As I wrote earlier, I think the arguments put forward in the Hacker NYT article “Is Algebra Necessary?” are not that easy to counter. There’s no one answer that pulls the rug from under it. It’s more like many arguments are needed. But this then reminds me of the physicist Richard Feynman who said something to the effect that “the only reason to put forward several arguments is that you don’t have a single good one” (quoted free from memory). But Feynman was a special guy – the world must have been simple to him.
So what are the counter arguments? One is the obvious one that just because something is difficult and hard to learn – that does not mean that you should not try – or that it is not important. The Hacker argument can be rephrased for other subjects: Why learn foreign languages, this is also difficult for most of us?
The discussion came up again when I had dinner with Susan Colley and her husband at their house when I arrived in Oberlin (thanks again for the wonderful smoked fish and cornbread – and was it spinach?). It’s more than two weeks ago now – time flies.
There is a misconception that it is possible to learn only what is precisely needed for your job or profession, Susan said. For once – when you are young you cannot know precisely what your profession is going to be. For twice – today you don’t expect to stay in the same job until you retire. For third – knowledge doesn’t work that way – it cannot be divided up like that.
There seems to be a paradox here. Knowledge needs a context. In Sweden it has been popular for some time now to speak of “situated learning” and there is school of pedagogy researchers working on it. I don’t know very much apart from what I’ve picked up in discussions and perusing publications. But the bottom line seems simple enough: We learn in a context, or knowledge is contextualized. This is probably correct – it squares well with the well-known problems with transfer of knowledge from one area to another. There is probably more to the theory than this – or there is perhaps not very much more to it – I sometimes get the impression that people in pedagogy has a tendency to take what’s simple and make it look more complicated. [Feel free to comment on this!] [And I’m not giving any references – this is a blog – not an academic text.]
What did I try to say? Yes, if knowledge is contextualized, perhaps you can turn that around and tailor-make courses and learning experiences to achieve a precise learning goal? Is this what teaching/learning bureaucrats (if the expression is allowed and whoever these are) are trying to achieve with setups like “constructive alignment” and the (in)famous Bologna process, or just in rewriting curricula in terms of learning goals?
If you’re likely never to need algebra – then why learn it in the first place? But if you’re likely to use some algebra – then what parts of algebra to learn? Clearly you see the impossibility to answer a question like that.
More confused than ever!