As experienced senior examiners of GCSE mathematics, we strongly rebut the argument presented by Jeffrey Robinson in his thesis claiming that pass marks have been manipulated over the years to artificially inflate exam grades at GCSE (Maths made easy, August 24; Leaders, August 29). The truth is, in order to accurately evaluate high, intermediate, and lower ability pupils, the questions and the corresponding marks allocated will inevitably change over time. When more challenging questions are introduced, naturally a lower mark will reflect the same level of proficiency as a higher mark on easier questions. This is simply how the GCSE works.

It is misguided to insinuate that standards have been lowered simply because grade boundaries in GCSE mathematics exams are now lower than in 1989. To draw a valid comparison, the content of the papers, along with the grade boundaries, must be considered.

Over the years, more regulations have been put in place to standardize the setting of examination papers for GCSE. In contrast, back in 1989, no such regulations existed. Today, papers are produced to a format that is agreed upon by all awarding bodies, ensuring that each paper targets 25% of marks to each available grade. For example, in the intermediate tier, the available grades are B, C, D, and E. Thus, 25% of the marks must target grade B topics, 25% grade C, and so on. Therefore, a grade C candidate would only find 75% of the marks accessible to them. To achieve a grade C, they would need to score approximately two-thirds of the marks accessible to them, which requires setting the C grade boundary at 48%.

But in 1989, there were no such requirements, and it was common for intermediate papers to contain questions targeting lower level mathematical skills. Additionally, grade B was not even available at that time on that paper.

The same holds true for the higher tier, where for the available grades A*, A, B, and C, 25% of the marks must target each of the available grades. Consequently, a grade C candidate would only find 25% of the marks accessible to them. This means that a boundary of 18% maintains the requirement to achieve roughly two-thirds of such marks.

Moreover, other agreed changes have made GCSE maths papers more demanding. There has been a significant increase in the emphasis on algebra across all tiers, and particularly an increase in the amount of manipulative algebra on intermediate and higher tiers. In addition, 50% of the questions now have to be answered without the use of a calculator, whereas in 1989, calculators were allowed for all questions. A comparison of questions shows that intermediate maths papers are now more challenging. In 1989, the intermediate tier included grades F and G, and there were easier questions available to candidates. But in 2001, only questions suitable for grades B, C, D, and E were included.

A better comparison would be with 1994, the first year in which grade B was a target grade for the intermediate tier. In 1994, the grade C threshold was 51 (in 2001, it was 48). In 1994, the grade B threshold was 80 (in 2001, it was 77). Additionally, in 1994, there was a substantial formulae sheet available, and there were no unstructured questions as there are now.

We are all either actively involved in the classroom or recently retired teachers. If Jeffrey were correct, his argument would be beneficial in improving the examination system. But since he is incorrect, he does a great disservice to the children taking GCSEs and the teachers striving to give them their best.

W Aldwinckle Dr MJ Handbury Chief examiners and 12 principal examiners Oxford, Cambridge and RSA (OCR) Examination Board