Saturday, June 7, 2008

A Lost Generation of Mathematicians

A new report by UK's Reform think tank is creating a lot of buzz across the pond (1, 2, 3, and many more). The report, titled "The Value of Mathematics", demontrates how standards are falling and the extent of damage to Great Britain's economy causes by lack of students with analytical thinking capabilities. Here is the executive summary. You can find the complete report here.
The UK’s maths economy which powers the financial services sector and wider industry is in danger of atrophy as fewer students study mathematics and attainment falls. At the core of this problem has been the diminution of the O-level/GCSE which has gone from being a key “staging post” to a “tick-box test”. Scores of less than 20 per cent on the top paper regularly suffice to gain a grade C, despite a much reduced level of difficulty. Many students are turned off by the narrow teaching which results, and this has led to a generation of “lost mathematicians”. Individuals lacking mathematical skills stand to lose £136,000 in income over a lifetime, and so have cost an estimated £9 billion to the UK economy since 1990.

Reform has conducted an analysis of O-level/GCSE examinations over time. From 1951 to 1970 these were a rigorous test of thought and initiative in algebra, arithmetic and geometry. Students were required to think for themselves. By 1980 questions were becoming simpler. Following the introduction of the GCSE there was a sharp drop in difficulty, with questions leading pupils step by step to a solution. Pass marks were lowered throughout the period.

The Gordian knot of political control has been tightened in an attempt to reverse the misguided trend towards “progressive” teaching. The unintended consequences of politicisation and centralisation of the subject are demotivation of teachers, a diminution of the enjoyment in mathematics by pupils and an exclusion of universities and employers from education policy. Steps to increase accountability taken by the Government and a focus on examination results have created unhelpful pressures on institutions and exam boards, which have in turn led to declining examination standards.

Relevance has replaced rigour in the belief that this would make mathematics more accessible. At the same time high stakes assessment has reduced what should be a coherent discipline to “pick ‘n mix”, with pupils being trained to answer specific shallow questions on a range of topics where marks can be most easily harvested. Instead a strong sequential approach ought to be taken building up a robust toolkit of cognitive and problem solving skills. In the modern global economy, it is the combination of core techniques, flexible thinking, logic and initiative that will be critical to future success.

The global maths economy is driven by high personal capability, initiative and logical thought. The top 5-10 per cent of mathematics graduates in the financial services sector practice “power maths”, modelling derivatives and understanding financial risk. These skills are at the pinnacle of the City hierarchy making their practitioners the new “Masters of the Universe”.

Yet the UK, home of Turing, father of modern information technology, and numerous recent prize winners such as Atiyah and Wiles, is failing to generate sufficient quality mathematicians. Financial services are being forced to recruit a high proportion of overseas graduates – as many as seven out of eight of all such posts. UK workplaces are finding themselves short of people with basic mathematics skills. Universities are being asked to select from a significantly reduced pool of applicants, a large number of whom are independently educated or from overseas.

Winning the battle of the maths economy will be critical to the UK’s future success. Current Government policy is too small scale to deal with the pressing nature of the problem. Radical measures have to be taken to move mathematics from “geek to chic”. Rigour must be central to this approach. The Government should step in and reverse the current inexorable drift towards modularising GCSE mathematics. A new Alexander is needed to cut the Gordian knot of state control and open up individuals’ and institutions’ ability to improve their own capability in the subject.

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