julietteculver.com

The myth that all educational content exists on the internet

September 2005

I think one of the myths I feel I keep hearing about university-level education is that all the required 'content' exists and we just have to facilitate students interaction with it, or that content itself is totally unnecessary and students can somehow invent it everything they need for themselves given the right stimuli.

From my experience, it just isn't. I studied Galois Theory in my second year at university. It's something most people who would call themselves a pure mathematician will have studied. It's not an obscure subject in the scheme of things, but most students struggle with it enormously.

However I've never seen a really good explanation of Galois Theory written down anywhere. Amazon lists only about three or four appropriate books on the subject (though I have to confess there is a new one on there I've never read). When I was a student I eventually did understand it because I thought about it all very hard and plagued my tutors with questions.

Now I could replicate some of the processes I originally went through in trying to make sense of the subject by asking the right questions to the students I used to teach and explaining the approach I took to trying to learn a strange new subject. But contact hours are always limited and however well I try to train them to solve mathematical problems, they're obviously not going to reinvent Galois Theory all by themselves. At some point, they are going to need hints in some form when I'm not there. And the 'right set of hints' is the content that doesn't exist.

When I taught the subject, I ended up essentialy writing these myself in the form of worksheets for the students to do between tutorials. Sometimes the questions in the worksheets were quite open-ended ('Go and find proofs of this theorem in two different textbooks - how similar are the two proofs? which do you prefer and why?') but a lot would be more traditional because you have to make sure the students don't go too far off-track and waste too much time getting nowhere when you're not there. I really don't think I could have taught the course effectively without spending a fair amount of time using my subject expertise to produce this 'content' for my students.