Has the Higher level Mathematics examination become easier?

It is difficult to examine carefully the GCSE Mathematics examination without appearing to sound critical of the pupils studying for their GCSE, or sounding like you are questioning their outcomes as being possibly unequal to those from past years. Saying that, there is much debate regarding whether the GCSE Mathematics examination is easier than the 1980s ‘O’level or even whether it is now easier than the GCSE from the late 1990s.

Here, I intend to cast a critical eye over the similarities, differences and changes that the qualification has undergone. Then I’ll examine a few questions from each era and leave the final decision as to whether GCSE Mathematics is now easier up to you.

Firstly, we must address the point that ‘O’levels were not intended for everyone. Many pupils took the CSE examination, which was intended to be easier and thus more accessible. By the mid-1980s, around 20% of the school population were taking ‘O’level Mathematics with the other 80% either taking a CSE or leaving without a mathematics qualification at all. We shouldn’t forget that a grade 1 at CSE was regarded as equivalent to an ‘O’level grade C, though many people still viewed it as an inferior qualification.

After Conservative Education Secretary Sir Keith Joseph decided to proceed with a merger of ‘O’levels and CSEs, the first GCSE courses began in 1986, and the first examinations were taken in 1988, though we should not forget that there had been trials previous to this full implementation. The central idea was that most subjects should be examined through tiered papers focusing on different parts of the grade scale, ensuring that each grade reflected “positive achievement” on appropriate tasks, rather than degrees of failure. As is currently the case, a grade of G is a pass, but that was quickly superseded by the idea that a grade C was a pass and anything lower should be considered a fail. GCSEs had the best intentions, allowing all pupils to learn the same syllabus and attain a grade C or better. Unlike a grade 1 at CSE, a grade C on a Foundation paper was indistinguishable from a grade C on a Higher paper. This though, was not the case with GCSE Mathematics.

For a long time (1988 to 2008) Mathematics was a three-tiered examination: Foundation, Intermediate and Higher, with respective grades G to D, E to B and C to A (later A* when it was introduced in 1994), though we should not forget that grade E at Intermediate and grade C at Higher were both meant to be “compensatory”. Now there is no doubt that under that system pupils taking Foundation were disadvantaged, as they were unable to attain a grade C, but it had its advantages for those on the Intermediate level, as they were able to attain a grade B without needing to study the most challenging parts of the curriculum.

Under the current two-tiered system: Foundation and Higher, the grades are G to C and D to A* respectively, with the Higher examination grade C now being possible to attain with around 30 to 35% of the total possible marks, leading to inevitable questions regarding the dumbing down of the GCSE. Unlike with the three-tiered system, a Higher paper now has approximately 50% of marks available for questions that are roughly equivalent to grades C and D, with a little overlap into grade B; though care must be taken when attributing grades to questions as many have such exercises are based around previous examination structures which have been superseded. So, given that grade boundary for a B hovers at around (or just under) 50%, we again see the ammunition those who claim that the GCSE has been dumbed down. In effect, a pupil doesn’t need to know any “true” Higher level mathematics in order to attain a grade B! Worse still, they can start an Advanced level course without having the proper GCSE foundations of study required for proper mathematical advancement. When a three-tiered system was in operation, only a tiny minority of Intermediate level students started on an Advanced course. We must therefore question whether the switch has hindered mathematical progression by setting unrealistic targets for students regarding their ability to study advanced materials.

What remains clear though, is that throughout the life of the GCSE, the syllabus has been mostly constant. I would estimate that some 99% of the syllabus from 1986 can still be found on the syllabus from 2010. Which then raises the inevitable question as to how examination questions have altered?

Most newspaper articles on this topic are disingenuous, using either questions from different tiers, or questions from different parts of the paper. What is more useful, it to look for similar types of questions and ask whether they are of similar difficulty.

Take this question from 1984’s ‘O’level paper:

Solve the simultaneous equations    3x+2y=-4   and  x-3y=17

And compare it with that from 1999:

Solve the following simultaneous equations  8x+3y=35      and   2x-5y=3

Finally, with that from 2011:

Solve algebraically these simultaneous equations  3x-y=1   and  5x+3y=4

All, I think you’ll agree are quite similar. Yes, that from 1999 requires a multiplication of both equations before elimination, but the other two have answers where one unknown (or both) is either a negative or a fraction. In many ways, pupils would find the question from 1999 the easiest, except that the numbers involved become quite large.

What is apparent though, is the differing levels of algebra. For instance in the 1984 paper we see:

Factorise  1-p-12p^2   and    Solve   2x+3=4(x+1)  amongst others.

At (around) the same question number in 1999, we find:

Find the solution for the following equation 5(a-3)=3a-19  and rearrange to make y  the subject of x=120y+136.

And in 2011 we find:

Solve 3(2x-5)=30  and   Write as a single power of  p     p^2  x p^6      and   (p^2)^6

Now, as any mathematics teacher will tell you, having a proper foundation in algebra is a pre-requisite for studying at Advanced level, we can see that these three are not similar in difficulty. Now, that is not to say that later in the paper we didn’t see more difficult algebra in 2011, e.g.

Factorise  10x^2+5xy    and Factorise and solve  2x^2+7x-15=0

But the question remains as to whether a pupil gaining a grade B will need to have answered such questions correctly to attain that grade, especially as a grade B is seen as a gateway grade for study at Advanced level.

Overall, whilst the three papers are quite different in style, many questions are similar in the topics they are testing. It is only the number at the “higher grades” that is inconsistent, with many more in the ‘O’level paper and 1999 paper than in the 2011 paper.

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