Pisa Results: UK Could Do Better

The Programme for International Student Assessment (PISA) test on a school table in Germany (Photo credit: Wikipedia)

The UK is ranked 26th out of 65 countries in maths, in the results of the 2012 Pisa tests (Programme for International Student Assessment), which were published today.

The tests in maths, English and science were taken by 500,000 15-year old students around the world. The top 7 places are filled by far eastern countries and cities. Shanghai came top of the league table (Chinese cities are entered individually, rather than the country as a whole). The highest place gained by a European country is 8th place, for Lichtenstein. The US came even further down the league table than the UK, coming 36th in maths. Wales was the poorest performing region of the UK.

Many educationalists have criticised the league table. Prof Alan Smithers from the University of Buckingham pointed out that in many Asian countries, pupils are coached specifically for these tests.

However, Christine Blower, leader of the National Union of Teachers, said the results showed that countries with successful education systems "pay teachers well, respect the profession and encourage collaboration between teachers and schools".

Naturally, Education Secretary Michael Gove blamed the last Labour government for the UK's poor performance. For Labour, Tristram Hunt said that the coalition government's policies were taking the UK towards a poorer education system, not a better one.

What do you think about the results of the Pisa tests? Is the UK lagging behind in these key subject areas? Are the Pisa tests an accurate measure of performance?

You can take the Pisa test here.

Alfred Russel Wallace 1823-1913

Alfred Russel Wallace
(Photo credit: Wikipedia)

Alfred Russel Wallace died 100 years ago today, on 7 November, 1913.

Wallace was primarily a naturalist, but he had a curious mind and was drawn to many academic disciplines, especially controversial new ideas. In particular, Wallace was most renowned for formulating, independently of Charles Darwin, of the theory of evolution by natural selection.

Wallace was beset by financial troubles throughout his life. He did not have a wealthy family and he made some unfortunate investment decisions. In addition, he failed to secure any long-lasting salaried position and had to finance himself through the publications he produced.

Wallace's financial difficulties were further compounded by an incident involving a wager, relating to the curvature of the Earth, one of his many forays into the field of mathematics.

John Hampden, a member of the Flat Earth Society, placed an advertisement in a magazine, challenging anybody to prove that there was curvature on the surface of any body of water. He claimed that he would offer a prize of £500 to anybody who could do so. Alfred Russel Wallace, who was short of money at the time, took up the challenge.

His experiment took place along the Old Bedford River in England and it involved setting up two objects at the same height above the surface of the water. At a third point he set up a telescope. The view of the river through the telescope confirmed that the level of the water appeared to dip the further the object was from the telescope, thus confirming the curvature of the Earth.

The referee for the wager judged that Wallace had won, but Hampden refused to accept the fact. He accused Wallace of cheating, published defamatory articles and sued Wallace for return of the money. The legal cases cost Wallace a great deal of money and a huge amount of time and effort.

When he died, aged 90, The New York Times described him as "the last of the giants belonging to that wonderful group of intellectuals that included, among others, Darwin, Huxley, Spencer, Lyell, and Owen, whose daring investigations revolutionised and evolutionised the thought of the century."

GCSEs Set For 2015 Revamp

Glenys Stacey from Ofqual
(Image from TES)

This week Ofqual have released more details about the new curricula for maths and English, when the GCSEs are revamped for first teaching in the year 2015 at the insistence of Education Secretary Michael Gove. Other subjects will be given the same treatment the following year. These will be the biggest changes to GCSE since their inception in the late 1980s. Pupils now in their second year will be the first to take the new GCSE.

Glenys Stacey from Ofqual pointed out that the most important changes in the new GCSE will be the new content in each subject. In addition to this:

- There will be only one exam, which will take place at the end of the two years of study;
- Grades will be awarded from 1 to 9 (with 9 the highest). With one more grade available than in the current system, this allows for more differentiation at the top end.
- There will be less coursework in most subjects (and probably none in maths);
- There will be a complete end to modular GCSEs.

