Geoff Tennant - Promoting access to mathematics for all
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14/6/15: one year to go - and 'hard' maths problems

It is, of course, the nature of ex-pat contracts that they are time limited.  Apart from anything else, it is recognised that having a presence in two countries is an expensive business, so this means that I get paid considerably more than a local person would for doing the same job.  This is one of several reasons why the expectation needs to be to work hard and look to make oneself redundant, in due course handing over work to other people.

Meanwhile, I came out here nearly three years ago on a three year contract with the understanding that, if mutually agreeable, this could be extended for a further two years.  So, what to do?  That I'm approaching a birthday with a 0 in it concentrates the mind slightly.

So, after a lot of thought, I'm thinking that I would like to return to school teaching in the prep school sector.  A number of reasons for this.  This is a sector I've not previously worked in, so a sense of going forward in life.  From a mathematics point of view, the 7-13 age range is fascinating, starting with a very concrete approach and finishing up with an abstract approach.  The engagement with the wider school life - particularly music and the pastoral side, also very happy to drive minibuses for sports fixtures - is very appealing.  And there are professional journals which provide outlets for writing which is very much the kind of thing I enjoy doing.  Put it another way, I'm supposed to be an expert on teaching mathematics in secondary (and increasingly primary) schools, but haven't done it myself for some considerable time now.  How can this be right?

So I'm happy now to tell you that I got as far as interview for a post in a prep school back in March, so that I wrote this blog post from my parents' front room - thank you, Mum and Dad, for putting me up when I'm back in the UK, or should that be putting up with me?  Part of the process was to teach a 35 minute lesson on the addition of fractions which proved really hard in isolation.  Apart from anything else, University lecturers haven't drawn breath in 35 minutes let alone done anything.  I ended up with the most hideously complicated PowerPoint presentation with multitudinous different routes through depending what the responses were, if you're interested please download the PowerPoint from here.  It includes an index page which was only intended for me to understand, at one stage I went to it and there was an audible gasp of horror - what on earth is going on here?  Anyway, I thought the interview went as well as it reasonably could but in the end the post went to somebody with direct experience of the sector, I can see that I'm a bit of a wild card.  But then I can't be constantly returning to the UK for interviews, it's both very expensive and very time consuming, so what to do?

Meanwhile, we have a change of boss at work - so good bye Pauline, thank you for everything, and welcome to Joe, look forward to getting to know you better soon and to working alongside you.  So I have agreed with colleagues at work that I'm staying until 31st August 2016, on the understanding that I will need some work time back in the UK in early 2016 to be available for face to face interview.

So, that's where I am!  As I say, prep school teaching is what I'm thinking is the right next move, but I'm open to other possibilities (one of which was put to me this morning, but you'll have to contact me privately to know more about that).  Opening position is I want to move back into my house near Tadley on the Hampshire / Berkshire border, but not necessarily.  Any suggestions gratefully received!  Will keep you informed - as far as is reasonably possible....

So, with the clock ticking, please note that I'm hoping to organise a trip up Kilimanjaro between Christmas and the New Year.  As I'm sure you know, Kilimanjaro is the highest peak in Africa and also is the highest in the world which can be climbed in the sense of a stiff walk, without specialist training and equipment.  If you're potentially interested, do let me know!

So, with an abrupt change of subject, you may have seen this story in the UK press this week about a GCSE mathematics question which was supposedly impossible.  I suppose I should be pleased when my subject gets attention, but I'm finding myself feeling a bit exasperated to be honest.

Firstly, let us be very clear, this was not an impossible question or anything like.  There have previously been problems with questions, particularly in A level decision maths, which are genuinely impossible, in much the same way as the question, "Describe the influence of Queen Victoria's reign on 18th century politics" is impossible.  But this is not one of them.  In fact, if you know what you're doing, the question comes out very simply indeed.

In 2007 the former Times Educational Supplement journalist Warwick Mansell wrote a book entitled, "Education by numbers: the tyranny of testing".  In this book he argues that increasingly the assessment systems were dominating how classes were taught, and includes a description of a training course but on for French teachers by a senior GCSE examiner, in effect telling teachers how to train youngsters to pass French GCSE without being able to speak the language at all.  Slightly bizarrely, as an opening exercise he got teachers trying to make sense of some text in Maltese.  Throughout the day, he kept on repeating, "It's difficult for the kids, think Maltese!"  Yes, but there's one very important difference here, isn't there?  In general, UK French teachers do not speak Maltese, have never studied it, nor is there any expectation that they should do so.  Youngsters doing French GCSE are supposed to be able to speak and understand French.  Aren't they?

Similarly, the underlying assumption seems to be that maths GCSE should be entirely straightforward, any need (as in this case) to bring together maths from two different topic areas - probability and algebra - seems to be deemed out of order.

In this blog post I argued that an awful lot can be achieved with a small understanding of mathematics.  The underlying premise here is that we should achieve very little with a lot of topic content.  Put another way, if there is genuine understanding as to how both probability and algebra work, there is no difficulty doing this problem, no need to revise to be able to do it.  Is any purpose served by being able to answer questions like this by dint of a huge amount of revision and training?  As is probably fairly clear, my answer to this question is a resounding no - but I'd be interested to know what you think on this point!

One final thing before I go.  I went to the IGCSE certificate presentation at the Aga Khan secondary school during the week.  This was a great occasion in which learnt something I didn't previously know from the 15-year-old valedictorian speaking on behalf of her classmates.

Question: what is the most important thing that parents do for their children?  Answer: provide wifi.  I didn't know that before last week.  But I do now.  And so do you.  Thank you for reading, I'll be back soon.

3 Comments to 14/6/15: one year to go - and 'hard' maths problems:

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Jenny Spence on 23 June 2015 11:00
Hi Geoff I shared your exasperation with the "hard" maths problem. I did it in about 30 seconds having not done any probability in anger for 30 years! But I had to see another viewpoint when I was talking about it to one of my friends who tutors children taking their maths GCSEs. The problem lies with the schools teaching to get children through the exam and achieving at least a C (for the league tables). So they are taught enough probability to be able to do a probability question. They are also taught basic algebra. But my friend said that in her child's school, only the very top set are taught quadratic equations in algebra, so any child not in that top set would never have seen n2 (n-squared) before and would be thrown completely. Although it's still very sad that children are unable to generalise in their maths - as you said, the problem was very simple when you just put n in instead of a number. By the way, we at St Andrews hope very much that you'll come back to your cottage - we miss you!
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Geoff on 23 June 2015 22:52
Thanks for getting in touch, Jenny. Your point about being taught very directly for the test to achieve certain grades is very 21st century, I think, and largely what Warwick Mansell's book is about. Let me try out a theory on you - one of the problems here is that, as exams become more important, so schools tend to concentrate on their finishing point as the key thing to aim for. So, 11-16 schools regard the all important thing as GCSEs, whereas in an 11-18 school, teachers of bright pupils in top sets will have at least 1/2 an eye on the demands of A level. What do you think? Note the point about moving back to St Andrew's, much appreciated.

Jenny Spence on 28 June 2015 12:54
I can't really comment on an 11-18 school as Nick and Chris both went to an 11-16. However, of course in the UK schools are ranked according to their results, both at GCSE and A-level, so at either level there will be the incentive to teach to the exam. Therefore I think the problem would probably still be there. And it's not really the bright pupils in the top set that we have the issue with, it's the next tier down.
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