When I learned calculating left to right it sped up so much of my daily arithmetic. I didn't learn to do that until I was 27. I feel like I wasted a lot of time doing it the hard way first.
This is what they're trying to do with the Common Core. We should teach everyone these strategies, not just let smart people figure them out for themselves have everyone else be left behind.
But they don't explain WHY! If they gave the kids even a basic bit of number theory, it would make so much more sense. If they want to teach the methods they are teaching, substitution and algebra need to be part of math from year 1 and commutativity and associativity need to be explained as more than just vocabulary words.
We tried that in the 70s. It was called New Math. It failed because parents and teachers didn't already know basic number theory. Some students (like me) were in special programs with well trained teachers, and became highly successful STEM professionals.
Hyperbole Much? Left behind from where? Seriously, a couple of parlor tricks are not gonna leave anybody behind. Use a computer and devote your higher cognitive skills for more productive endeavors.
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.
You're missing the point. Many maths students learn to dislike math because they cannot remember the rules, or they find them frustrating to use. They are often trying to appease the teacher by mimicking the process.
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.
Firstly, I think you probably mean +0.01 +0.70 +6.00
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.
Borrowing?