deal about the world that it lives in, ensuring that the process is effective and comprehensive, the child needs to learn a great deal of geography , history science and mathematics from which the child can develop it’s own channels of interest ,while gathering outside experience in , working with and talking to people in all walks of life, under the supervision of a scholastic situation.
So we simply have the first four years with our parents wherever possible.
For the four to eight years of age stage we would spend it in a school situation where Maria Montessori would be entirely at home and approve of.
From eight to twelve years old the child should be subject to accelerated learning doing everything necessary to fast-track its education, to become computer literate within the entire meaning of computers acquainted with their abilities, at ease with their use, learning sports, learning to cook and prepare their own food and look after themselves, preparing those children to be introduced to the practical world outside school.
From 12 years of age to 16 years of age our children need to be actively engaged not only in continuous learning, but with continuously changing experiences, of course they still need to be looked after, but a child brought up with the concept of education based on the three principles of,
SHOWING DOING KNOWING
will be adequately prepared to deal with the world,
From 16 to 17 years of age every child should have a one year apprenticeship/work experience, in whatever choice of chosen career it wishes to take up.
TESTING ITS PREFRENCE
After one year working within the areas of the expertise that the child is inclined to pursue and study further, the child would be capable of making its own decision, as to what further education it required, broadly speaking from 17 years of age to 20 years of age. It is my opinion that the government should provide adequate university training for children of 17 to 20 years. As a natural right of society.
Far from being a control freak, providing education for the over twenties should involve some self-help, any education whatsoever, that is not based on 50% practical and 50% theoretical is in no way whatsoever helpful to a young person developing their future career.
All educational facilities beyond 20 years of age need to relate to working experience and university combined if they are to be helpful in the preparation for a useful life. Of course many children will wish to travel at 16 years of age, and for many children of this age practical working experience, will give them a balanced view of the world, allowing them adequate experience to choose a career and way of life for which they themselves feel they are best suited.
Having spent such a long time studying such a small area of education, spending thousands of hours, considering the possibilities of perfect education in developing early arithmetic and reading ability I am somewhat biased in my educational thinking.
I am totally convinced that simply by giving the fingers the names of the numbers we use for the meaning of the numbers from one to ten, will clearly establish meaning within any and every child's mind at the earliest point that we can establish those ten numbers.
That means virtually perfecting this just as quickly as the child is capable of speech.
The meaning of ten symbols should be
( A UNIVERSAL PROCESS)
every Childs first family lesson.
Our normal mother, is concerned to teach the child to count to one hundred, if we follow on from the baby signing, which is becoming ever more prevalent, with naming the fingers we can rely on the child itself developing a natural number awareness.
For a modern child brought up with every modern convenience it is essential that it spends some time in formal teaching, but for that formal time to be comprehensive, and systematic, carried out on a continuous basis, evaluated continuously, in its efficacy, road tested at every opportunity, building into standard practice, where standard practice itself will perfect.
My personal efforts are related to two things, teaching every child in the world the name of its finger from one to ten and providing it with a counter, called Abacus One.
Following my letter to you, accompanied with many of my working papers, I am appealing for your consideration, and approval of my simple systematic and proven steps, essential in providing vital stepping stones within education, of course the government will need to validate my hypotheses but they are more likely to do it, if you give your approval of it.
My personal experience of educationalists is such that I find them in particular to be the least intellectually curious of
any profession, we seem to have got that completely wrong.:dazed:
Thank you for reading my letter so far and hopefully the work that I have sent to you with my hypotheses on the simplicity of mathematical awareness and the possibility of it becoming readily available for every child on earth,
John Nicholson
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 14-03-2007
MY OWN DAUGHTER GETS THE PICTURE
This is by far the most interesting topic I have looked at so far. I have
enjoyed looking at his work and find his work is crucial in helping to influence politicians to change the way math’s is taught.
Brian Butterworth is a neuroscientist at the University College London. He believes numerical knowledge is innate and universal a basic capability to be ranked alongside seeing and feeling. I plan to look at his reasoning behind this theory and his ideas on what he calls the number module. I will consider evidence found by work with new borns and animals. I then plan to discuss his discovery of dyscalculia a condition compared to dyslexia and colour blindness. I shall look at his focus now before concluding with what his work means for us.
First of all Brian Butterworth was himself not highly educated in math’s. He in fact gave up mathematics at the age of sixteen. His interest in it only re emerged as a psychology student. He became interested in the foundations of mathematics. This mere speculation on the topic turned into an actual research project when he recognised some of the people in his clinic as having what he termed numerical disabilities. These people’s memories and language skills were good but they could no longer do the kinds of calculations they use to be able to do. These could some times be incredibly simple calculations. This is what got him started in believe in the existence of what he later went on to call a number module.
