On the eve of a new academic year of teaching and as usual I'm worried about getting the balance right. It's the usual conflict. Students are required to know the subject well enough to pass exams at various points during the next 8 months. There are various methods and techniques I can employ to ensure this happens. But if that was was the only focus of the course then I'd be guilty of "teaching to the test". Students would probably pass the exams but they'd be ill-equipped to handle new material or cope with even small variations on what they've already seen.
As a maths teacher I want my students to be independent learners. For me that means they are able learn from their mistakes and that they have strategies for thinking about and solving mathematics problems in a very general way. The intensity of my course - the amount of time allocated and the material that the students are expected to know - means that I definitely won't get enough sessions emphasising skills required to be an independent learner.
In practice what will probably happen is that I build some kind of activity into most classes where I get the students thinking about how to solve a problem that isn't textbook. There are plenty of teachers blogging about how to do this and lots of real world scientific examples to draw on.
Anyway, I'll record the best examples of my strategies here!
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Dr Adrian Jannetta. Amateur astronomer, maths teacher and science enthusiast.