Thursday, 24 November 2016

New GCSE Grade Boundaries - my thoughts

I am going to start this blog by making the point clear, it is impossible to accurately grade pupils on the new GCSE for Maths. Completely impossible. Anyone that tells a pupil that they have achieved a particular grade is at best making an educated guess and at worst is making something up. If there is any way you can avoid giving pupils grades, making predictions of pupils eventual grades or even talking about future grades with any stakeholder then you should take the opportunity and avoid it like it is a highly contagious illness.

That said, many schools are not giving departments and heads of maths the opportunity to avoid it. There are plenty of schools out there requiring staff to predict grades for pupils (some as low as in Year 7!), or provide current working grades. Even when schools don't require this, Year 11 pupils looking at the next stage are being asked for predicted grades in English and Maths from colleges or other post-16 providers. I have been in touch with many new department heads that are struggling to answer the demands of schools, parents and pupils with regards the new GCSE grading and so this post is designed to give some support and guidance for anyone who finds themselves in this unenviable position.

You will hear people say that you cannot grade at all for the new GCSE, and I can see where they are coming from (see paragraph 1!). I do believe that it is possible to make some educated guesses about what the landscape is going to look like - we do have a reasonable amount of information to work on and one thing mathematicians are good at is building models for situations with many variables. We just have to be clear about our modelling assumptions and how that affects the accuracy of the predictions from the model. Lets start with the information Ofqual have provided:

This is probably the most viewed guide that teachers and schools have with regards the new grading. The key line in this is actually 'Students will not lost out as a result of the changes'. That means that if you have a kid in front of you that is a nailed on C for the old GCSE, they are at least a 4 on the new. Similar for A and 7, and G and 1. Of course this doesn't help with the borderline kids, but it is somewhere to start. The most updated postcard also has this information:

What this means that if you are assessing pupils (mock exams or similar), once you have set the 4 and 7 boundary, you can set the 5 and 6 boundaries arithmetically. Although it doesn't say it here, I am reliably informed (he says, waiting to be shot down!) that the same is true for grades 2 and 3; they should be set equally between 1 and 4. The upper grades can also be calculated, using the tailored approach for grade 9. The tailored approach can be summarised as:

Percentage of those achieving at least grade 7 who should be awarded grade 9 = 7% + 0.5 * (percentage of candidates awarded grade 7 or above).

By my calculations on last years figures, this will mean nationally about 15% of the pupils awarded 7+ will be in the 9+ bracket, which will end up being about 2.4% of the total cohort (based on 15.9% A* and A in 2016 translating to a broadly similar proportion for 7+). Of course if your cohort is very different to national then it shouldn't be massively far out to apply the tailored approach to your A and A* figure from last year (if you have one - I don't as this is the first year for GCSE) once you have adjusted for differences in the starting points of the cohort. This means we can have a reasonable stab at a grade 9 boundary for any mock exam we set. The grade 8 boundary should then be set halfway between 7 and 9.

Using this approach it should be reasonable to generate some grade boundaries for a mock exam by looking at kids that would definitely have secured a C, A and G on the old GCSE exams, using their scores to set grade 4, 7 and 1 boundaries respectively, and then calculating the 9 and the others using the calculations Ofqual provides.

Another approach that we (and several other groups have employed) has been to combine papers with other schools all doing the same board. This has allowed us to use proportional awards to set the 1, 4 and 7 boundaries statistically rather than through moderation - although it is still a bit unclear as to precisely what proportion will be used for the 4. This is the approach that the PiXL club among others also used, although from some points of view with varying degrees of success.

This is all well and good for individual schools and cohorts, and setting retrospective boundaries when cohorts have already done mock exams, but what can we predict about the final exams? The true answer is very little, but perhaps not absolutely nothing. Using what we know it is possible to make some predictions about the likely distribution of the grade boundaries going forward, but with a very large margin for error built in, primarily because of the very different style that the assessment has which is very hard to quantify. We do know though that the balance of difficulty will shift in both sets of papers so that 50% of the Higher tier paper will be aimed at grades 7 plus, and similarly 50% of the Foundation tier will be 4+, which is between 10 and 20% increased on the current top two grades in each paper.