Stacey says that the new GCSE will allow pupils to gain a real confidence and competence in each subject. She also expressed confidence that these would be the last big changes to the GCSE for a significant number of years, giving more certainty and stability to the exam system for both schools and pupils.

In the maths GCSE, pupils will be expected to memorise many more formulae, such as the quadratic formula, the sine and cosine rules. Until now, these have been provided on the formula sheet.

These changes only apply to the set of GCSEs offered by the English exam boards. The exam boards in Wales and Northern Ireland are not obliged to follow suit. If the GCSE in these parts of the UK remain as they stand, the divergence from England will become significant, with the qualifications having little in common but the name.

Are you a teacher or a pupil? What do you think of the proposed changes to the maths GCSE? Let us know by email or comment on this post.

Clegg Attacks Free Schools

Nick Clegg says that free schools
should work to the national curriculum
and hire only qualified teachers.

The debate over free schools has resurfaced with the Deputy Prime Minister Nick Clegg now voicing his disapproval of the precise freedoms that they have. In particular, Clegg argues that they should not be allowed to recruit teaching staff who do not have a recognised teaching qualification. Additionally, he feels that these schools should be obliged to follow the national curriculum.

His comments come shortly after several controversial incidents at free schools. These include the now infamous Al-Madinah school in Derby, whose lessons were often failing to meet the requirements, according to a recent Ofsted report.

The Conservative part of the coalition government disagrees. It maintains that free schools have been outperforming schools in the mainstream state sector, and will continue to, simply because of the new freedoms they have been given. Education minister Liz Truss says that in the private school sector, appointments of non-qualified teachers has been the norm for "hundreds of years".

It is still early days for free schools. Some critics have gone further than Nick Clegg and suggested that academies and free schools are both stepping stones on the road to privatising education. Teaching unions have also voiced scepticism, suggesting that the government is trying to water down the status of professional teachers and discredit the teaching qualification.

Clearly it is possible for a school to use any freedoms in a positive and constructive way. On the other hand, without good leadership, a school that does not have the structure imposed by a national curriculum and the requirement to employ only qualified teachers, could find itself floundering, as has been shown.

What do you think about free schools? Let us know with your emails or comments.

Post-16 Education Revolution Begins Here

Teenagers in England will have to stay at school or in training longer from today. The "participation age" has risen from 16 to 17, although in the rest of the UK, it will remain at 16. From 2015 this rises again to 18.

However, unlike previous increases in the school leaving age, it does not mean that teenagers will have to remain in school. As an alternative, they could enter some form of work that includes an element of training, such as an apprenticeship.

This change has been introduced on the same day that pupils who do not get a grade C or higher in GCSE maths will be required to continue studying the subject during their subsequent schooling.

Schools and teaching unions are already talking about the increased pressure on already-stretched teaching staff and/or the need to employ more staff.

The government says that employers are complaining about a lack of basic numeracy and literacy skills among those applying for their first jobs and this has motivated both changes. However, there will not be sanctions imposed on any teenagers who fail to get some kind of training. The government says that the changes are aimed at increasing educational standards, not about introducing penalties. In reality, the new law would be difficult to enforce: how do you prove whether or not an employer is providing adequate training for a young employee.

Let us know what you think about these two changes. Will they provide valuable skills to those who have missed out in previous years? Or is this just another unnecessary change brought in by a tinkering education secretary?

GCSE Results Fall Again

"Methody" Methodist College Belfast. Once again, Northern Ireland pupils obtained better results than their counterparts in England and Wales. (Photo credit: Wikipedia)

The GCSE results for 600,000 teenagers in England, Wales and Northern Ireland, released today by the Joint Council for Qualifications (JCQ), show a small, but significant drop in the number of A*-C passes.

Grades have fallen for the second year in a row with 68.1% of exam entries being graded between an A* and a C - a fall of about 1.3% on last year. In maths, the fall was 0.8 percentage points from 58.8% to 58%.