Brian through his research claims theres a physical sector of the brain what he calls the number module which is part of our genetic inheritance. This he feels provides the foundations for our mathematical knowledge. Therefore he believes we all have some sort of awareness of numbers and some sort of ability to answer questions such as how many? goes back to human pre-history. This ability to count and calculate is not result of an invention but due to the evolution of specialist neural organisations for perceiving "numerosity" the amount of objects within a set. In his book "The mathematical Brain" he says "We are born with a core sense of cardinal number". This means we understand that collections have a number associated with them. This is proved by his and others work with new borns. Since the 1980s Brian Butterworth says reports appeared showing how newborns that hadn’t learnt to count were able to recognise the number of things they saw at a glance. Scientists have discovered certain tests to show how interested a baby is for example the more a new born is interested in a topic the more they suck on a dummy. Therefore by wiring this teat up you can see how different things make the child react. Tests have proved that if you show a new born two things and then another two things even if you change what they are the child will loose interest. If you then add a third there interest will return. If you continue to show three objects even by changing these objects features such as colour or shape the child will still loose interest. However by removing one to make two the Childs interest reoccurs. This proves that even new borns have this core sense. This in itself is a crucial development that needs to be recognised and publicised further. This could mean that this number module Brian identifies could be the foundation all of our later mathematical work is built on.
If Brian’s theory is correct we should all be capable of being numerate and the main attribute to distinguish geniuses is practice. However is initial identification of the people in his clinic he described as numerical disabled proves this is not the case. Brian says that this is due to them suffering from a condition he calls dyscalculia or asyculia. Dyscalculia is used to describe those people who are born without possessing a sense of numbers. Acalculia who have lost there sense of numbers in later life maybe as a result of a stroke for example. Both of these types of people have to lead their lives completely devoid of numbers which in our modern society were we are dependent on numbers. Dyscalculia and acalculia creates to main problems for the individual firstly they can not select the larger of two numbers so if you said five and 3 and asked which was larger they would not know. This is critical with the way we learn to count when we learn on our hand initially if asked to add 5 to 3 we would count three on our fingers and then count up on the other fingers and then recount, We then learn to just say three and count up five and say eight. Finally we learn to count on from the largest number so we would recognise five being so and count up three till we concluded the answer was eight. The people however who suffer from this condition can’t move to this step as they do not recognise the larger number. The second problem that this condition creates is they can not just see the amount of objects that are there. So they can not recognise as you or I if we held out our hand that there were five fingers they would actually have to count them to identify that there was five objects. Therefore they can’t perceive numerosity. This is similar to conditions such as dyslexia and colour blindness but effects the not our ability to see or read but our ability to recognise numbers. It infact relates more to colour blindness as the condition dyslexia although always exists in victims sufferers can over time with the right help become good readers. Sufferers of Dyscalculia and acalculia however like those of colour blindness never become good calculators. The solution is therefore more to do with coping methods. For example I read that some sufferers carry a calculator which could be adapted to a pocket abacus.....This problem is hardly recognised even though research has shown that unto 5% of the population suffer from it almost the same amount that suffer from Dyslexia which is now greatly recognised. It has also been proved that this condition can actually be a greater hindrance to getting a job then either colour blindness or dyslexia.
Brian’s current research I think is even more crucial to our work he has started to look at the idea early mathematical ability might be related to certain physical skills. He is working with victims of Dyspraxia. These people have difficulty controlling their bodily movements. Although Brian believes we all possess this number module which is the foundation that later mathematical ability is built. (Except sufferers of Dyscalculia) why do we as adults not all possess the same mathematical ability? This is due Brian believes to the theory of nurture not nature. He believes practice makes perfect. So although in the western world we suggest some one who is good at something as say having a gift he would believe they are better because they have practiced more so that is the reason for their increased ability. This is very relevant to the abacus. Brian recognises that we start to count on our fingers and only later weabandonn them for a calculator well people with Dyspraxiamay suffer poor finger dexterity so he is researching how this condition affects their mathematical ability. One case he looks at is a lady with no arms or legs but she says when she does mental arithmetic she puts her imaginary hands in front of her and uses them. This shows that although we may all be born with the same basic capabilities the difference in the level of adult performance will depend on our experience and education. Brian actually believes that we could improve our understanding of mathematics if we based our education more firmly on the mathematical toolkit we were born with. This is crucial as the abacus is the next natural step from counting on the fingers. We can only hope that politicians begin to realise that math education can be greatly improved for all children through a better understanding of how the brain processes maths. We know the existing evidence shows how the use of the abacus can greatly enhance a Childs natural mathematical ability as even when it is taken away they still refer to it in their brain their mental image just like the women with no arms or legs uses her imaginary hands top count.
You must try a contact Brain as I believe he must be interested in the abacus. Anyway really enjoyed looking into his work its amazing...
LA NICHOLSON :yes: THE COOLEST OF THE COOL
__
Goverments Teachers Parents Turn The Teaching Clock Back - OECD Expert - 14-03-2007
Thanks for this John.
You can read a conversation with Brian Butterworth at: http://www.brainconnection.com/topics/?main=conv/butterworth
Cheers,
Christina
Goverments Teachers Parents Turn The Teaching Clock Back - geodob - 14-03-2007
Hi John,:hols:
It's been ages?
I'm really happy that you are looking into the issue of developing a 'Sense of Number'.
