Monday, 4 May 2015

Should Google be allowed in public exams?

Mark Dawe of OCR
believes it is "inevitable"
that search engines
will be allowed in exams.
The head of exam board OCR sparked a controversy this week when he said it was "inevitable" that search engines, such as google, will be allowed in public exams, such as GCSEs and A-Levels.

Mark Dawe told BBC Radio 4's Today programme that allowing internet use in exam rooms would reflect the way pupils learned and how they would work in future.

He said that students would still need a basis of knowledge and that they would have limited time to conduct searches.

Regarding when these changes might be introduced, Mr Dawe said: "It's very unlikely to happen in the next few weeks or next few months, but it's certainly inevitable, I would suggest."


If you are a pupil reading this, you might be thinking that such a move would make your exams - and your revision programme - a lot easier. But would it? Clearly the exams themselves would adjust to the changes. There would be fewer questions where the answers were easily "googled". The questions would become more about how to apply the knowledge you have, rather than about how much you remember. A part of the skill set required for these new examination would be on your ability to find the relevant material on the web, how to collate this information in a sensible way and into a usable form, being able to discern between good reliable information and nonsense (of which, as you know, there is a lot on the web).

In A-Level maths, for example, it is possible to find the solution to any integral on the web. So the questions may become more about applications of integration: real world problems. Questions may become more wordy in mathematics. Problem solving skills will be required, since the candidate will need to know what form of integration is required, or even whether a question requires integration or differentiation, rather than the exam paper presenting an integral and asking the candidate for the solution. So examination writers would also have to take on an entirely new set of skills.

The Campaign for Real Education condemned the idea as "dumbing down". Their spokesman Chris McGovern said: "We have a crisis in standards in this country." He added: "You can have an exam in how to use Google - that's not the same thing as having a history exam or a geography exam.

It is important to note that when calculators were first introduced in public exams in the 1970s there was a similar furore from some parties.

What do you think? Should Google be allowed in public exams?

Friday, 16 January 2015

UCAS Expresses Doubts Over A-Level Changes

English: Entrance to UCAS The organisation whi...
UCAS - the organisation which is responsible for managing more than 2 million applications to higher education courses in the UK.  (Photo credit: Wikipedia)
UCAS, the universities admissions authority, today expressed serious reservations about the changes to the structure of A-Levels, proposed to begin this year.

UCAS, citing the results of a survey it conducted, said that schools were still undecided about which courses to offer from September, when the changes begin. In addition, it stated that some pupils may be put at a disadvantage by the changes, in particular the proposed decoupling of the A-Level from the AS.

Some universities have already expressed grave concerns about this aspect to the change. Last month we reported that Cambridge University had written to schools to ask them to continue teaching the AS, which will become optional. Amid the confusion, the changes to maths and further maths have already been delayed until 2017.

The Department for Education say that the decoupling is intended to allow students to study a subject more deeply for two years, without being distracted by exams halfway through.

Universities make offers before final grades are published. One of their objections is that, without an AS result to look at, it will be more difficult to target offers at the right candidates.

In addition, the universities will be faced with candidates presenting complex combinations of results, with the introduction of the new system being staggered over three years in the various subjects.

Many pupils benefit from the AS-Level as a staging post to the A-Level, because it provides them with a confidence boost, especially those who had not gained top results at GCSE.

UCAS warned that the confusion caused by these changes will not be over until 2020.

The chief executive of UCAS, Mary Curnock Cook, said that the picture will be complicated further by the fact that pupils from different parts of the UK will be sitting exams with the same names (A-Level, AS-Level and GCSE), but with different structures and grading procedures.

Labour has committed itself to reversing the decoupling plans, but as we reported in our previous article, any reversal would be fraught with difficulty.

Friday, 19 December 2014

Maths at the Cinema!

Turing at the time of his election to Fellowsh...
Alan Turing is played by Benedict Cumberbatch
in  The Imitation Game (Photo credit: Wikipedia)
You know how it is, you wait 10 years for a decent film about maths and then two come along at once.

Showing at the cinema at the moment are Interstellar (a Hollywood big budget sci-fi affair, starring Matthew McConaughey and Anne Hathaway) and The Imitation Game (a more thoughtful and moving account of Alan Turing's life and work, starring Benedict Cumberbatch).

In Interstellar, the crew of a spaceship search for a wormhole near Saturn in an attempt to find a planet suitable for human habitation, with planet Earth become distinctly unfriendly for humans. Interstellar takes on board some of the more remarkable aspects of relativity and deals with them in a surprising, but mathematically correct, way. Ultimately, humanity is saved by the solving of the "Gravity Problem", and it all boils down to a mathematician solving one equation, so the film loses marks on this somewhat facile point.

The Imitation Game is an excellent dramatisation of Turing's life, but does contain some quite extreme, some might say inexcusable, artistic licence. His character slips too easily into the ready cliché of being work-obsessed and unable to communicate. And the veracity of the story is dubious in places, such as Turing's being in the clutch of a Soviet spy. But if the film's appeal means that more people are made aware of his extraordinary life and work and the beautiful potential of mathematics, then its filming is a good

Sunday, 7 December 2014

Changes to A-Level Maths and Further Maths Delayed

Maths exams will become more "rigorous".
The UK Government is planning to delay the changes to A-Level mathematics and further mathematics that were to be introduced with first teaching in September 2016. The delay of one year comes amid concerns that pupils will not be sufficiently prepared for the new exam.

