10/06/2015 07:08 BST | Updated 10/06/2016 06:59 BST

Making Maths Count in the UK

Last week's furore with one of the maths GCSE papers raised some interesting points. There were a number of difficult questions including the now infamous one referred to as the Hannah's sweets question..

Last week's furore with one of the maths GCSE papers raised some interesting points.

There were a number of difficult questions including the now infamous one referred to as the Hannah's sweets question:

"There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0."

The solution is within the ability of an A* student but the topic, probability, should be one that even average students would attempt. By combining the creation of a quadratic equation with probability, only the very best students are likely to have obtained the correct answer.

To really understand why the level of anger directed at edexcel, the exam board, was so high, it is important to know the grade boundaries for this exam. In June 2014, a score of just 26% resulted in a passing C grade, with 44% being enough for a B grade and 62% for an A grade. Even an A* only required a mark of 80%. With an average student obtaining less than half marks, it is hardly surprising that this question went viral on twitter.

What is really concerning is that questions like this may well become the norm in two years' time. The Department of Education's "Mathematics: GCSE subject content and assessment objectives" document, released in 2013, outlined the changes that must be made to the GCSE maths syllabus for students being examined from June 2017 onwards. It is the sample exam papers created by three of the exam boards that have come under fire recently for being too difficult. The Office for Qualifications and Examinations Regulation (Ofqual) stated that while the higher papers would stretch the most able students, "OCR, Pearson and WJEC Eduqas need to refine their higher and foundation tier papers to sufficiently differentiate across student abilities." In other words, the proposed exams are too difficult for the average student.

As part of its conclusion, Ofqual also stated that the boards' higher papers "compare well with papers from a range of already high-performing countries." Which countries is it referring to? Top of the list in the Programme for International Assessment (Pisa) results from 2012 were Shanghai-China, Singapore, Hong Kong-China, Taiwan, Korea, Macau-China and Japan. Where was the UK? Down in 26th for maths. Given this, it might be seen as being fair to aspire to the levels of some countries in the Far East. But is this reasonable? How do the educational cultures compare?

Take a look at education in Singapore. Figures published in 2005 showed that 63 per cent of those aged over 15 who were no longer students had achieved nothing better than a primary school education. What steps has Singapore taken to improve this situation? Around a quarter of all public spending goes on education, more than double that of the UK. Training drives for new staff have resulted in many classes having two teachers, and all new staff receive continuous personal training and development from senior teachers.

In English primary schools, teachers only need a C grade at GCSE to teach maths; in Japan, most teachers at the same level have a maths degree.

Making exams more difficult will not raise the quality of secondary education in the UK. Proper investment in specialist teachers in primary school and better qualified teachers in secondary schools would be a start. And when a quarter of all UK secondary school maths teachers do not have a maths degree, is it any wonder that our students are poorly taught and ill-prepared for their maths exams?