Thursday, 30 June 2011

The yin and yang of maths education - part 2: My journey into this thinking.

File:Yin and Yang.svg
I took my GCSE in maths in the very early days of that exam - when it was supposed to be a revolutionary change from O-level.  And what a revolution it was!  Previously my set would have done O-level in a year (at 15) and then AO-level in the next year (age 16) so that the most able could go on and do A-level the next year and Further Maths the year after that.

All of a sudden we were doing GCSE.  Over 2 years so we had time to grow.  With barely any defined content apart from some odd stuff on shears I seem to remember.  Instead we had to do 6 extended projects which we designed ourselves.

It was complete and utter chaos.  Our poor teacher had no experience in running classes in this way and suddenly he had to supervise 34 students all doing their own independent research but being marked to a core scheme.  The intensity of the strain on him meant that those of us who had completed two pieces of work to a decent standard (only two were graded) we left to our own devices while he struggled to help the others through.  We played a lot of cards.  It was fun.  It made me think, a lot, about what the heck was going on?

After 2 years of that the school thought we simply couldn't do A-level in a year.  We hadn't done AO-level- how on earth would we cope with a whole A-level in 9 months (Sept to May)?  They didn't know what to do with us.  We told them to let us try and, for reasons no-one could fathom, we coped.  Instead of one or two completing further maths, 7 of us did and instead of 1 or 2 going to Oxbridge, 6 of us got in that year.  Weird!

What we'd been through wasn't sensible.  It wasn't sustainable.  It wasn't fair to teachers!  But it was interesting.  I can still so clearly remember the contents of one of my independent investigations.  I developed a great deal through doing it.  But how much time did we waste which we could have spent studying stuff?

It was no wonder the traditional teachers complained and there was a swing back to knowledge and skills based learning.

When I entered teaching I came to understand the frustrations of the teacher who was great at teaching kids mathematical knowledge and skills but who felt overwhelmed and frustrated by the idea of teaching them how mathematise the real world or to construct mathematics for themselves.  Until you've seen people doing the latter well and have experimented with it for yourself, it's really difficult to imagine, especially if you're working in a teaching environment which is structured with the assumption that traditional teaching will be taking place. I've watched teachers try and fail to make the shift in their teaching.  I've watched some come to demonise constructivist teaching because it hasn't worked for them.

On the other hand I've seen the most incredible and inspiration teacher from the constructivist paradigm lock themselves in a world of beliefs which denigrate traditional modes of instruction.  "Exams are bad", "you should never test kids", "you shouldn't grade kids and so on."  For me these arguments have some meaning and validity.  I have always tried to be aware of the contexts and particular students where such actions can be counterproductive.  But on the other hand I've seen how most kids love to collect badges, to tick boxes, to achieve closure and completeness.  How if you ask them to climb a ladder they will say 'how high?'  And I don't see that this is a bad thing. 

Most teachers clearly belonged either in one paradigm or the other and I deeply admired teachers from both, provided that they were at ease talking about why they were as they were, their motives were sound, they were sensitive to childrens' needs and they were at ease with and, when they had the energy, interested in teachers who were different to them and ideally keen to see if there was anything worthwhile for them they could learn from them. 

Some heads of department lay in the traditional paradigm but tried to make as much time as they could (without compromising the teaching of core skills) in curriculum planning for activities which focused on developing students' investigational and thinking skills.  I understood exactly where these teachers were coming from.

Other departments put the constructivist approach first (in a wide variety of ways) and signficantly subordinated the teaching of core skills and exam preparation.  Now where this worked well it worked brilliantly and I think this was because teachers who constantly teach in this way are constantly educated and developed through their own teaching.  They therefore become exceptionally skilled teachers.  If they can combine this level of skill with secure exam preparation you get an incredible maths department that students and educated or aware parents love.  But if less skilled teachers try to imitate this structure of teaching without proper support it can all go rather wrong.  So wrong, it seems, that we needed an inspection regime which abolished all departments of this type, good or bad (my apologies to those departments which struggle on against the odds and are, in my opinion, the exceptions which proves the rule).

So that was the background to my thinking.  The interactive teaching technology with personalised tracking came along..... and I'll write about how that changed things in my next post.

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