It’s been very interesting recently looking over the new draft GCSE specifications and looking ahead at current year 8 students and seeing what different colleagues think about the approach to take in light of these changes.

As previously mentioned I think the top 2 sets in my school (mostly level 5s on entry and those going aiming for As at GCSE) will not have to be taught in a different was as most of my colleagues already teach purely for understanding and take the opportunities to develop problem solving where possible. Apart from some extra challenge for the very best, which I completely support, it will ask more of these students but will be a straightforward change. I teach the top year 7 set currently and can’t wait to see how they deal with some of the more advanced topics that have been added, although I do expect some to struggle with these new concepts.

The better grade B students who currently sit higher will have to be pushed further as I would expect they should be getting at the very least a 5 on the new system, but would have to be challenged to reach a 6 (I’m a firm believer in high targets, 4 levels is the only option). The weaker grade B students look like they will face a higher paper containing many questions beyond them. What tier they are entered at will be an interesting proposition in a few years time, as without knowing what they will need to achieve to reach a 6, it’s going to be hard to judge whether it is realistic for them.

The grade C students will be challenged like never before if they want to reach a 5 by the looks of it (with the aforementioned caveat of not knowing any boundaries), since as suggested by exam boards and others, it’s about two thirds of the current grade B. The benchmark looks like it will be a grade 5, raising the demands of getting this considerably. With so many new topics to contend with and the increased emphasis on problem solving it will take a much more long term strategy in order to push so many more students to this new standard.

My year 8 set is the lowest we have and has some very weak students in, as a very long term prediction I would expect them to achieve something around a grade E, possibly a D, on the current GCSE when they reach the end of year 11. This means they will also find a large portion of the paper inaccessible and will be more easily thrown by problem solving questions than more capable students. 

I’ve had multiple discussions with a colleague who is teaching a more able set in year 8, all around 4c at KS2 so exactly the type of students who will be most affected, as they are the most difficult to get grade Bs (and in many cases Cs) from. The big question is how to approach the B grade topics that have been added to foundation content, do you wait until they have mastered everything that is needed before hand? 

As I see it there are two broad ways of approaching this problem; you either wait until they have mastered (largely) the pre-requisite topics or you push them on earlier and accept that small mistakes will still be present.

Ideally we would like all students to have mastered each topic before moving on, I think almost everyone would agree this is impossible for the middle ability students. The problem with waiting for middle ability students to master slightly more challenging topics is that they aren’t always capable of achieving this, but may be able to get 75% mastered with the understanding largely correct.

The overall mathematical fluency, confidence and ability just isn’t there with the middle ability students I see. They can work well, strive to understand what they are doing but will always miss the subtleties that those nearer the top will get. Do you keep persevering with this or move ahead and accept that there are small details that are missing?

I have found more success by moving forward rather than getting bogged down over small details, the advantages of having middle ability students experience more mathematical concepts and topics has the effect of raising overall fluency than trying to master each small section one by one. As mathematics is so inter-connected this effect is clear, being able to deal with all fractions confidently translates to many other topics and raises their overall fluency in mathematics. I’ve found much greater success when I’ve pushed a group on to a more advanced topic in a previous unit of work and revisited it further down the line (later in the year or the following one) and as their overall ability has increased the topic at the lower level is found to be easier as they have more fluency overall and get used to working at a higher level. I will point out that it is common for good higher students to struggle with the more basic algebra topics as they over complicate topics (eg; factorising into a single bracket seems to be a common one that gets confused with quadratic factorisation).

There is a potential stumbling block here which is that unless you teach purely for understanding, emphasising the need for understanding why students are doing what they are, the whole thing will fall apart. I don’t believe you could manage this by teaching method based strategies as this doesn’t raise overall fluency but compartmentalises each topic as a skill rather than part of a bigger picture.

The question of when sufficient mastery of each topic has been achieved is one which cannot be stated in simple terms, I do it as much through instinct than, for example, giving a short test of the topic and having a boundary required to move on. I wouldn’t move on too quickly should a class need further practice on any topic, but equally I wouldn’t hold the majority of a class back were several struggling.

Every topic is different and needs particular consideration as to the progression from the basics to more advanced topics and there are some essential topics which have to be mastered as much as possible, but I firmly believe that the more maths a student sees, the better they will be overall. Everything has a link to many other topics and each individual skill is utilised (maybe in a different form) in many different areas so everything is useful.