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In June 2017, students in England sat the new 9-1 maths GCSE papers for the first time. The change was more than a simple altering of grades from the previous A* – G to 9 – 1. Many topics were moved from AS-level maths into the Higher level GCSE syllabus with a similar dropping down of over 15 topics from Higher level to Foundation level. For example, a barely numerate student struggling with Foundation level now had to tackle the likes of trigonometry, factorising quadratic expressions, vectors and simultaneous equations to name but a few.

The drive for harder exams was fuelled in no small part by the UK’s poor showing in the Program for International Student Assessment (PISA) tables. These provide education rankings based on international tests taken by 15-year-olds in maths, reading and science. In 2013, the UK ranked 26th in maths. Education Secretary Michael Gove said that since the 1990s, test performances had been “at best stagnant, at worst declining” and promised reforms.

Even though the exam boards made resources available for teachers and schools, it became clear early on that there were problems. The Sample Assessment Material created by three of the exam boards was found to be so difficult by the maths regulator, Ofqual, in 2015 that each had to issue new, easier sets. “They fail to differentiate effectively across the full range of ability. This is due to the assessments being too difficult,” Ofqual concluded.

Then there was the confusion as to what a pass grade would be. Grade 4 was referred to as a ‘standard pass’ and grade 5, a ‘strong pass’ by the then education secretary, Justine Greening. Ofsted, the school inspectors, stated that schools would be measured on their number of GCSE passes at grade 5 or above. So is a grade 4 really a pass? Schools accept a grade 4 as a pass that allows students to move on to A-level subjects; universities also stated that a grade 4 will be accepted as a pass.

When the first set of results came out in August 2017, students needed a mark of just 17% to achieve a grade 4 pass at Higher level. A grade 7, which Ofqual aligned with an old-style A grade and most schools had intended to use as a benchmark for progression to A-level, was just 51%. To achieve a maths GCSE grade A the previous year required a mark of 70%.

This begs two questions:
• In what measure in a developed country can 17% ever be acceptable as a pass mark?
• How can students who effectively failed half the questions on the papers possibly progress to A-level?

At the top end, where a grade 9 was given to just three per cent of students, the grade boundary was 79%. Only three per cent of students achieved over 80% in these new exams – yet both Ofqual and the exam boards stated they were satisfied with this state of affairs. Really?

In the November 2017 exams, the grade boundaries fell even further: 13% for a Higher level grade 4 and 47% for a grade 7. Given that these could only be sat by those who had taken the June exam, the decrease in grade boundaries was hardly surprising.

The Foundation level maths course is intended for those who find maths challenging. But given that maths heads of departments in schools are under pressure to deliver pass grades, it is going to take a very brave person to sit any students for Foundation level when a Higher level pass requires such a low mark and obtaining a grade 4 at Foundation level requires a mark approaching 50%. The fact that Foundation students will be getting the vast majority of each homework, test and exam wrong is a soul-destroying situation yet that is what will be happening. The educational wellbeing of students no longer comes first.

How did we get here? The green-eyed envy of PISA achievements by countries in the far east has led to an untenable new education system. In Japan, teaching maths in primary school requires a maths degree; in the UK, it’s a GCSE pass in maths – and that’s the real problem. Maths needs to be taught by specialists in primary schools (rather than the current situation where a single maths specialist acts as an authority on the subject within a school) to bring up the general level of numeracy before transfer to secondary school. Reasoning and problem-solving skills, cornerstones of the new 9 – 1 maths syllabus, also need to be developed.

A 2011 government report stated that 26.6 per cent of secondary school maths teachers did not have a maths degree. While having such a qualification doesn’t necessarily make for a good teacher, it does give the required depth of knowledge. Honing teaching skills can be done through continued professional development.

Just for a moment, fast forward five years. The student who ‘passed’ maths with 17% last June has taken A-levels in, say, philosophy, sociology and politics, obtaining good enough grades to go to university. Towards the end of their course, they decide to become a primary school teacher and do a PGCE (where 99% of those completing the course pass). Next stop: teaching maths to a primary school class of students. And we think the situation can’t get any worse? It really is an absolute farce.

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The recent 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?

Originally published in The Huffington Post
http://www.huffingtonpost.co.uk/vic-lennard/making-maths-count-in-the_b_7550528.html

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When I started teaching, classrooms still contained blackboards and chalk and the personal computer hadn’t been invented. When I stopped some 10 years later, technology had stretched to whiteboards, wipeable markers and the BBC B.

