Make the 8 a 10 and break down the 5 into 2 and 3, with the 2 going into the 8 to make 10, then add 3 to the 10 to get 13.
Who thinks like that?
I didn't watch the youtube, but I will admit that this is the kind of logic that my mind goes through for a lot of arithmetic. It works for me, but I'm not sure I could explain it well to someone else. And I am certain that it's not a mechanism that works for everyone.
A possibly better example than solving 8+5 might be how would you solve 97*3 in your head? I think that many people would juggle the numbers so that it's 100*3 - 3*3, which is easy to work out in your head (or mine at least) as 300-9 = 291. I know that how I'd do it, and it's a similar transformation to 8+5 being the same as 8+2 + 3 = 10 + 3 = 13. It's just that the 8+5 problem is pretty simple by itself, so there's probably less need for the transformation 'trick'.
I think that there are different ways of approaching arithmetic, and that there's not 'one-true-method' that works for everyone. Each person should find their own best way to working out basic arithmetic, and I think the best elementary math teachers are the ones who are able to somehow guide different students to the different ways that work for them.