Though I have recently redefined it as 'Sense of Quantity'?
Number is a Verbal or Visual Symbol associated with a Quantity.
But to begin with, a recognition of Quantity needs to be developed first?
Where we can look at 2 fingers or 4 fingers, and recognise them as a Quantities.
Without attaching a name or symbol to the quantity.
So that one can recognise the quantity of 4, as being made up of 3 plus 1 objects, or 2 plus 2 objects. Without having to associate a verbal or visual symbol with it.
So that Quantity has a physical identity, that can be physically divided into units.
Where this Sense of Quantity needs to cultivated, and refined. Before abstract Verbal and Visual Symbols are associated with Quantities.
Though a quantum leap, is the transition from quantity as 'individual units', to 'groups of units'. Then 'groups of groups', and so on.
From 1 to 10, to 100, to 1,000 and so on.
This is why historically throughout the world's cultures, a variety of Abaci were developed. Where the Abaci was used to represent Quantity.
Though this explains an anomaly in third world countries, where children in fact have a stronger grasp of maths than children in first world countries?
Yet the contradiction, is that whilst they might have a stronger understanding of for example; 694 as a quantity. They might not be able to associate it with a verbal or visual symbol; 'six hundred and ninety four, or, 694.
Whereas,in Western countries, we have the opposite situation?
Where they will know the visual symbol of; 694 and verbalise it as: six hundred and ninety four.
But it may have sense of Quantity associated with it.
The great value of the Abacus, is that it develops a foundation of Maths as Quantity.
Which can be later given abstract Visual and Verbal Symbols.
Geoff,:tourist:
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 15-03-2007
:adder: :pcprob:
Good morning from England Geoff, it is a very nice to have you back, as you noticed there is a letter from my daughter in Australia, she is living in Melbourne, arrived back in Australia almost as I was leaving Australia last year in late October, we have been at war for some time, but thankfully she appears to have married a very nice young Australian musicians of Chilean extraction and they appear to be quite happy. Of course in Australia it is always difficult with getting the right papers to enter it, young Europeans appear to be able to stay there for a year, and then move on, but in her case, she has returned to your country.
There were having a difficult time starting life together in a rented flat in Melbourne, so simply because she needed a little chash, she was more tractable than normal, and agreed to do me some research work, on a number of people, first of all she read everything she could about Maria Montessori, and then wrote me and fine essay on it, secondly she researched the lady in America who developed the L. abacus Mrs Joan Cotter
And finally she has just completed the short work, (posted here) on Brian Butterworth and his research.
From her personal essay it is easy to see that at last the penny has dropped with her, she can now understand what her father has been doing in the garden shed for 10 years, she has a degree in criminology, but very nature she is drawn more to business then towards crime, we only have one life and it is vital to spend it in doing something we like, something that we are really interested in and something that we live for day-to-day..
Of course I was interested in my farming and thoroughly enjoyed it, extending my business beyond the bounds of common sense, and unprotected from predators trading as a private person rather than a business Ltd.
Unfortunately the whole thing bit me, but it led me towards something that I have really enjoyed thinking about, something which I now regard as the most important thing that I have ever done, or our ever likely to do.
That is to become interested in the human brain, researching and thinking how it works and how we can encourage it to work perfectly, how we can ensure that every child on earth has an equal opportunity with their education, and from then on to throughout their lives, it becomes ever more obvious to me that simple mathematics is the key to the human brain.
In every society and that every age we use our fingers to count and tally with, time and time again I have been back to relating fingers to numbers, but from a mental point of view only, I was nearly there from the beginning, it was only after developing a system of rapid arithmetic using your fingers to count to 10, as system that I'll described as
“a sum a second
rapidfire visual arithmetic, the purpose of which is to establish visual appreciation of individual numbers, perfect spatial ability.
The one thing about mathematics that is most important, is potential accuracy.
In the end without being perfection in arithmetic, or having the individual possibility of perfection, we are simply going nowhere, so moving on from the exercise
a sum a second,
the penny finally dropped with me.
Because we all use our fingers to count with, and we all need to create numbers from left to right, before we transfer them into a column, as far as a young child goes, we do not need to hammer meaning into the words, all we need to do is christen each finger individually, of course one and 10 are easy, moving on from one and 10 number two and number nine are like brothers to one in 10, from there I moved onto the thumbs enough difference here to create an L. with the left-hand teaching a young child not only the fact that thumb is five but that is its left-hand, moving on from my kitten exercise twin kittens I was able to give that kitten the name five and the right-hand kitten the name six after the thumb, looking at my hands in the dark or half-light the difference in the finger lenths, mean that we have the number naturally once we associate it with the fingers, holding my hands flat and pressing them towards a wall on the edge of a piece of furniture, with my hands palm down, those are extensions from my ancestors front feet used as pads, but now developed into human hands, i have the middle finger on each hand extending beyond the others, of course every finger has a different length, we are so naturally aware of it, we completely ignore it.