The overall proportion getting the top grades A* or A fell from 22.4% to 21.3%. And the overall pass rate also fell marginally, for the first time since the GCSE exam was introduced 25 years ago.

One factor that may have contributed to the drop in grades is the increasing trend for schools to enter pupils for certain GCSEs - particularly maths and English - one or even two years early. The JCQ have criticised this approach, claiming that pupils are missing out on the chance to gain better grades - and on the extra years of learning.

In addition, there is a trend for pupils to be entered for more than one exam in the same subject, whether it be for different boards or different tiers. There has also been a marked increase in the number of pupils taking the IGCSE, as well as the traditional GCSE. In these ways pupils can take the best result, but the overall statistics are skewed downwards.

Critics say that these trends are a result of schools chasing places in league tables, including the new English Baccalaureate, which rates schools on the number of pupils getting good GCSEs in a range of core subjects.

There was a big fall in pupils getting top grades in the science subjects, following the introduction of new syllabuses and exams.

Brian Lightman, head of the Association of School and College Leaders, said that schools, students and teachers are working hard in a constantly changing and turbulent environment. He also pointed out that piecemeal changes to the exam system make it impossible to compare grades from one year to the next.

Last year the grading of the English GCSE resulted in a legal challenge by some schools, when the grading standards were deemed to have changed between the January and June exams.

Only in Northern Ireland was there a rise in grades. A total of 28% of entries were graded A or A*, compared with 21.2% in England.

With the modular system soon to be scrapped in England, Northern Ireland still has to decide whether or not to continue with modules, or follow England's lead with a single end-of-course exam. Wales has already decided to continue with a modular system for GCSEs.

A-Level Results Show Slight Fall in Top Grades

More than 300,000 A-Level students in England, Wales and Northern Ireland have found out their A-level and AS results today, and join the scramble for university places.

The results, published by the Joint Council for Qualifications (JCQ), show that there has been a fall in the proportion of A-levels awarded top grades for the second year in a row, after three decades of steady increases. 26.3% of all entries were given A or A* grades this year, a slight fall from 26.6% in 2012. Previously, the proportion getting top grades had risen each year since 1980.

The national pass rate rose marginally to 98.1%. This has also risen for about 30 years.

Continuing recent trends, more students are taking A-levels in maths and science and there is a continued fall in those taking languages. Maths rose by just under 3% and further maths by 4.5%.

Girls are still ahead of boys when looking at the top grades, A or A* (26.7% for girls compared with 25.9% for boys), but boys this year were more likely to get the A* grade (7.9% of boys' entries, compared with 7.4% for girls).

The university admissions body Ucas has said that 385,910 students have already been accepted by UK universities, 31,600 more than at the same point last year.

The UK government claims its reforms to make it easier for universities to take on the students that they want to recruit have sped up the process of accepting students. Under these changes, universities in England are being allowed to admit as many top-performing students (gaining ABB or more) as they want to. For students with lower results, universities are allocated a quota of undergraduates they can recruit. Last year, thousands of course places were left unfilled.

The change was introduced to allow the most popular universities to expand. It came in alongside higher tuition fees, which rose to a maximum of £9,000 a year from autumn 2012.

Students in Northern Ireland continue to perform best. 83.5% of entries here scored between an A* and a C and 30.7% were awarded the top grades of A or A*. In Wales, these figures are 75.2% and 22.9% respectively and in England 77% and 26.3%.

From 2015 the government plans to introduced major changes to A-levels. The AS-level will no longer count towards the final A-level grade and, with modules being phased out, all exams will be taken at the end of the two year course.

Congratulations to all those who gained the grades they were looking for today - and best of luck to everybody looking for a university place.

Happy Birthday Andrew Wiles

Happy 60th birthday Andrew Wiles, eminent British mathematician, most famous for his proof of Fermat's Last Theorem.

Andrew Wiles. Image courtesy of Wikipedia.

