Part of the problem is cultural - it's socially acceptable to "not be a mathsy person" in many circles, and almost a badge of honour in some. Another problem i

Part of the problem is cultural - it's socially acceptable to "not be a mathsy person" in many circles, and almost a badge of honour in some. Another problem is that the discovery learning approach can lead to some horrible failure modes for math. I've seen cases where an hour of proper instruction can go further than a whole term of trying to see if they can find it out for themselves. Case in point: the rule of three. If 10 apples cost $20, then 5 apples cost ___? You can spend ages thinking about what it "means", or you can learn that you write down a 2x2 table, multiply across the diagonal and divide by the number in the corner.