## Maths and Numeracy GCSEs

A while ago I read this piece from @bigkid4 about his vision for the future of maths exams. It’s a great piece, with plenty of food for thought, and I’ve thought a lot about it since. Then the other day I was listening to Colin Beveridge (@icecolbeveridge) and Dave Gale (@reflectivemaths) chatting on their podcast “Wrong But Useful“, about the need (or lack of) for all pupils to study maths to GCSE level. Colin suggested a similar idea to @Bigkid4’s blogpost, which was to split the subject into two qualifications. A “Numeracy” one and a “Maths” one, making the Numeracy compulsory and the Maths optional. (nb I have no idea is Colin read this blogpost, but I know it’s an idea I, and others, had had prior to reading it. Great minds and all that…)

Colin and Dave had a long chat about this on the podcast (which was excellent as always- if you aren’t a listener, but like maths, then become one! You won’t regret it!). They postulated that the numeracy qualification was perhaps not big enough to be equivalent to a GCSE and they had a few nice ideas about what could be on it.

That got me thinking, *if we did split it, what should go where? And could the numeracy alone be a GCSE?*

I think that we could create a stand alone GCSE, but I would call it “Numeracy and Problem Solving”, I would keep the subjects together until KS4, ensuring a basic grounding in each. I would like to see plenty of number on the NPS syllabus, including Fractions, Decimals and Percentages. Certainly things like interest, compound interest etc are paramount in a world of unscrupulous bankers and payday loan sharks. I would like a massive part of it to be around estimation and checking (and, of course, rounding!) include a focus on the all too often missing “common sense“! I would have some basic probability on it to ensure pupils know how daft some gambling is. I would like to see some modelling on there too, as I feel that is a neglected skill at KS4, and one that is extremely important. There would be a large focus on problem solving, and I think it would be imperative to include a bit of basic RAT Trig (Right Angled Triangle Trigonometry. I would say “and Pythagoras’s Theorem”, but that would anger Colin, so I will say “including Pythagoras’s Theorem,” instead). I guess it might seem strange at first, but I know that it’s a skill joiners use, and others in trades that pupils who I know wouldn’t choose maths have ideas to go into.

I also think that charts etc should go here (although boxplots, stem and leaf and any of the other nonsensical ones should be scrapped and forgotten about forever, along with transformations by hand!)

That would leave maths. The higher number stuff would be here (prime factorising, etc). The majority of GCSE algebra would be there too, and some a level stuff too (I’d forget about the GCSE nth term stuff, and go straight to the A level stuff!) I’d like an introduction to calculus and an introduction to topology. Some higher probability stuff, and a good basis to build A Level stats on (variance etc). Perhaps and introduction to matrices and complex numbers too!

I think there are many positives about these ideas, but I would worry about the take up of maths GCSE, and the potential damage that could do to maths A Level and undergraduate take up further down the line.

If you have anything to add, please comment, and if you have any links to other blogs etc around these ideas, I’d love to have them too.

This is exactly what is happening in Wales. From 2015 there will be 2 maths qualifications, Maths and Numeracy. The numeracy qualification will count in the level 2 inclusive. The finer details are still being thrashed out but we are looking at sitting numeracy in Year 10 and then if successful Maths in year 11. In theory this exam build on the literacy numeracy framework which is now statutory in Wales.

Damian

Fascinating! I had no idea. I shall watch with interest to see how it unfolds! Please do tweet, or comment on here, if anything is announced that I may miss.

Reblogged this on The Echo Chamber.

When I were a lad back in 1970s Scotland we had ‘O’ Level Arithmetic (the only Arithmetic exam). It was pretty basic stuff.

Mathematics was a separate exam entirely and of course that could be taken from O level to Higher.

I understand that since then some genius changed all that in the name of progress. That might explain why my pupils can’t count e.g.

Me “what is 1 1/2 times 4?”

Them: “8″

Me “But 2 times 4 is 8, isn’t it ?”

Them: go into a huddle. Eventually agree that 2 times 4 is 8.

Me: “so 1 1/2 times 4 can’t be 8 then, can it?”

Eventually one says “why not?”

They were a group of 2 boys and 2 girls, all aged 14 to 15.

I imagine every dodgy salesman and loan shark will be rubbing their hands with glee.

That certainly is worrying, and I agree dodgy salesman, and loan sharks and worse, will be rubbing their hands.

This is what happened when my mum was at school in the 1950′s. It was arithmetic for all and Maths for the numerically talented.

Interesting, although I feel more than arithmetic should be in the numeracy one, I do think basic arithmetic is lacking in a lot if young people.

In my opinion I don’t agree with this idea. This will vary across regions and schools, but basic numeracy skills should be just that, basic, and assume you’ve been learning about them since primary until you enter KS4 and GCSE level where new concepts are introduced. There simply isn’t enough content for a standalone GCSE anyway, so it just seems illogical.

However, you could possibly create a double award, and still make both aspects/areas of mathematics compulsory. As algebraic skills along with geometry are essential for problem solving, the ability to comprehend parameters, constants and variables. Basic intro to calculus, matrices aand determinents is a good idea too. Too steep of learning curve from GCSE to A-level, and does lead to a lot of students getting lost and almost giving up

In my opinion, anyone willing to learn can study mathematics, all aspects of it. It’s a beautiful and elegant language, and as a physicist I appreciate it everyday.

I agree that anyone can, but I’m not sure everyone should be forced to it. I think there could be a full GCSE, but if not, how about a separate numeracy qualification?

I also take your point on the fact that basic skills should be embedded by KS4, but all too often they are not, especially with the lower attainers. I think the spiral nature in which maths is taught maybe to blame here, I am leaning towards thinking a mastery curriculum would be better( https://cavmaths.wordpress.com/2013/12/07/manglish-and-a-mastery-curriculum/)

As I say, I’m not sure this is the best proposal, just some thoughts I have. I agree Maths is beautiful and elegant and I too appreciate it every day!

The standards in GCSE Maths have been falling year on year, something needs to be done quickly