The draft maths A Level- initial thoughts

So the drafts of the new Maths and Further Maths A-Level courses have been released and the Department of Education and Ofqual are in a consultation period. (You can download the drafts and find more details on the consultation on it here.)I am left pondering the rationale behind the summer holidays consultation periods that the department seem so fond of, you could say it is an attempt to reduce consultation as most involved with education are on holiday and not thinking about work. Or you could say it was to give those same people more time to consider it. I think it will probably reduce the amount of responses.

I have had a quick read over both drafts, and wanted to make a few initial remarks here. I will be spending some further time on these and putting together a fuller response to them as part if the consultation, which I will also publish here.

A Level Maths

The overview

The big change is, of course, the switch from a modular to a linear course. This has also been coupled with a,switch to a course that us 100% prescribed. I think that a linear model may be better than a modular model, but I did like the choice element offered previously. Students with no interest in physics who want to study psychology or biology etc don’t necessarily need mechanics, and would benefit from doing a course that is more stats heavy. Likewise, a student who wants to go into physics would benefit from a heavier mechanics load in their qualification.

Overarching Themes

These seem to be fairly similar. There is a bigger focus of set theory, which I feel us good. I was disappointed not to see more of this on the reformed GCSE. There appears to be a bigger emphasis on proof, it mentions contradiction, exhaustion, deduction, but no specific mention of induction. A stronger emphasis on this can only be good.

This section also alludes to a bigger emphasis on problem solving and modelling, which is one of the main applications of mathematics, so more focus here can’t hurt either.

The Content

This seems to be what you might expect. It covers the majority of the current core modules, a fair bit of mechanics 1 (and higher) and stats 1 (plus the binomial distribution, which appears on stats 2 for some boards.)

There is more mention to modelling throughout, and it looks as though they have brought linear programming into the algebra section, which also includes a bit around looking at transformations of the normal curve. The rest of the curriculum which pertains to the current core modules is very similar. Solids of revolution have gone, and been replaced by newton-raphson, but that seems to be it.

The stats has lost some if the nonsense involved currently (an end to stem and leaf! Hurrah!) and is more focused on the important bits, like probability theory and the two big distributions (Normal and Binomial).

The mechanics section looks exciting. It is based around forces and kinematics (of course) but is more advanced than the current m1, incorporating the calculus that doesn’t come into the current mechanics course til m2/3.

What should have been there?

There is no mention of graph theory, the best part of the current D1 module. I think that’s a real shame as it is newer than the majority of the syllabus and is vastly different to what students have learned before now. I know that universities were keen for this to be on there.

Something else the unis wanted to see on the a level was an intro to Matrices and Complex Numbers. These are two topics important in many courses (engineering, computing, etc) and they have to be taught at the start of such courses, so I was expecting to see these, and would have liked to see them too.

Further Maths

Unlike the Maths course, this one includes an element of choice, kept up to the exam boards. There is core content listed but this only accounts for 50% of the course. This gives the boards an opportunity to diverge. Surely we will see graph theory here, and hopefully game theory, knot theory, perhaps caos theory?! Will any be brave enough to include quaternions?! There could be massively different courses between boards, or they could all go with the same, safe choices.

Core Content

The core content is drawn from the current FP1-3 modules, (plus volumes of revolution from the current core.)

It looks to have a good basis, covering complex numbers, matrices, hyperbolic functions, polar coordinates (Grrr) and builds on the topics from the Maths Alevel such as calculus, vectors and differential equations.

Conclusion

I was expecting a massive change to the curriculum. When the review finished for the other subjects we were told maths would be released later as it needed the mist significant changes. But the changes to the curriculum are not massive. The majority of the core maths is still there and the major bits of stats and mechanics are there. The most significant change is the switch to a 100% prescribed curriculum, something I can see arguments for and against.

Similarly, the further maths core content is the same as it currently is. The 50% left to exam boards could be the same as we have now, or could be radically different, depending on the courage of the exam boards. We won’t have a solid answer until they release their materials.

If you are involved with teaching maths, or are a mathematical researcher, or based in any job or uni department that depends on maths, do have a read and respond to the consultation. It closes mid September. I’d also love to hear your views