Someone has had fun writing a
Wikipedia article on rigour, and in particular, the section on rigour in mathematics is OK. Suppose you spot a pattern, say, that every multiple of 3 has its digits add up to a multiple of 3. Then to use this pattern, just from having spotted it, to claim that 126981 is divisible by 3, would lack rigour, and in a rigorous mathematics curriculum, a student who did this would be penalised. To be properly rigorous one should first prove that the pattern always holds, and only then apply it. Somehow I doubt that the maths curriculum your schools are about to switch to is going to be rigorous in that sense, but you can dream...
