Reform Mathematics

Thanks to Ken Mackenzie over at Bad Science for the heads-up on Reform’s concerns about mathematics education. The authors (Laura Kounine, Professor John Marks and Elizabeth Truss) are not happy.

I know you should not judge a book by its cover but I cannot resist observing that the title page is purple and page 2 is solid purple. Until now I’ve always regarded excess purple as the preserve of the more mystic woos.

In the first paragraph of the Executive Summary on page 7 we find the interesting assertion that:-

“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″

This statement ignores the fact that increasing the number of people with a skill set does not increase the number of jobs requiring that skill set. Later this statement is clarified by saying that the City and other employers have to employ mathematicians from abroad, particularly France, as the UK does not produce enough. Using the authors’ own logic this would mean that we are shafting the French economy but for some reason they make no mention of this.

Page 17 carries a short table showing that the UK has 119 maths graduates per million of population compared with 160 for France 66 for the USA and 55 for Germany.  Question for the reader, which of those has the larger GDP per head?

About those economic costs…

The figures quoted above, assuming a forty year working life, suggest 150,000 people with inadequate maths skills, which does not seem to be a major problem. However, on page 17 they quote a Government estimate of 15 million adults struggling with basic mathematics.

On page 18 they show their working for their economics cost calculations:-

“If the number of A-level mathematicians had remained constant (as a proportion of all students), there would have been an additional 430,700 over the period.

“Each of these students would have earned an additional £3,080 per year equating to £136,000 over their lifetime [I make it £123,200 for a 40 year working life]. The total gain to the economy over the period [1989 – 2007] would have been over £9 billion”

That 430,700 extra A-level mathematicians is an accumulative total so they would have worked from 0 to 18 years over the period, depending on when they left school. The average is thus 9 years. According to my calculator. £3,080 per year multiplied by 9 years multiplied by 430,700 extra students comes to over £11.9 billion.

If you are going to criticise the state of mathematics education, you really shouldn’t make arithmetic errors.

As to the maths education, on page 11 they say:-

“From being required to know arithmetic, algebra and geometry in depth during the years of O-level (1951 – 1987), candidates now have to exhibit a degree of familiarity with a much wider but shallower curriculum including handling data (statistics), vectors, transformations and using and applying mathematics.”

Later they say that data handling also includes graphical representations.

From a science viewpoint, I would say that learning statistics and how to apply mathematics is surely a good thing but the authors actually explicitly complain about practical applications creeping in (page 12).

The appendix contains a number of examination questions from papers over the past fifty-odd years. I have only two points to make regarding them:

1. The algebra and geometry questions from the early years are not noticably more difficult than those from the later years.

2. Kounine et al write “In 1990 new topics were introduced”. These turn out to be inequalities, vectors and matrices. I hate to piss on their chips but I studied these subjects for mathematics O-level in 1975. So not new in 1990 then.

There may be problems with the delivery of mathematics education in this country, and there may even be economic consequences of this alleged failure but this document fails to make the case for either proposition.

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3 Responses to “Reform Mathematics”

  1. pyjamasinbananas Says:

    So let me get this right, employers, and the economy, are crying out for more pure mathematics and less applied maths like statistics?

    Where exactly are these pure mathematicians going to be working? It doesn’t appear to be financial services!

  2. pyjamasinbananas Says:

    I liked this bit:

    “While some courses have been extended from three to four years, this has been in order to compensate for a decline in standards in A-levels rather than an increase in the difficulty of courses.51
    “51 Times Higher Educational Supplement (2008), “Why we can’t turn our backs on the league-table generation”, 1 10 January. Imperial College London, for example, has turned its three-year BEng course into a four-year MEng because “half the first year is taken up with remedial teaching”, according to the university’s admissions chief David Robb.”

    Whereas the RSS says:
    “In the physical sciences and engineering, however, it has become clear over the past ten or twenty years that the three year degree was no longer providing an adequate foundation for more advanced studies. In mathematics, this recognition led the LMS, IMA and RSS to commission the
    Neumann Report, which was published in 1992. The Report, and the consequent submission to the Department of Education and Science (as it then was) by the Joint Mathematical Council, identified three factors that there was an urgent need to accommodate:
    “(i) the continuing changes in secondary mathematics education and in access to higher education;
    (ii) the continuing growth of mathematics, both in depth and in breadth, leading to the danger of overload in undergraduate courses in mathematics;
    (iii) the increasing need to ensure comparability with mathematics degree courses in the universities of continental Europe”.
    The chief recommendation was the establishment of a four year undergraduate degree, with a title such as MMath to indicate that it was at masters level but not the same as the MSc. The Government accepted this recommendation and made the four year degree eligible for mandatory funding. Consistent with the aims of the degree, it was differentiated from the BSc. MMathprogrammes have been designed to allow students to go into the subject in more depth than typically happens in the BSc, rather than being a mere broadening of their mathematical experience.”

  3. Damned If you Do, Damned If You Don’t « Education Watch Says:

    […] been here before, and fairly recently too. The Reform paper was pretty rubbish, has OFSTED done any […]

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