If you calculate your change without borrowing you just did common core math.
Borrowing?
Borrowing?
Compare that to how you could solve the problem in your head.
.01 + .70 + 6.00
For my example I bet you'd think 5¢ + 50¢ + $5.00 to compute your change.
Also, when you say the +0.01 and +0.70 there, aren't you implicitly borrowing anyway? It's just "easier" borrowing -- you say that 0.09 + 0.01 = 0.10, as opposed to explicitly borrowing the 1 to the second decimal and subtracting the 9. Similarly, you say that 0.30 + 0.70 = 1.00 instead of borrowing the 1 to the first decimal.
I can see why this makes mental maths easier, but I don't see that it is any deep conceptual improvement over the borrowing. Is one of the goals of Common Core to improve mental arithmetic? If so, then this makes sense. Otherwise, unless you properly explain why the two are equivalent, and why the other method is faster, it's more like a neat sleight-of-hand trick that might leave kids slightly more confused about why it is "better" than the borrowing method.
[Reference: Non-American, non-parent who knows very little about the American education system, but has some friends teaching in it.]
All math solutions will be equivalent. And it isn't a parlour trick. It's teaching kids to think about breaking down problems into smaller units and composing a solution. The rote algorithms work, but training kids to execute an algorithm won't help them understand.
The long form subtraction algorithm isn't a skill that carries over to multiplication. Breaking a problem into smaller components, composing a solution, and checking with your original estimate does carry over. And not just multiplication but programming as well.
EG:
$20 - $14.45 = ...
$6 ($0.45 excess)
$5.60 ($0.05 excess)
$5.55 ($0.00 excess)
$20 - $14.45 = ...
$0.05 ($14.50 total)
$0.55 ($15.00 total)
$5.55 ($20.00 total)Once you know the basics of how to do something you do not need to continue to get better at it if your computer can do it better for you. Learn something else with the saved time.
Edit: Quick example: Is like marveling that you can do arithmetic in your head with 100 digit long numbers. Impressive? Yes. Useful? Nope. Is actually less than useful because all that time wasted you could have used it to learn something else.
Meanwhile, the better students don't bother memorizing the rules, they just focus on solving the problem. Once they see how the problem is solved, those rules either come naturally, or are supplanted by some other process that also works.
This is not about parlor tricks, but about creative thinking. How do you determine whether your 'trick' works or not? How do you know if the problem is solved? Most students believe a problem is solved when they get the 'right answer' -- which often includes "doing what they were told." This is NOT how you identify a solution to a problem. The students who are left behind are the ones who never figure this out.