Crikey, I was totally lost by the posh name given to this type of maths! But now having read Aaron's explanation I have to admit that this IS actually how I work out large sums in my head. Okay I know 35x2 is 70, but for something like 15493 x 3 I would break it down into a combination of smaller sums and then add them together!
In this case I would do
15x3=45x1000=45000
500x3 = 1500 (rounding the 493 up to to 500)
545000+1500=46500
500-493=7, 7x3=21
46500-21=46479
It's a strategy for mental maths I think that most of us DO actually use in real like but don't think about it because it's something we do automatically.
I agree that kids are taught WAY differently than we were and that is a huge struggle for parents at home. I often have to stop my DH from insisting on showing the kids 'the right way to do it' (ie the way we were taught). As my children have moved through school I can see that they do get to that stage eventually, but they progress from a much more visual representation of numbers to start with.
And speaking for myself, these alternative learning strategies are incredibly helpful for my youngest who has learning difficulties.
Oh ... and our school does periodically have parent evenings whereby parents are invited along to workshops to learn about the different teaching methods.
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