Having divided their hands into twin kittens palm down, move them towards the wall only two fingers touche the wall, I have experimented on numerous friends asking them to do this with their eye shut considering that their fingers relate to ten from left to right very few of them even knew the name of the middle finger on the left-hand and only the Conservative member of Parliament for Beverley could tell me the number of the middle finger on the right-hand.
So we have a simple exercise here, we can create a visualization, and engage the mind to make a permanent memory instantly in an adult of the number of its middle finger of both hands, of course it is not a child we are teaching, but many children will learn this and remember it just as quickly as an adult, so now we have established the beginning and the end of the count we have established the middle finger of both hands, in reality we have an established number for the left-hand thumb and the right-hand thumb, we even have a plus we are permanently establishing the left-hand.
I was told by a neuro linguistic programmer that having been taught both left and right left me more mixed up then if I had only been taught the left-hand thank you Bill for this.
After years of not knowing how to relate to left or right without thinking of the side of the road that I drove on. I established a quicker method of learning left and right from producing an L. and an even quicker method while explaining that to Toney Buzan, where I happened to wink involuntarily with my left eye, from that I realised that I could think left immediately just by winking with that eye alone, it has worked perfectly for me to produce left immediately ever since, obviously a different part of my brain is giving a signal to the eye and I am able to identify left and right almost instantly.
When it comes to numbers of course, we need to establish numbers, and the meaning of those numbers perfectly, so when we have identified most of the fingers on our hands simply looking at forth finger at the end of a row of similar, clearly identifiable between the third finger the longest finger and the thumb, we can create individual recognition instantly of four, transferring the same situation in the opposite mode, we can clearly identify seven lying at the left-hand side of four fingers between something different
( the longest and middle finger) and the thumb that we name six we have a natural seven.
So earth shatteringly, we have a method of number recognition based on our hands.
The most involved human, in touch with a child learning to speak, is of course its mother, if we adopt this method of establishing the number of 10 universally, it means that every mother needs to be aware that all she needs to do is to teach her own child the
number /name of each finger
and leave it to normal human intelligence to establish meaning.
It is normal in a mother to try to teach her child to count first of all to 10,
a second stage to 20, and finally to count to 100, as far as a mother is concernd, this simple rote learning is the only vital mathematical thing, she is aware of unless she either is an educationally minded person, a paediatrician, a physicist, or a mathematician.
In my research on Abacus use, I wrote to Terence Tao a young Australian child, a mathematical prodigy of Chinese extraction. His mother was a physicist his father a paediatrician, Terence's IQ is to 220 which IQ fanatics considered to be one in a million.
My question was did you use an abacus in your early education, while he did not use an abacus in his early education, of course with a mother totally aware of numbers, he would have been taught numbers in relation to his fingers, at the earliest possible age, and was likely having natural language ability at an early age to developed a good understanding of numbers in relationships with its parents.
Most of us do not have parents on the one hand a physicist and on the other hand a paediatrician, but we all need to become perfect in mental arithmetic, and perfect in understanding mathematics, Brian Butterworth tells us that it is possible for almost all human beings to take their individual ability in mathematics to any level they so wish, I could not agree more with him, I see mathematics as a series of small lessons, which when they are taught well and correctly can ensure perfect arithmetic ability, all we have to do to establish meaning within numbers, is to teach every mother that she must teach Her child the name and number of every finger.
The principles of my educational format, the principles of the abacus and the alphabet LTD A&A
Are COPSL in reverse,
LOGIC SIMPLICITY PERFECTION ORDER CONCENTRATION
They have all to be used in all basic skills training.
:detective:
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 30-04-2007
:choc:
Number Blindness: A Hidden
Challenge for Mathematics
May 2000
by Ashish Ranpura
It's hard to imagine an aspect of daily life that is not touched by numerical ideas: telephone numbers, street addresses, radio stations, bus schedules, currency, and time all depend on a rich awareness of numbers and their meanings. The concept of numbers is ubiquitous in the modern world, and it seems at first inspection that anyone with fundamental misconceptions about numbers would be quite apparently handicapped.
This conclusion is so compelling that it remains virtually unquestioned in mathematics education. Students who appear to have fundamental difficulties with mathematics are told to study harder, to pay more attention, and to spend more time working through drills. In many cases, they are tracked into increasingly rudimentary mathematics courses until they are hopelessly behind their peers. In all cases, both teachers and students are frustrated by what seems to be a tremendous chasm separating those who "get" mathematics and those who don't.
Recent research on how the brain processes math offers some hope for bridging that chasm, suggesting that the fundamental misconceptions students have about numbers may stem from a subtle mathematical impairment. A 1998 report published in the Journal of Pediatrics estimated that approximately five percent of the school age population has some degree of dyscalculia, a sort of "number blindness" that is an impairment of the ability to recognize or manipulate numbers. This [suggests] that for some children, creative teaching techniques and studious discipline are not enough for a productive math education. Mild dyscalculia may easily go unnoticed, leading some students into educational settings that can offer only frustration.
As data about dyscalculia accumulates, it is becoming clear that math education could be improved for all children through a better understanding of how the brain processes math and what can go wrong with that processing.
