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There is clear evidence that concerns over mathematical education has a long history. The Cockcroft Report 1982 into mathematical education refers to reports that date back to 1879 raising concerns about mathematical standards.

There has been a vast amount of research into the subject across the world, and if there was a simple answer to developing standards of mathematical attainment, then surely someone would have found it.

Dylan Wiliam (2011) reported that despite the vast amount of time, resources and effort that went into the primary mathematics and numeracy hours that it did not change the standards of mathematics significantly.

The Cockcroft 1982 Report into mathematical education took five years to research and write. It undertook an in depth review of the subject and recruited advice from a whole range of professional sources. There is no evidence the report is not relevant to children's education needs today, but the mathematical skills that children need to develop in modern everyday life are changing.

Research illustrates that there is a seven years spread in mathematical attainment which is related to the spread of working memory. It conforms to bell shaped standard distribution curve, where most children are clustered around average.

Pisa Myths

The problem that has arisen is that Pisa has given the impression that western countries are under- performing in comparison with Far East countries, especially in mathematics.

The B.B.C. Wales 2016, "School Swap: South Korean Style" illustrated that in Seoul South Korea, which is a high Pisa ranking country that children were obsessed with mathematics. Children were learning up to 10'clock in night classes, they were working child labour hours. They were also receiving private maths lessons at home.

If someone wants to become accomplished at playing a musical instrument or chess player, for instance, then they will need to devote a great deal of time practising it. Basic fluency requires 6,000 hours of practice.

We all do not appreciate how much time we need to devote to develop and retain our language fluency. Irrespective of how much time is devoted to developing fluency, there are limits to the fluency that can be achieved, especially the breadth of what can be fluently applied. These limits will be different for each individual.

The problem with Pisa is the myth posited by Andreas Schleicher, Head of Pisa is that it is desirable and possible for all children to reach Far Eastern standards of mathematical attainment. What is not considered by Pisa is the 'how' this can be achieved.

There is a myth that people in the United Kingdom are not very good at learning second languages, but the problem is that there are limited opportunities to apply languages like French in everyday life.The development of mathematical fluency cannot be divorced from how often it is applied. Mathematics is topical.

Mathematics could be described as like learning tricks, children may be able to fluently apply the working out of area tricks, for instance, but not working out fraction tricks. Most subject capabilities, unlike languages, tend to be topical. The problem is many of the mathematical tricks that children learn in school is they not need to regularly applied in their everyday lives outside the classroom.

If children experience a broad school curriculum, then their mathematical fluency will inevitably less than those who do not. There will always be issues of subject breadth and depth within subjects and the curriculum as a whole.

Doom and Gloom

The risk with the 'doom and gloom' view of mathematical learning is that proven practice can often be abandoned on the speculative hope that standards can be raised. This is happening in England, where the Westminister Government appears obsessed have been obsessed with Far East rote teaching methods.

The problem with learning mathematics is that it relies upon working memory. It is the capacity we possess to hold numbers in our head when we do mental arithmetic. If we try to process too many of them and, or larger numbers, then our working memory will become overloaded. All our working memory capacities are different.

Learning mathematics and second languages will always be difficult for a proportion of learners, because their working memory is limited.

The National curriculum was overloaded and too broad. Time is a factor in all learning. This has reduced the time that could be devoted to concentrating on developing the basic skills.

What is Realistically Achievable

The problem that exists in society is that mathematics is posited as a important subject to learn. Andreas Schliecher appears to be that he wants all children in the world to become highly proficient in mathematics. He cites Pisa as demonstrating what can be achieved, but insufficient attention is given to precisely determining what is important about the subject and what can realistically be achieved without curriculum distortion.

The fundamental issue is that despite the changing technologies of the world children learning potential has not significantly changed. Michael Gove claimed that he wanted to eradicate illiteracy in his life time, but there is no 'magic bullet' answer to that problem. Mathematics will always be a difficult subject to learn for many learners.

There comes a time when it must be accepted that if all efforts to improve mathematical standards have failed, then there is a need to stand back and accept it will always be a difficult subject for a portion of children to learn and apply. Cockcroft (1982) claimed that even intelligent people found mathematics difficult.

There is no doubt that there is a need for more mathematician and scientists to be created to serve the future needs of our changing society. Whether all children should and can reach the same 'set' standard of mathematical attainment is a very different issues. Cockcroft (1982) called for mathematical examinations to be created for children of lower learning potential that will give them a sense of accomplishment, as opposed to failure. A basic mathematics G.C.S.E. has been created in Wales.

The Lack of Qualified Mathematics Teachers

A significant problem in the United Kingdom is that teaching is the low status of the teaching profession. Teachers are subject to enduring implied criticism because of the standards war and the challenge of dealing with truculent children. Rarely is anything positive said about teachers. Mathematically qualified teachers are not entering the profession.

The problem with secondary mathematics is that it not only requires a secure fluent understanding of the subject to effectively teach it, but it also requires a well developed teaching skills to teach it. The two are not the same. Even mathematics graduates can find it difficult to teach mathematics.

There remains too many teachers who have not be trained to teach mathematics teaching the subject in schools. There is a similar problem in Australia. It is not surprising that children are under performing in the subject.

There is evidence that some of the most unhappiest teachers in the school system appears to be mathematics teachers. 50% of all teachers leave the profession within ten years of entering it.

Plenary

There is evidence is that the enduring concerns about mathematical standards are directly attributable to the Pisa rankings. The fact it is desirable to increase the number of mathematician's in society does not mean that there is an easy way to create this. What precisely is important about the subject is not explicit. It is not only what children achieve in maths in school at any given age that is important, but it what they retain develop from what they learnt in school.

There can will never be a simple answer to the question of developing mathematical attainment. An almighty amount of research has been devoted to researching the subject. The most basic mathematical everyday life needs are changing. Developing mathematical literacy, thinking appears to be the most important skill of all because it is enabling and adaptable.

There have been concerns about mathematical standards since 18xx. There has been vast improvement in how mathematics is taught to children in the United Kingdom, which has been designed to overcome the difficulties that working memory creates in the subject. The most of effective means of improving standards will be to fully implement Cockcroft 1982, but it must be accepted that mathematics is a very difficult subject to teach and learn.

See Quotations Cockcroft

Cockcroft Report (1982)

D, Heylock (2009)

D, Heylock (2003)

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