What is the truth behind the debate about falling standards? Are examinations getting easier? Or was the Myths series in The TES, which ended last week, right to suggest that the extent of dumbing-down has been exaggerated?
Research carried out at King's College London and Durham University strongly suggests that secondary pupils' understanding of mathematics has stayed the same since the mid 1970s. So, in mathematics at least, standards have not fallen - but nor have they risen.
Exam pass rates in mathematics have certainly risen very dramatically. In the early 1980s, just 22 per cent of pupils obtained the equivalent of a GCE O-level grade C or above, whereas this year 57 per cent of 16-year- olds gained a GCSE grade C or above. But we are in danger of fooling ourselves if we point to these examination grades as evidence that 16- year-olds are better prepared mathematically than previous generations.
To investigate how pupils' mathematical understandings have changed, we tested 3,000 key stage 3 pupils drawn from a random sample of schools across England in summer 2008. We gave them a set of tests in algebra, ratio and number. These tests were originally sat in 1976 and 1977 by a similar group of 11 to 14-year-olds. The results show that, at Year 9, current performance is broadly similar to that of 30 years ago. An increase in understanding of decimals is balanced by a decrease in fractions. In all areas, there are now greater proportions of pupils with very low attainment. These are interim results, based on a sample that is slightly skewed towards higher-attaining pupils. Nevertheless, the overwhelming conclusion is that standards of mathematical understanding have not risen over the past 30 years.
So, if mathematical understandings have not improved, why have GCSE results got so much better?
Qualifications like GCSE maths have undoubtedly become more important for a greater proportion of the population since the 1970s. Reflecting this, the past 30 years have seen a raft of measures directed at improving performance: the national curriculum, national testing, the national strategies and increasing accountability through Ofsted and league tables. Secondary schools are now "measured" on how many pupils achieve GCSE maths. As a result, GCSEs have not become "easier", but they have become more routine and predictable.
Schools have focused much more on getting "good" GCSE results and teachers have undoubtedly become better at preparing pupils for the examination. There is much to be celebrated in the hard work of teachers and pupils in achieving these results.
But there is a danger that in focusing on test performance, we focus only on test performance. We need to remember that GCSE is only a measure of mathematical attainment. Teaching to the test is fine provided the test is a valid one; teaching exclusively to the test is not. GCSEs matter, but mathematical understanding matters more.
Our study relates specifically to algebra and ratio. Along with geometry and statistics, these are the core ideas of secondary school mathematics. Multiplicative reasoning - ratios, proportions, percentages and the like - provides vital mathematical tools for the informed citizen. Ratio and proportion, for example, underlie the mathematics of risk and probability. They are therefore essential to making sense of the risks involved in personal health and financial decisions or in debates as diverse as climate change or MMR vaccinations.
Algebra is fundamental for any advanced study not just in mathematics, but also in the other STEM disciplines of science, technology and engineering. It is, to quote physicist Richard Feynman, the language of science. Without algebra and multiplicative reasoning, advanced scientific, engineering and statistical work is simply impossible.
Secondary pupils do not appear impressed by the GCSE examination results. Since 1995, English pupils' attitudes towards maths have declined. Consistently, research studies report that students in England find maths boring, irrelevant and difficult. Even relatively successful pupils feel that they have failed at maths. Numbers taking A-level mathematics are down from around 80,000 in the 1980s to a current figure of 60,000. Insufficient numbers are studying mathematics, science and engineering at university. Universities themselves are lowering their requirements for mathematics A-level in the face of falling numbers of applicants.
In this climate of fewer absolute numbers and increasing competition from subjects like economics, it is no surprise that university lecturers complain about the mathematical preparation of undergraduates. Mathematics education is indeed facing a crisis.
If as a nation we really want to increase participation in mathematics and other STEM disciplines, we cannot simply focus on public examinations. We have to take the problem of increasing mathematical understanding very seriously. A consensus is building around this issue. The new national curriculum does place considerable value on mathematical understanding. So, too, does Ofsted.
Actually doing this will require a sea change in school mathematics. We will need examinations that are less predictable and routine. We will need to support teachers in developing mathematical understanding - through better textbooks and curriculum materials and evidence-based approaches such as formative assessment. But all this will be to no avail unless we can convince many more secondary pupils that mathematics is sufficiently interesting and engaging to be worth doing.
This very significant challenge has been recognised by the Economic and Social Research Council in funding our study and the four related projects that comprise part of its Targeted Initiative on Science and Mathematics Education.
Our study, Increasing Competence and Confidence in Algebra and Multiplicative Structures, is due to report in 2012. Watch this space.
- Dr Jeremy Hodgen, Senior lecturer in mathematics education, King's College London.