We also know about the shift of material so that the Foundation tier will assess some material that is currently only Higher, and some of the material currently on Higher will no longer be assessed on Higher. Factoring all of this in we can make adjustments on current boundaries to make educated predictions at new boundaries. I will start by looking at the AQA boundaries for last year:

These are the boundaries converted to percentages for last year, and from these we can make some sensible adjustments. Given that there is now no D grade material on the Higher paper, it makes sense that the award of 3 (there is still a discretionary award of 3 similar to the current E award on the Higher) will come down towards where the E is now - around the 8 to 10% mark. The grade 4 will then have to come down as well to reflect the fact that all the D grade material is gone. With the D currently at 17.7% it is reasonable to predict that the 4 value will fall somewhere in the range of 15% to 25%. The B grade at 53.1% will also come down to nearer the current C grade - this won't translate automatically into 5 or 6, but given that B falls between 5 and 6 then 5 is likely to come in in the high 20s or low to mid 30s, with 6 likely to fall in the mid to high 30s to low 40s.

I can see these being accurate to within 10 to 15 marks at a maximum, and significantly closer in some cases (points for me if I get any of the spot on!).

A similar 'analysis' of the Edexcel boundaries yielded these results:

A big assumption here is that pupils continue to score better on Edexcel than on AQA, which by all accounts is not a good assumption to make. The tests from Ofqual suggested that pupils answered the AQA papers better than then Edexcel ones, so this second set of boundaries may well be less accurate than the others. Ultimately though, if you have nothing else you can use, and you absolutely must talk about grades etc with SLT, parents etc then this is the absolute best guess I can come up with; of course it remains to be seen how good a guess they are, so use these are your own peril as they come with precisely zero guarantees!

1. Smashed it!! Good work Pete this was my main job this weekend... Will be alot easy to set grace boundaries for the mock using your framework... PS we need to go for a curry/beer soon...

1. Glad it is of use Kaps - definitely up for a get together soon. I am seeing Graham Sparks in a couple of weeks as well; we are at the same mastery training session for NCETM on Monday and Tuesday 5th/6th December.

2. Be wary though, the boundaries listed are for the end of Year 11, may not be applicable to mocks directly. The calculations should be though - if you can set your 1, 4, and 7 boundary then you can set the others.

3. Ey ey Captain! ðŸ˜‰

4. Thanks very much for this. Is there a mistake on the last table, the one for Edexcel? There is no grade 5, and the grade 1 mark seems so much higher than for AQA...

1. Hi Dominic - the missing grade 5 was an oversight; based on current boundaries it would be about 180-ish. Also the grade 1 is in line with what it takes to get a grade G on the current Edexcel papers, but as the blog says at the minute pupils find it easier to answer the Edexcel questions than the AQA. I think this will change in the new GCSE and that Edexcel and AQA will be closer together than previously. To be honest I am prepared for the 1 boundary to be lower even than 46 if (as seems to be the case at the minute) the weakest pupils do have real trouble accessing the paper. It could well fall below 35 marks for a 1, with a knock on effect on the 2 and 3 boundary.

2. But like I say, I will be happy if I am within 10 to 15 marks of it to be honest!

5. Hello! How did you calculate a 3 on HT? I thought it was going to be 0.5(difference between 5 and 4) and then take that off a 4? This might make yours a little too lenient!? @MrGibbsMaths

6. Hi Peter, just read your post as we attempt to grade our mocks for the 'required' mock results day that we do. We're using Edexcel and I just wanted to check your table for Edexcel as the higher grade boundaries are exactly the same as the AQA higher ones, is this a copying error or did your analysis just provide same outcome.

1. Hi there, yes the current boundaries for Edexcel and AQA are very similar on Higher, which is why they came out the same. Do note though that I do say that this is based on current boundaries, which are higher on Edexcel for Foundation that AQA. I expect that to change with the new GCSE so would be wary of the Foundation boundaries for Edexcel that I have posted - I expect them to be significantly lower in the final mop up.

7. Hi Peter. Our head of maths said these were very good at the end of August. Our head of Science has asked if you can be mystic meg for Science as well? Many thanks Chris

8. I was quite please with them, particularly at the mid-range on Higher. Unfortunately I have no basis for experience in Science. The process isn't rocket science though: if they can find out what percentage of 16 year-olds score G+, C+, A+ then you can set a 1, 4 and 7 boundary. Calculate 9 using the tailored approach. Set the others in between. This will allow reasonable grade boundary set for any mock exam they run. In terms of the future, I would need a lot more information - changes to content balance in the paper, proportions of pupils at the major boundaries, the usual grade boundaries for the old papers and how variable they are etc. There is probably an experienced head of science out there that can use this information to do the same as I did for Maths though - it takes a bit of gut feeling as well.