Developing a Sense of Number
Our ability to understand and manipulate numbers goes through a series of important developmental stages well before we posses any recognizable mathematical talents. Dr. Karen Wynn, a child psychologist at the University of Arizona, has demonstrated that infants as young as 6 months expect that adding one object to another object will produce a set of two objects, and that infants are quite surprised when these arithmetical expectations are violated.
The infantile sense of numbers is restricted to collections of only four or five objects, and the data suggests that infants and adults manipulate such collections using a mental process quite distinct from counting. For small collections, both adults and infants perceive the "numerosity" of the collection directly, somewhat like we perceive shape or color. This direct, intuitive perception of numerosity is called subitization, and it is the first number skill that we develop. When we see three objects, we don't count "one, two, three," instead we are simply aware of the group's "threeness." Most people can subitize up to seven or eight objects, switching to a variety of counting strategies for larger collections.
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 30-04-2007
:autumn: HERE I AM
:pcprob: AN OLD FARMER KNOCKING SENSE INTO TEACHERS HEADSMathTrek: Brainy Figuring
by Ivars Peterson
In pondering the possible relations between inventive thought in mathematics and bodily phenomena, the mathematician Jacques Hadamard (1865-1963) sounded a note of despair in his 1945 book The Psychology of Invention in the Mathematical Field.
"While mathematicians have not sufficient knowledge of neurology, neurologists cannot be expected to penetrate deeply (as would be necessary) into mathematical studies," Hadamard wrote. "Will it ever happen that mathematicians will know enough of the subject of the physiology of the brain and that neurologists know enough of mathematical discovery for efficient cooperation to be possible?" he asked.
That gap is beginning to close, particularly with the pioneering work of Stanilas Dehaene, a mathematician turned cognitive neuropsychologist, who works at the Service Hospitalier Frédéric Joliot in Orsay, France.
In the May 7, 1999 Science, Dehaene and collaborators at the Massachusetts Institute of Technology present the first hard evidence that two quite different modes of brain activity underlie our inborn capacity for mathematics.
Their study indicates that learning the multiplication table is akin to memorizing a laundry list, whereas learning how numbers relate to each other appears tied to visual intuition about space.
Using brain-imaging techniques, the researchers discovered that calculating an exact sum, such as 53 plus 68, and estimating which of two numbers is closer to the right answer, such as deciding whether 53 plus 68 is closer to 120 or 150, activate different parts of the brain. Performing exact arithmetic uses a region of the brain usually active during verbal memory tasks, and puzzling out approximations exercises the visual side.
In sum, the study suggests that mathematical ability results from the integration of two nonnumerical circuits in the brain, remarks neuroscientist Brian Butterworth of University College London in England in the same issue of Science. One is the left frontal lobe, which controls linguistic representations of exact numerical values, and the other involves the parietal lobes, which control visuospatial representations of approximate quantities.
Mathematicians have long reported that they rely more on mental images than words to arrive at new insights. Albert Einstein (1879-1955) once stated, "The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined."
The findings suggest that understanding relationships among numbers involves some sort of spatial tool, such as visualizing a number line. Such visual aids may be important sources of mathematical intuition. Developing skill in their use could be crucial for budding mathematicians.
At the same time, behavioral experiments with test subjects fluent in Russian and English indicated that learning how to calculate sums mentally in one language may not help much when performing the same summations in a second language. Yet making approximations is equally easy in both languages.
The language-related distinction also showed up when the researchers trained and tested the bilingual volunteers in more complicated mathematical operations, such as addition in a base other than 10 and the approximation of logarithms and square roots.
This is just the beginning, however. "Even the simplest arithmetic is more than just fact retrieval," Butterworth comments. Moreover, the parietal lobes may serve other mathematical functions as well, including some involvement in exact calculations.
"It is worth noting that the parietal lobes. . .are part of the neural circuit that controls handshapes and finger movements," he adds. "This raises the possibility that these brain regions contribute to finger counting and finger calculation-an almost universal stage in the learning of exact arithmetic."
In the end, studies of how the brain functions while doing mathematics may have implications for how mathematics is taught, potentially leading to new, improved ways of teaching arithmetic to children who struggle with numbers.
:yes: FOR ME PIECE AT LAST JOURNEYS END
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 05-05-2007
Apart from polishing the techniques which is your lots job (teachers) i feel that it is time for me to move on.
Easy Learning with abacus and alphabet is no more then a ruse to hide the vital principals of early education that i believe in.
SATURATION MATHEMATICS ALWAYS VERY EARLY AND CONTINUOUSLY THROUGHOUT THE CHILD'S SCHOOL LIFE
ALONGSIDE SATURATION READING USING SIMPLE LOGICAL STEPS
One international method internationally applied and recognised should bind humanity together more then anything else.