On returning to teaching as a private maths tutor I spent a day in a local secondary school to see how technology was being used. Interactive whiteboards and their linking with in-class computers makes the teaching environment a lot better than in the late 1970s. Lesson preparation is much easier – no more creating purple Banda masters and duplicating using a mixture of isopropanol and methanol, though the smell was quite enticing!

If there is one part of technology that has made a really big difference it has to be the internet and online teaching resources. Sites like BBC’s GCSE Bitesize are brilliant for students while tried-&-tested lessons from the likes of the TES (Times Educational Supplement) site can save hours in planning.

On the homework front, a number of websites offer comprehensive packages to which many schools subscribe. A good example is MyMaths (www.mymaths.co.uk). For less than £600 per year a secondary school gets a huge interactive resource covering National Curriculum level 2 through to A-level. Unlimited access for all students and teachers, online homework tasks, an assessment manager and booster packs are just some of the advantages.

So what could be wrong with the scenario of personalised homework for all students? From the teacher’s perspective, not much. Cuts down on setting homework, taking in exercise books and handling marking. But there is a huge downside.

Anyone who has marked GCSE papers or worked with the marking schemes that are made available will appreciate that most marks are given for showing the correct methods and working out. In fact it’s possible to get a grade A without having a single correct answer! How? If small mistakes are made, the answer would be wrong (which usually loses one mark) but all method and working out marks would be obtained – and that’s the lion’s share of the marks. How do you show method and working out with online resources such as MyMaths? You can’t. So how do students get used to showing methods and working out? They don’t.

Technology is a brilliant helper but the problems start once you become a slave to it. MyMaths has its place in maths teaching but from what I’ve seen, too many teachers are using it instead of setting proper homework. This might be expedient and provide a short-term answer but until GCSE exams are taken online too, such a lazy approach will adversely affect students’ grades – especially those on the margins of passing.

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As someone who taught maths for 10 years in the 1980s and has recently come back to maths tutoring, a look at the syllabus from Edexcel, the main examining board, shows that little has changed.

Most of my years 10 and 11 students are studying for Edexcel GCSE with a few sitting for the IGCSE version. IGCSE? That’s International GCSE. Available in more than 100 countries, it doesn’t have to adhere to the national curriculum. For example, there is no compulsory study of Shakespeare in English. Perhaps this is part of the reason why in 2006 the Qualifications and Curriculum Authority, which assesses the strength of various qualifications, deemed that IGCSE was “not suitable for assessing what pupils in England learn.” State school pupils do not sit IGCSE exams because the government has not approved them for state school funding.

The real value for IGCSE in maths is that it prepares brighter students for their AS-level studies by including extra topics such as calculus, set theory and functions.

Sounds reasonable – until you realise that a local non-state school will only allow students to take the higher level of IGCSE maths with grades from A* down to E. The easier foundation level, with grades from C to G, is not offered.

One of my students at this school mentioned the higher level pass mark for a grade C. I thought they had made a mistake. When a second pupil made a similar comment and that their teacher had quoted this figure, I decided to investigate.

So, what do you need for a grade C?

Twenty-four per cent. Yes, you read correctly – 24%. In any other walk of life such a figure would be viewed as an abject failure but not, it appears, for Edexcel’s maths IGCSE. It’s easy to confirm this as all subject boundary marks are freely available on Edexcel’s website. Just 42% obtains a grade B, 61% a grade A and 80% a grade A*. More scary, a grade D, viewed as barely a fail, can be obtained with just 12%!

Thinking that this might be an IGCSE issue, I also checked the standard GCSE maths grade boundaries. Over the past five years, the highest mark required for a grade C at higher level was 28%; last November a student would only have needed 23%. The anomaly appears to be confined almost solely to maths GCSE.

On checking with Edexcel I was informed that the low mark was due to the discontinuation of the modular exam. As this had been taken at three sittings and the current exam is at one sitting, the lower mark boundaries reflected this and is unlikely to change in the near future.

The real question is: why are schools forcing weak pupils to sit higher level not foundation level? There’s only one answer: to maintain academic results. It’s easier to get 24% at higher level than the 67-70% required for a grade C at foundation level. Does it benefit the students? Certainly not. It’s questionable whether 24% shows even a basic level of numeracy.

The end result will be that in the future, all employers will need to give prospective employees a comprehensive numeracy test…

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