> What really surprised me was the core principle at British unversities - "don't assume prior knowledge of anything"...
I think it is a good thing. There is a big difference between doing well on a test and understanding the subject. You may think you know basic algebra because you can find the correct value for x, but chances are that you don't really know what you are doing. So having a refresher course telling you what you are actually doing when solving an equation, and how it fits in the big picture is valuable.
The thing is: when you relearn these basic subjects, you do it with a wider field of view. For example, when I first learned derivatives, I knew it had was about rate of change, and I knew the formulas, but I didn't quite get the relationship between slopes and derivatives. It came back later, as I was more familiar with things like linear interpolation and how to manipulate curves in general.
Yeah, I'm not saying that it's a bad thing, just that I was really surprised by it. In the entirety of my Polish education it was drilled into our heads that we had to be super good at algebra for example, because "no one at university will wait for you to learn, you have to know it before you start" - and then I went to a British uni, and well, people did wait for us to catch up, which lead to me having a very relaxed 1st year, while I know from my friends that at Polish unis the 1st year is actually the worst one as that's where a lot of people get kicked out for failing exams and there is a lot of catching up to do. In a British uni it was the opposite - I have no idea what you'd need to do to get kicked out of the course in 1st year, I've never heard about that happening to anyone, while in some Polish courses the attrition rate is above 50% in the first year.
UK universities generally have a low attrition rate (at least to failing exams). If you struggle with the subject you may wind up dropping out on your own due to stress, but if you stick with it you'll probably still technically get a degree, just a third or an 'ordinary' (which is basically a fail: I don't know many employers which will count it as a degree).
Also, the way mathematics is taught at high school might not prepare you well for the way you use it at university.
Maths in high school focuses more on applying methods (taking a derivative etc.); maths at university (even on a CS course) is more about constructing mathematical models and arguments.
It can almost feel like a completely different subject.
It is interesting that you say that because I had huge variations in my test results, dropping from top of my class to the bottom in an instant, then back to the average.
At one point I met a guy who was working on ways for computers to solve math problems. He told me that early college level problems are actually easier to solve than high school problems for his algorithms. The reason is that while college problems have more steps, and are therefore harder for students, you essentially just need to string theorems together. High school level problems are simpler (less steps) but require significantly more intuition.
And that's what I think happened with my grades: I was never good at math, but I had good intuition. And the switch from using intuition to using actual rigorous mathematical thinking killed me. It was like a completely different subject, and it took me years to catch up.
I wouldn't say if was it was different when it comes to applying methods vs constructing models.
I think it is a good thing. There is a big difference between doing well on a test and understanding the subject. You may think you know basic algebra because you can find the correct value for x, but chances are that you don't really know what you are doing. So having a refresher course telling you what you are actually doing when solving an equation, and how it fits in the big picture is valuable.
The thing is: when you relearn these basic subjects, you do it with a wider field of view. For example, when I first learned derivatives, I knew it had was about rate of change, and I knew the formulas, but I didn't quite get the relationship between slopes and derivatives. It came back later, as I was more familiar with things like linear interpolation and how to manipulate curves in general.