As I write, the first GCSE maths exam is just two weeks away. Pupils up and down the land are juggling extra revision time with lesson time and enough free/social time to keep their sanity.
Some are doing this better than others.
What can we do with our lesson time to help put the finishing touches on the culmination of 11 years' worth of schooling?
Quick read: What are the most effective GCSE revision techniques?
Quick listen: How to give pupils a deeper understanding of maths
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Questions in the GCSE maths exam broadly fall into one of three categories:
1. Things that pupils have to know.
2. Things that pupils have to be able to do.
3. Things that pupils have to be able to work through.
Each of these requires a different approach to supported revision, and needs attention in how we support pupils in planning revision.
1. Things that GCSE pupils have to know
Essentially: key words, formulae and conventions.
Knowledge like “bearings are measured clockwise” or “the formula for the volume of a pyramid is ⅓ × base area × height” are all things that pupils need to be able to walk into a GCSE exam and be able to recall at any point to support any question.
These facts are in the realm of memory, and so memory strategies are needed for them.
Some of the things we will do with pupils in these last few weeks include:
Collective memory – Collective memory is a nice way to prompt pupils to focus on and recall facts and formulae. Tes has a great explanation of collective memory approaches, as well as resources to support it
Flash cards – Pupil-created flash cards are great for memory. Writing the key topic/idea on one side of the card and then the facts/formulae on the other can give opportunities for lots of different activities. For example, a pupil could have a card which says “Volume of Pyramid” on one side and “⅓ × base area × height” on the other. With lots of these cards pupils can then self-quiz or quiz each other. This website can be used to do this as a class activity using their brilliant “Recall formula (shuffled)” option, which can also be limited to just Foundation or Higher formulae.
Mnemonics and other devices – I am pretty sure that most teachers will already know the power of mnemonics, acronyms, and the like. Creating these can be a fun little activity that can be thrown in between other activities to add some lightness and break up more serious practice session.
2. Things that GCSE pupils have to be able to do
These are typically processes that pupils have to go through. Questions like “Solve this equation” or “Calculate this percentage” are all things that pupils have to be able to do, either as standalone questions or as part of a larger question.
It is pretty much agreed that for pupils to get better at these, or to stay sharp, they need to be practised. We will often start revision lessons with this sort of basic skills practice, and there are a couple of great things you can do to facilitate this:
One website that is part of the staple diet for my pupils is MathsBot. The "Retrieval Facts" generator in the GCSE resources section can help get a good mix of memory and practice, but the really good practice stuff is in the "Question Generator" and "Starters and Drills" sections. You can mix as many different topics and many different difficulties as you like, and stagger the questions so they get harder as you go (in the “Topic Ladder”) or have banks of similar difficulty questions.
Not related to the former, but the website MathsBox has some great skill check sheets that can be used over and again with pupils. Although you do have to subscribe, the subscription is very low cost and there are free samples on the website as well so you can try before you buy.
The PixiMaths revision mats are fantastic sources of related basic skills practice. You can download them and the answers here and the mats are in PowerPoint, so they can be edited and displayed over and over again.
3. Things that GCSE pupils have to work through
By “things that pupils have to work through”, I am really talking about those sorts of questions that pupils have to interpret, or that bring in multiple areas of maths.
Practice papers are an obvious source of mixed practice, but there are other great approaches:
SSDD problems – standing for “Same Surface, Different Deep”, these questions are designed to look similar at first glance, but to require different mathematics/approaches to solve. You normally get four of them around a single stimulus or “surface”. A big collection can be found on Tes Maths Advisor Craig Barton’s site.
Goal-free problems – the idea behind goal-free problems is that pupils get to focus on the maths they are applying, rather than actually trying to answer a specific question. Research in cognitive science suggests that this could be an effective strategy for allowing pupils to learn more from the process of solving problems. This also mirrors a strategy we often tell pupils to apply to exam questions; namely just try and do something even if you can’t work out the answer to the question. The website Goal Free Problems has many of these that can focus on the different GCSE strands of number, algebra, geometry and measures, ratio and proportion, probability and statistics, as well as fully mixed banks of problems.
Back to PixiMaths again, but this time for her excellent revision booklets. Sorted into problems for pupils aiming for different odd-numbered grades, the practice is massed in different areas, but the booklets can be used very flexibly and provide a huge number of practice questions.
Finally, you can’t write a post about revision materials without signposting the queen of the revision material collection, Jo Morgan, and her fantastic site Resourceaholic.com. In particular, this link, which hosts a great array of revision materials if you just fancy a change.
You can also find all of the Tes revision articles on its Revision Hub.
No matter what specific materials you use, the important thing is to not allow pupils to neglect any of these three different focuses – together they make for a successful GCSE pupil!
Peter Mattock is head of maths at an 11-16 school in Leicestershire and author of Visible Maths