Posted by: Administrator | 22/11/2009

Paul Busch: “Use of Maths” and LMS Education Policy

I just read the recent ACME consultation paper on the question of the Use of Maths A-Level and think that a 2-pathway approach would be appropriate, which ensures that  Maths – like English – continue to be compulsory at least at “(school) foundation level”, with 2 hours per week over two years.   The time of 2 years is far too short and precious, in my view, to play with any further refinement of pathways for those who may need mathematics in their future professions. Having to make a choice between such pathways would be premature for most students at age 16 anyway.

By the way, a two-tier system with a basic and an advanced maths course for the two or three years before Abitur has worked well in Germany’s high schools for many years.

My personal criticism of the ways in which school mathematics is treated goes deeper: Rather than being concerned with introducing more refined provision, one should give up the fixation on league tables and the life lie that wants to make us believe in the ever-increasing quality of A-level performance (and the ever-increasing intelligence levels of the population that one might need to assume to explain this phenomenon). League table pressures have led to a situation where many schools drill their students to pass exams (“jump hoops”) rather than help them understand mathematics. One should instead focus on ways to convey to students the experience that maths is something that one CAN in fact understand.

For many years (in my case 14 since I started working at a UK university) we have seen increasing numbers of first-years who have only learned to mechanically perform pre-formatted and long-rehearsed tasks without really knowing the what and why. Very often student feedback reflects the expectation that we should continue to treat them that way.  As a colleague’s anecdote has it: challenged by students, he told them that he had to set them some unseen exam questions to test whether they were able to apply what they had learned and think for themselves to solve a problem; the students replied: if you had taught us properly in the first place, we would not need to think.

It seems to me that often it takes the students and us almost into their 3rd year of study before that mind-set has been broken and they do actually start to think on their feet. I would like to dream that one day a school system has been put in place with teachers able and allowed to induce the students to enjoy doing and understanding maths. When my youngest daughter started her final two years of high school in Canada after her GCSE in the UK, she came home one day saying excitedly how thrilled she was that one could actually understand subjects like maths and physics!

That the opposite seems to happen more is evident from anecdotes such as the above or this one: having learned that besides sin(x) and sinh(x) there are also functions cos(x) and cosh(x), some students have in fact concluded that besides sign(x) there also has to be a function called cogs(x).  This is not a joke, nor an isolated instance. It shows what kind of thinking may develop in schools and is brought into universities, on the strength of good enough grades in A-level maths. When my daughter was exposed to trig functions in year 9 the first time, she was just instructed to perform calculations on her calculator. When she asked her teacher what this “sin(x)” meant, the teacher said it would take too long to explain, this would come in a later year.

So, I’d rather wish to see the real issues being addressed instead of being contented with the chimera of ever improving A-level statistics. Introducing a “vocational” maths pathway is not the answer; managing three different maths streams is bound to cause excessive administrative burdens on teachers and schools and takes away even more the ability of teachers to focus on their job.


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