“The new mathematics GCSE will demand deeper and broader mathematical understanding. It will provide all students with greater coverage of key areas such as ratio, proportion and rates of change and require them to apply their knowledge and reasoning to provide clear mathematical arguments. It will focus on ensuring that every student masters the fundamental mathematics that is required for further education and future careers. It will provide greater challenge for the most able students by thoroughly testing their understanding of the mathematical knowledge needed for higher level study and careers in mathematics, the sciences and computing.”
This is Mr Gove, in October 2013, announcing the outcome of the consultation over the revision of the Mathematics GCSE syllabus.
I am sure that the majority of us welcomed the decision to improve rigor and the prospect of more challenge. With the steady decline in grade boundaries I have become used to steeling myself up for the first full staff meeting back to school in September, “I see the maths results are good again this year. Well they would be when 35% will get you a grade C. In my subject that wouldn’t even get you a grade E.” “Wow, maths really has been dumbed down hasn’t it, when walking round as I was invigilating I did the calculator paper in my head.” [Actual comments from colleagues] Your experience may have well mirrored that. So yes, let’s standards higher, let’s get more rigor, more challenge.
And now we know how that is supposed to be achieved: broader, deeper content; more contact time. Bring back matrices, bring back some calculus into the higher tier, drop trigonometry back into the lower tier – all good sensible adjustments, but what exactly does that mean for the Foundation level students that sit in front of us? What does that mean for those of us delivering the Foundation tier?
The content for the Foundation tier has been fleshed out to resemble what only a few years ago passed as an Intermediate tier, that halfway house that was a good booster for a student predicted to fall on the D/C boundary.
The key assumption with all this upward revising of standards is that the ability levels of the students we teach, especially at the less able end of the scale, have had a corresponding shift. Initially, at least, this will not be the case; the changes to KS3 will not have bedded down and filtered through yet. This leaves us with the realisation that our haul of ‘good’ passes, in the short term, may fall.
For Foundation level students I believe the key issue comes with the adjustment of the Assessment Objectives – especially AO2 – where students are expected to reason, interpret and communicate mathematically. Can my lower ability students make deductions, inferences and draw conclusions; can they construct chains of reasoning; can they assess the validity of an argument?
The way that these skills can be developed in our students will centre on a more investigative and, dare I say it, project based approach. Confidence with vocabulary and method is increased dramatically with greater interaction – ‘doing’ maths. By this I do not suggest that whole chunks of the scheme of work be devoted to some expansive tasks.
Every half term set aside some lessons which provide some practical work which draw together a number of strands:
- I have a Y11 class at the moment who are all boys, with nearly all of them involved in one sports team or another and some of them doing GCSE PE. I could focus on the layout of a soccer pitch, basketball court or a track and field arena, and look at area, perimeter, trigonometry, scale drawing, construction, loci, percentages, ratio. Get students to look at variations in pitch sizes, and so on.
- Boys or girls could enjoy designing a bedroom/kitchen/bathroom: area, perimeter, percentage, costings (within a budget) and amounts (or floor covering, wallpaper/tiling, paint, furniture), scale drawing.
- Students who enjoy travelling or geography could work on journeys: bearings, timetables, speed, travel graphs, angles of elevation/depression, scale drawing, volume and mass (of luggage).
Identifying something that will grab the attention of groups of students and designing something along these lines will go a long way.
Getting students to collaborate, discuss and explore is really good for vocabulary and method and stimulates a better understanding and connection of a variety of strands. These will encourage and develop reasoning, an ability to make inferences and deductions, and check out the validity of an argument.
Above all this kind of approach will develop confidence – a vital attribute that our lower ability students need.
By Colin Stobart, Collins GCSE Maths Teacher Pack author