Following advice from the exams regulator Ofqual, teaching will now start in 2017, with the first exams for the new A-Level taking place in June 2019. Ofqual said the delay would mean that students on the new courses would have taken the new maths GCSE being introduced in 2015, and would therefore be better prepared for the new A-Level. It will also allow more time for schools to prepare for teaching the new AS- and A-Levels.

At the same time as changes in the content, the structure of A-levels is being overhauled and many schools are struggling with these planned changes. From September 2015 AS-Levels are being separated from A-Levels, which will become two-year courses, with grades decided solely by a final exam.

The changes, devised by the previous education secretary Michael Gove, are one part of a drive to make the exam system more rigorous. However, some universities have said they want schools to continue with AS-levels. Cambridge University has said that AS-Levels are vital to the university selection process and has written to schools asking them to continue with AS-levels.

Teaching unions, including the National Association of Head Teachers, have welcomed the delay, citing the extra time for schools to prepare as a key factor.

The Labour Party have said that if they come to power, they will reverse the decision to decouple the AS from the A-Level. However, the practicalities of this are fraught with difficulty, with the newly decoupled AS-Level due to be taught only 4 months after May's general election.

Tuesday, 21 October 2014

Martin Gardner, born 21 October 1914

Martin Gardner, an inspirational problem-setter and fun mathematician, was born this day 100 years ago. He died only 5 years ago and this blog celebrated his life then. Re-read the article on the life of a true 20th century great.

Thursday, 25 September 2014

e

Leonhard Euler is widely considered one of the...
Leonhard Euler is widely considered one of the greatest mathematicians. (Photo credit: Wikipedia)
In Our Time on Radio 4 introduces us to e, the irrational number that underpins so much of our modern mathematics.

e is an infinite decimal, like pi, and is approximately 2.718. It is irrational, transcendental and a part of what is often described as the most beautiful equation ever written.

Pi has been known about since the times of the ancient Greeks, but e was not discovered until the 17th century, because the mathematics required simply did not exist. The ancient Greeks' fear of the infinite was a part of the reason they did not stumble across it.

Jakob Bernoulli was the first mathematician to discover e cropping up in his studies of compound interest. A little later, John Napier invented logarithms, using a base approximately equal to 1/e. These huge tables of numbers took Napier 20 years of his life to devise and were designed to make multiplication easier and more accurate. Logarithms were later refined by Henry Briggs.

e also appears a lot in modern calculus. The function e to the power x has a gradient which always has the same value as the function itself. When Leibniz and Newton discovered calculus they used infinite sums to form the derivative of the exponential function.

Later the natural logarithm was found to be the area under the curve y=1/x.

e was named by Euler, the great mathematician of the 18th century, possibly the greatest mathematician of all time and probably the most prolific in terms of publications. But he did not, we are told, name e after himself. Instead, he thought e to be the first letter of the alphabet not widely in use in mathematics. Euler showed e was the sum of infinite series and introduced his famous Euler identity, which many mathematicians consider the most beautiful equation ever written.

To give just a few applications, e crops up in radioactive decay, in the normal distribution in statistics, and in the prime number theorem, which tells us roughly how many primes there are below any given integer.

Thursday, 21 August 2014

GCSE Results Day: Maths Results Rise

GCSE students in England, Wales and Northern Ireland have been receiving their results today. The results show that 68.8% of entries scored A*-C, up from 68.1% last summer, although there was a marked fall in English GCSE grades.

Students sitting their GCSE Maths exam.
Photo: Wikipedia.
There have been warnings of volatility in this set of results following an overhaul of the exam system. The most significant impact on this year's results has been the big fall in students taking their GCSEs a year early. Schools have been discouraged from such multiple entries following changes in the way school league tables are compiled.

Fewer fourth years taking maths GCSE meant there was a sharp improvement in maths results: the percentage achieving A* to C grades rose by 4.8 percentage points to 62.4%.

The overall pass rate was 98.5%, down 0.3 percentage points. 6.7% of entries were awarded an A* grade.

Girls are still doing better than boys at GCSE, with 73.1% of girls' entries achieving A* to C compared with 64.3% for boys.

In England, but not in Wales or Northern Ireland, this is the first year of results following moves towards exams at the end of two years, rather than including coursework and modular units. The results for GCSE English seem to have been most affected by this change, with the number of A*-C grades down 1.9% to 61.7%.

In Wales and Northern Ireland, these changes were not introduced and the three regional sets of GCSE exams are now beginning to diverge in various ways, including the subjects being taken by students.

While the government are defending the changes being made, Chris Keates of the NASUWT teaching union said this year's students had to "cope with a raft of rushed through and ill-conceived changes to the qualifications system and so today's results are especially commendable".

The National Union of Teachers' leader Christine Blower said that the headline figures "mask underlying issues which will only become clear over time".

Have you had your GCSE results today, or are you teaching GCSEs? How did your school fare following changes to the structure of GCSEs this year? Let us know at info@mathsbank.co.uk .