That's a picture of some blueberry muffins I made on Monday - taste good, look good I was very pleased. Pleased until I started thinking: what am I pleased about? That they came out well I guess, but what was my input? I followed a recipe which is, by its very nature, an algorithm so would I have known what the problem was if something had gone wrong? Probably not.Which brings me back to the question: what am I pleased about? It seems to me that I'm pleased that the muffins 'worked' after I blindly followed some instructions - sure I recognised some of the ingredients but did I understand what was going on? Not really. This got me thinking about mathematics teaching. How often do our students blindly follow recipes to be pleased when the right thing appears? How often are they able to see what the problem is in their working? How often can they tell when a solution doesn't fit with the problem? These are all things which we should be considering when we are teaching mathematics - is the understanding there?
I'm hungry...off to get a muffin!
4 comments:
Life was a simpler time when I knew how to differentiate but not how it worked, I used the think that was the aim of maths, working out how to do something, then using that recipe to complete it for other things. It's probably why I struggled a bit at university, but eventually I think I got it.
If you could get kids interested in why things work, not just how (and within that, how to answer questions to pass exams) you'll have a class of incredible mathematicians!
Hi there! Thanks for the great message. It's something that I have been thinking a lot about...should I know what it was that led me up to this point, I would be able to adapt my ideas and concepts a lot more easily than if I only knew the end result.
Another example that came to mind was the French phrase 'Je voudrais'. This is often taught to students as a way of politely requesting something. However, by teaching it in such an isolated fashion it is easy to think of it as some sort of independent construction which, in fact, it is not. Should however the learners be shown how to construct the conditional tense they are that much more empowered and may even be able to discern what je voudrais means themselves.
the show i told you about:
http://www.sothebys.com/video/privateview/L08027/index.html
you'll see some both symmetry of design and recursive idolatry.
he does well encapsulating modern infatuations. but i hate him. and that's what he wants. which makes me hate him even more.
http://www.tandf.co.uk/journals/cfp/tmaacfp.pdf
i like the serial idea for solving equations.... comic books in the maths classroom...
wanna be my editor?
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