Teacher and parents working together
a constantly reviewed, adopted and adapted, METHODOLOGY to suit all children
we can waste no more time arguing while the
WORLD BURNS
OUR TRIBE MAN IS IN GREAT DANGER FROM ITSELF
WE HAVE TO SIMPLIFY THE WAY WE LIVE
CONSERVE OUR NON RENEWABLE RESOURCES
DEVELOP OUR ABILITY TO HARNESS POWER FROM THE TIDES THE WIND AND THE SUN
GROW AND PRESERVE SUFFICIENT FOOD TO ENSURE OUR PEACEFUL SURVIVAL
BUILD FOR ETERNITY
I am moving on in my educational research to concentrate on
THE STORY OF ME ----------------:tourist:
Our common human history
the common history of everyone-----------:anyone:
that means you
every colour every nationality every language every religion every philosophy ever great one, ever good one every bad one every kind one every greedy one, every wise one, every silly one.
yes, my friend that means you.
i only need one of you to help please let it be you.----------------:pcprob:
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 06-05-2007
After almost ten years of exploring for myself just how we humans learn anything and every thing I am bound to have some fixed ideas and some new ideas, I never approached my research as a teacher more as a business man solving a problem.
ok you lot (teachers) already had some of the answers, but not all of the answers, my personal research led me time and time again to consider
Maria Montessori, and what she new and did, she obviously became fassinated,like myself and others on here by the human mind, her whole life was a dedication to the idea of human possibilities, she could not stop, inventing gadgets to teach more effectively with, I could see that happening to myself, but I shall fight against it.
What I want is effectiveness, we are in the world of instant access as regards information, conclusions on abacus effectiveness will be proven shortly in trials taking place within different English speaking countries.
We have to consider what science is telling us; let us use the same tool as Maria used common sense applied with experimental practice.
if you were to teach only mathematics and reading education would still take place in a perfectly natural manner, news papers, vast areas of television programs, on the job training, trade and individual interest magazines alongside vast libraries of books many which will obviously soon come on line, and of course the wonderful present of American war research
THE INTERNET
we have built a new world but we can not build a new man.
he will still be greedy, he will still be lazy, he will still be afraid, he will still be isolated he will still suffer from self doubt, he will still have no sense of a combined human future, only education and experience will save this planet from destruction, we can not leave every thing to some one else to do we have to take part in the road to the future.
There is no better way to prepare yourself for the future other then to understand the past, there is no better place for a young child to be the a safe school with a program
Education preparing children for the future, I started to write this with a typewriter, but quickly realized that I needed to move to a speech recognition system, I have far more to say about what I think on this subject, then I can possibly type even if I was able to type fast on for a year, so I have resulted quickly to my old friend the speech recognition system.
Even if we were to think about the possibilities regarding this system itself, the profound affect on the whole world, purely from the use of this system, will have a massive personal effect on everyone's life, not from the things that I'm saying, those are just the ramblings of one concerned individual with the future of the planet,
The massive ability to spread ideas quickly and profoundly throughout the world, is where speech recognition will come into itself, as soon as any individual has an idea, it can be given the world airing, if 20 people read one idea, they will generate a hundred new ideas from that Idea, it is not having ideas that concerns me, it is the application of good ideas that concerns me, for good ideas to spread and be useful we have to have a fertile breeding ground, that fertile breeding ground is our educational system, but the first thing that has to be done, is to remove the weeds from that educational, it is blocking the light and air, and then we have to fertilized that educational system, we have to prepare it to take on board new concepts new ideas, to be able to consider ideas and develop introducing the abacus as the world's system of entering arithmetic capability simply into the brains of millions of children, is not more than a first step,
After years of considering mathematical appreciation within the young child, after coming round to it on umpteenth time, I realize that the answer is of course within our hands, they clearly represent 10, thorough understanding of numbers one to five is a first step in the concept of numbers, wants five is properly understood by any child, twice five follows very quickly,
The simple statement we do not know what we do not now.
Time and time again in my research, small pieces of information prevent children from understanding larger pieces of information, my partner recently pointed to a map, showing the movement in the provision of new larger store, she said Lookout clear that his, she knew every piece of the city, and all will I knew the city, with a map presented did not have the same meaning to me,
I pinpointed the original shop, and simply could not relate to the new location.
What is this proves we may ask what this proves you may ask,
For me it simply proves that we see something, we do not all see the same thing.
We are each totally different and unique, very few of us have similar life experiences.
With virtually never reach the same conclusions, about anything, everything we need to do of a permanent nature, as to have consensus behind it,
In matters of mathematics, we have to be perfect. In matters concerning reading we need to be effective, in matters of speech, we need to be clear.
Intensive examination of every step we take in early education, and the application of it needs to be examined minutely, every new idea needs to be explored, and if it proves effective, adopted modified considered utilized, absolutely abacus will be introduced eventually into English-speaking education purely from proven ability to teach effectively and rapidly.
Looking at teaching itself considering that the mother's domain is the child until it is four years of age, in the main part, from four years of age, five or six hours a day become the responsibility of the state, in the United Kingdom in the last 10 years every primary school has been filled with computers, no child however difficult the circumstances of its family, is prevented from computer realisation and awareness.
Massive steps in technology, regarding effectiveness and the lowering of the price of laptop computers, means that the Western world, is within sight of a laptop for every child virtually as soon as they go to school,
However the abacus and the alphabet, will always come between the mother and effective use of the Internet and the computer, so we may just as well buckle down to understanding and producing the best brain effectiveness of every child, as we provide them with their own personal computer.