In the summer of 1986, based on the progress made by fellow mathematicians, Andrew Wiles realised that a proof of a limited form of something known as the modularity theorem might then be in reach, which would be a crucial step to a proof of Fermat's Last Theorem. In secrecy, Wiles dedicated all of his research time to this problem. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. In August that year, it turned out that the proof contained a gap. Wiles tried to fill in this gap, but found out that the error he had made was significant. The key idea for circumventing this problem came to Wiles on 19 September 1994. Together with his former student Richard Taylor, he published a second paper explaining this work-around and in doing so, the proof was complete. Both papers were published in 1995 in a special volume of the Annals of Mathematics.

Fermat's Last Theorem had thwarted and tantalized mathematicians for 350 years. Hundreds of attempts had been made at its proof, both by professionals and amateurs. Until its proof, it was probably the most famous unproven result in all of mathematics. When Fermat published his conjecture, that

has no integer solutions for n>2, he also wrote in the margin of his book that he had discovered a truly remarkable proof, but that he did not have enough space to write this proof down. We still do not know what was going through Fermat's mind at this point, but it is likely his proof was flawed. One thing is certain: it was not the same as Wiles's proof, which relies on an enormous amount of twentieth century mathematics that Fermat had no access to.

Paul Erdös 26 Mar 1913 - 20 Sep 1996

Happy birthday to Paul Erdös, who would have been 100 today if he were still with us.

This Hungarian mathematician, was one of the 20th century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. He loved to set problems for others to solve and would often offer cash prizes as rewards for correct solutions to the problems. These rewards ranged from $5 to $10,000 depending on how difficult he judged them to be.

At age 20, Erdös discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and later moved to the USA. His Jewish origins made a return to Hungary impossible. However, he was affected by McCarthyism in the 1950s and he spent much of the next ten years in Israel.

Having written many hundreds of papers Erdös became history's most prolific mathematician. He wrote over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927.

Pi Day Live

Thursday is the annual Pi Day (because Americans would write the date 3.14).


This year, Marcus du Sautoy is hosting Pi Day Live. It's a free interactive online event that is open to all.

The number pi has intrigued mathematicians throughout the ages and this fascination has shown no sign of stopping. In recent times mathematicians have employed super-computers to calculate pi to over a trillion decimal places.

In Pi Day Live, Marcus du Sautoy will be asking whether the techniques used by the ancients to calculate pi can still be used today. And if so, which ones are best? As a part of the interactive audience, you will be a part of answering these questions and more.

To take part, visit the event's online lecture theatre, or go to the event's big screen to watch online. All you need is access to YouTube to get involved.

Brightest Shine Less Brightly At 16

Institute of Education (Photo credit: Wikipedia)

A new study has highlighted the differences in mathematical ability between the children of different countries at different ages. According to researchers at the Institute of Education in London, England's brightest primary school pupils are on a par, mathematically, with the those from Taiwan and Hong Kong. But by the time pupils reach 16, the comparative performance achieved by the top 10% falls. Overall the English pupils came 28th out of 65 countries at this age.

When looking at the average scores of the entire cohort, the pupils from east Asia performed better than those from England at all ages, but the gap didn't widen as the pupils became older.

What is going on here? There is no doubt it is disappointing, but what or who is to blame?

a) The curriculum? Is the curriculum too narrow at secondary school? There is no doubt that the very brightest pupils in UK schools will absorb everything they are taught. So are we simply not teaching enough? Do the top 10% need extra challenges?

b) The teaching? There is a long-standing debate over whether, as a society, we value the work of teachers enough. Would increasing the average pay of teachers encourage better, more inspirational teachers into the classroom? Would this really make a difference in educational standards?

c) The culture? Is there enough of a culture of learning in our schools? Are there schools in which pupils learn little or nothing mathematically? Are there schools in which the poor performance and behaviour of a section of the cohort is adversely affecting the chances for the brightest to progress?

d) The basics? Interestingly, the Institute's report's recommendations suggest taking a new look at the way mathematics is taught in our primary schools, despite the brightest pupils apparently being close to the top of the world rankings at this age. Are we failing to build the foundations of a successful mathematics education with our primary education?

