As I said before, I wonder if "teaching" math processes...like long division and multiplication, mixed fraction solving...too early is taking away from the overall understanding and problem solving skill that are so important for solving word problems...
Any thought?
I should say that I'm not a teacher of children and I acknowledge that what suits my DS might not suit all children, but... yeah. I think the issue is teaching an algorithm at a stage when it looks to the child like magic. If the child really understands why the algorithm works - I don't mean so that s/he could write a formal proof of it, but so that s/he can see which modifications of it are legitimate and which are not, through really understanding what the algorithm does and why this is a useful thing to do - then learning the algorithm should be quick and easy, and might even be unnecessary, as s/he might be able to invent one when it's required.
On the other hand, if the child doesn't have the background understanding or isn't developmentally ready to learn what's needed, then the algorithm is hard to learn and prone to being misremembered. It will then certainly not be correctly remembered in later life. The child might be able to do that kind of question in a test, but won't have much chance of doing problems that require a slightly different method. It's hard to think of a case where there's really any point in that sort of learning.
There must be a middle ground - a tricky judgement area for teachers, I expect - where the child hasn't quite got there but almost, such that practising the algorithm might actually foster the missing understanding.
As a parent, I try to watch how much input DS needs to do a problem. If it's a quick hint/reminder (e.g. recently when he was trying to turn a recurring decimal into a fraction, and couldn't remember how to go about it, "what I'd do is multiply by something so as to get rid of that pesky infinite decimal" was enough to remind him broadly of the technique he needed - see how little info there is there compared with the full algorithm) then I see the problem as being in his ZPD and don't worry. If he needs a hint, and then another hint, and still isn't there, I reckon he's missing something and go for a more basic problem.