Early association with a computer, means extremely effective awareness of it uses, and capabilities within it uses, but just like a television, if we leave the choice of program to the child, we can expect nothing but a simplistic utilisation of it.
Young children should be allowed to television sets of their own, television sets unconnected to the millions of television programmes from which they can learn nothing whatsoever,
Effective monitoring of what they see on television sets at home and in the classroom will enhance the fair world awareness; mankind is common ancestry can be shown effectively by a television programme, developed around the story of human evolution.
We need to combine history and geography in order to give a child world awareness
at such an early age, the human mind is capable of vast memory ability, when it is provided in story form, some things can be quickly understood visually, some things can be quickly understood we show each other how to do those things, the abacus and basic arithmetic education, is best illustrated by showing and doing with her hands fingers and at abacus.
Visually a child has to be aware of the world, so they need to be provided with globes and fact flat projections of the Earth, they need to build a visual awareness of the skeletons of geography, where are the seas, where the land masses, where other countries of the world situated, which in the cold countries, which are the hot countries, which our wet countries, which other dry countries,
The child needs to build a skeleton of the world quickly and effectively, the child needs to build a skeleton of world history, and that early history is best told in story form,, those effective and important individuals who have played a vital part in world history need to be identified and placed within time zones and geographical regions which will effectively build into long-term knowledge.
For me this is my next personal challenge, the world is full of good ideas, they need to be identified, co-ordinated and utilized, and effective geography history combination program for a fall to eight-year-old child is extremely urgently required.
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 06-05-2007
the rest
:adder:
Looking at the human brain development of a four-year-old child, it is launched generally understood by science and practice awareness, that the child is capable of learning vast amounts of information almost subliminally, letters teach the child what we need to teach the child, let us consider natural brain development and just how we can enhance it.
Spending a great deal of time, in one manner for a child, is extremely boring, we need to explore and examined the recognised intelligences that we possess, utilising those different intelligences should be combined to develop the physical awareness of Brain, for example taking mathematics, we can move from simple exercises utilising the fingers to count with, to utilising abacus to count with, ensuring that the child can do and achieved perfect arithmetic quickly, but we must not overtaxed the child, virtually moral arithmetic test for a young child, needs to be beyond 10 minutes, we can let them get their fingers in paints and print numbers effectively with their fingers, which have let them draw different groups of numeric arrangements, we can let them discuss number situations between themselves, we can organise games where they effectively need numeric awareness to take part in,
can provide them with puzzles which taxes their imagination, we can utilise everything that Maria Montessori utilised in teaching mathematics and every modern facility we possess as well,
It is my opinion that the four-year-old child needs to spend the morning was considering numeric related entities, within a class situation, sometimes a one-to-one situation, sometimes a small group situation, helping each other, teaching each other, playing and learning with each other.
Children are naturally tired later in the day, this is always been the time was convenient for them to listen to stories, written stories read by the teacher, or listen to from electronic form can be combined with historical and geographical issues in order to build the child's awareness of man's development of the Earth other countries within it.
All young children need to develop an awareness of a second language, all young children need to spend time in an art and musical activity as well as being guided in effective sport and play these are common themes, we must examine them and improve on theme,
My concern is with effective neural development, ensuring that we develop a thinking and doing child, that we develop a child, that grows up independently minded, a child that can think for itself, a child that examines everything it is told with a critical eye, each of us, has the potential of mammoth personal ability, if we are taught efficiently and effectively between four and eight years of age.
A child of eight who cannot read well, nor manage arithmetic well, will be damaged for life without exceptional energy put it to their later development.
:autumn: :autumn: :autumn:
nowt but work.
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 20-05-2007
The Concept School of the future
The concept schools of the future where the pupils do the teaching and the teachers sit around thinking of better ways to do it.
The ex-parental Concept School of the future.
Where children simply teach themselves.
Of course You will ask how do they do that.
We do it naturally, we spend our whole lives teaching each other, all the simple and complicated things that we have to do.
Just look around you,who will help to teach you to speak, who corrected your vocabulary, taught you how to ride a bicycle who taught you to swim, who was it that taught you to play chess, who was it then, that should have taught you how to play chess.
Who was at that taught you how to drive a car.
Who was at that explained to you that kindness was a gift that would be repaid three times over,
Imagine that, imagine showing kindness, and having it repaid, three times over.
Of course we have to analyse kindness, of course we have to understand the meaning of kindness.
We have to understand the value of kindness, it is the most important human gift we have, it is the most important gift we can develop.
It is the natural gift of having been given, when we have it, it will have enhanced our lives for ever.
In my own case my father gave me understanding of common sense but as regards kindness my mother gave me the gift kindness, her own family was disrupted, her father was a Miller grinding and selling grain and flour, during his job he daily transported flour from his mill in Beverley distributed by two horses and a wagon.
