Hannah's Sweets

Quite a few GCSE students were stumped by a question about Hannah's sweets on yesterday's higher tier Edexcel paper.

The question was:

Hannah has 6 orange sweets and some yellow sweets.

Overall, she has n sweets. She takes one sweet from the bag and then another.

The probability of her taking 2 orange sweets is 1/3.

Prove that: 

The question is not actually that difficult if you remember how tree diagrams work.

When Hannah first takes a sweet there are 6 orange sweets out of n, so the probability of her choosing orange is 6/n.

When she chooses her second sweet there are now only 5 orange (if she chose orange the first time) out of a total of n-1 sweets.

You multiply the probabilities along the branches of a tree diagram, so

 Multiplying the 2 fractions on the left gives:

Cross-multiplying gives:

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?

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.

The GCSE is Dead - Long Live the EBacc

Michael Gove, the Education Secretary in England, has a well-known dislike for the GCSE. Yesterday, he announced plans for its abolition.

Michael Gove, Education Secretary in England
announced plans for the English Baccalaureate yesterday.

If the name English Baccalaureate rings a bell, it's because it already exists. The EBacc is currently a system used to measure the performance of schools, using the results of pupils in key subjects. Now the EBacc is to become a formal qualification.

The EBacc will be introduced for core subjects (Maths, English and Science) from 2015, with a staged introduction for other subjects. It will be based on a final exam at the end of two years' study. There will be fewer resits, no modules and no controlled assessments. All marking will be external.

There will be one exam board per EBacc subject. Exam boards will bid for the right to run an EBacc in a particular subject for a five year term.

The Liberal Democrats appear to have had a minor success by persuading the Education Secretary to drop his plans for a two-tier system, which would have been a throwback to the days of O-Levels and CSEs.

The Welsh and Northern Irish devolved governments now have a big decision to make. They may decide to follow the English lead and create new Baccalaureate exams of their own. Alternatively, they could stick with GCSEs. This approach would risk giving pupils a qualification that has been deemed to be lacking in rigour in England. One head teacher in Northern Ireland I have spoken to has already said they would consider using qualifications offered by English exam boards.