We would be very interested to hear your view. Email info@mathsbank.co.uk .

Is Gove's GCSE U-Turn Enough?

Another week, another controversy in the Department for Education.

After criticism from teaching unions, academics and fellow MPs, Michael Gove has withdrawn his plans to replace the GCSE with English Baccalaureate certificates in key subjects from 2015. The Commons Education committee had said that Mr Gove had been trying to implement "too much too soon". In his Commons speech reversing his plans, Gove did, however, say that he has asked Ofqual to ensure new GCSEs would be in place by 2015 in seven subject areas: English, maths, the sciences, history and geography. GCSEs for all remaining subjects would be reformed by the following year.

Now, the head of England's exam regulator Ofqual has warned that these changes may be too rapid. Glenys Stacey has replied to Mr Gove, saying that she will delay the education secretary's GCSE changes if there are problems with the timetable. She continued "The timetable for qualifications development that you have set out is challenging." She expressed concerns about maintaining the quality of qualifications if drafting new curricula within such a short timeframe and pointed out that she would be conducting her own consultation with the exam boards.

Other criticism has come from the head of the Mathematical Association, Peter Ransom. He pointed out that "The 2015 schedule for implementation is so ambitious that no time will be available for piloting, reflection and refinement."

Dr Kevin Stannard from the Girls' Day School Trust expressed concerns that many aspects of Michael Gove's Baccalaureate plans may still be pushed through in the GCSE reform "on the mistaken assumption that the DfE has done a U-turn."

The Department for Education maintains that it will act quickly in order to address a loss of rigour in GCSEs.

All of this comes on top of stories about bullying by Michael Gove's special advisers and controversial plans for the privatisation of academies.

Gove Lays Out Plans to Overhaul A-Levels

Michael Gove plans to reform A-Levels
and scrap GCSEs. Photo: commons.wikimedia.org

Education Secretary Michael Gove today lays out his long-awaited plans to overhaul the A-Level system in England.

He says that his ideas will make A-Levels more rigorous and reduce the number of exams taken.

The major changes under Gove's reforms will be these:
- AS levels will no longer count towards a full A-level but will become stand-alone qualifications;
- It will no longer be possible to take individual modules; the course will be examined with one final examination;
- There will be a bigger role for universities in monitoring the content of each A-level.

Mr Gove has outlined his plans in a letter to the examination regulator Ofqual. He says A-levels do not provide the solid foundation students need. Mr Gove claims that pupils spend too much time sitting examinations and too little time thinking deeply about their subject. He has previously described the modular system as comprising "bite-sized" units of learning.

The Russell Group of top universities will have a role in supervising the content of A-levels, ensuring they are sufficiently challenging. This is a compromise position that the universities are happy with; Mr Gove had previously consulted with the universities about their being involved in setting the exams.

The new structure will be introduced in England from 2015. Labour's education secretary Stephen Twigg has already accused Mr Gove of "turning the clock back" and narrowing people's options.

Teaching unions have also been quick to express their doubts. Brian Lightman, general secretary of the Association of School and College Leaders (ASCL), said his union was "not convinced" that AS-levels should be separated in this way.

AS-levels, as a stepping-stone qualification to an A-Level, were introduced by the last Labour government under reforms known as Curriculum 2000. The new proposals effectively move the A-level system back to where it was before Curriculum 2000.

Mr Gove's reform of A-Levels come alongside his plans to scrap GCSEs and replace them with English Baccalaureate Certificates (EBCs) from 2015.

As with GCSEs, Northern Ireland and Wales will have to decide whether to stick with their existing A-Level structures, or to follow the new model to be introduced in England. Scotland's schools do not use A-Levels at all.