My grandmother said that he had a horse which could not pass an open pub doorway, I have explained my love of food in the same manner, I had a car which would not pass an open fish and chip shop door after 1013 the evening of course English drinking up time was 1030, I'm sure you will take even longer to make something of this writing then it has taken me to give you the ideas in a few moments with a speech recognition system.
I was trying to write the word system it needs to be included at the end of the last sentence, somehow or other of them must be punctuation, and of course unless I find automatic punctuation, I will just have produced the longest sentence in the world.
To be of great value words simply have to be precise,
The title of something is most important it have to be considered and reconsider until perfection is obvious.
Somewhere I have recorded the philosopher who said when he was asked to explain an idea quickly, and the person that was asking is said to him, never mind the preciseness of the words, just tell me the idea.
The philosopher realised of course that unless the words were precise, beautiful ordered and sufficient they were of no use in explanation of such wonderful ideas as he was personally capable of.
Just take that one and consider it for ETERNITY.
Language is OUR human gift, it is the manner in which we think and teach and consider,
Of course I must try and remain closed to the point it is very difficult for me to remain thinking about one thing for very long life interrupts our thoughts, and the essential thinking that we must do to make progress is always difficult to concentrate the concentration is vital when considering the future of our planet,
And so to work,
Maybe word this morning is just a collection of rumbling ideas, Oh HOW I love the word IDEA,
I adore considering and creating new ideas, if we are to have a useful future it has to be based on many things but let kindness be its cause, let kindness be its manner, let kindness be its end.
In mathematical terms why does the idea kindness multiply itself naturally BY THREE, I suppose it is just the act of kindness committed by one, given naturally to another, and available for everyone else.
As a young man I traveled around Europe in the method of the day hitch hiking which was of course the method of that time, not everyone had a car, and some of those people that I had showed kindness to some of those people that had not, so I became the beneficiary of much kindness, it is a rare occasion when I failed to pick up a genuine hitchhiker.
So I suppose we have the explanation why kindness is represented by a multiplication of three, the initial act of kindness, the return of an act of kindness, and the continuation of kindness itself,
Let me blow my own trumpet, tongue in cheek of course. Many years ago I picked up a hitchhiker, he was desperately short of money, when he left my car I gave him £20, he thanked me and said that he could not take, because he would not be able to find me to give it back, I told him not to worry all he had to do was to give it to the next man he met that needed it.
Kindness is the gift that Maria Montessori, gave to the world children, kindness in teaching, kindness in explanation, kindness throughout our daily lives, kindness throughout pro-business lives, and kindness within our personal lives.
I see Maria Montessori in the manner of my own mother, I see Maria Montessori in the manner of my all mothers aunt, my mother's mother had a difficult life, she was obsessed by security after finally kicking grandfather lying in a drunken stupor taking her two children in a pram and leaving him. She returned to the family farm, from which her own mother had now died, she then left her children with her sister while she went out to support them.
My grandmother worked extremely hard all her life, she was a determined woman, determined to succeed determined to be the best for her children, determined to behave correctly.
My grandmother sister had no children of her own, she was grateful of the opportunity to bring up our nephew and niece. It was my grandmother sister, and her kindness to those people that worked for them that is so impressed my mother.
Whenever my mother inquired to my aunt why she gave so much away, she always made the reply that everything you give is returned to you threefold.
So there is a practical story, of the benefits of kindness, I can see the personal benefit in satisfaction that Maria Montessori felt through carrying out her work, for me Maria Montessori will always be the most important woman ever having lived on earth, that has ever lived or is ever likely to live,
My own mother, Irene Kell was for me, in the manner of most humans, the teacher of most importance.
Normally mother's teach their children to count to 100 and ignore mathematics, of course they still have to teach their children to count to 100, but they can no longer ignore mathematics, they have to take one more step, they have to teach their children the name of each finger from left to right illustrating their natural language and value from one to 10.
If every mother in the world does this, and every child in the world is taught on abacus, we have cracked the principles of mathematics, and mathematics teaching for eternity.
It is just as simple as that.
There is no such thing on earth as a school claiming to be run on Montessori principles without an abacus featuring within mathematical education.
Maria Montessori developed her first school 100 years ago, we have two investigate what she understood 100 years ago in order to make progress in simple education, there are obviously multitudes of educational ideas that have been developed since that time, but creating is central mathematic awareness has not been one of those basic ideas capable of being bettered in a hundred years.
I rest my case
:tent:------------------------:pcprob: still working:tourist: reading my abacus
Goverments Teachers Parents Turn The Teaching Clock Back - John Nicholson - 27-05-2007
:am: LOOKING FOR THINKING LINES
FOR EVERY CHILD
-------------Perfect numbers
---------will
-----------Develop a perfect brain
-----------------------------------Saturation mathematics
---and symbol recognition
-------------------------------------Is the gift of
The abacus and the alphabet
-----------------------------WHEN
Used everyday for 15 minutes
---------------------------------between4 and 5 years of age.
---------It guarantees that every child will read normally and develop
natural mental arithmetic ability.
----The human brain is capable of instant understanding
When
-------The cognitive highway is paved with our written language
:autumn: --------------:autumn: ------------:autumn: