Dear Frustrated Parent,
Feel bad. I have a Bachelor of Arts Degree in English, and five seconds is three too many. However, if you actually read the problem (see? English Degree!), what is asked of you is to spot the mistake, and then verbalize what the person did right and how to fix the mistake. For example:
Dear Jack,You don't get to tout your calculus credentials if you can't tell the difference between '306' and '316' on a number line. But this is a very well-constructed problem: children are not asked to display the mere technical mastery of mechanically producing the right answer, they are asked spot how that process can go awry, and to verbalize their understanding of the conception and the mistake. Good, good stuff.
To subtract 316 from another number, you need to jump back three hundreds, one ten, and six ones. You got the 'hundreds' and the 'ones', but you forgot the 'tens'. Just remember it next time and you'll be fine!
Someone Who Read the Problem and Can Count
Now: ignoring the fact that this has nothing to do with Common Core, and ignoring the fact that our parent's frustration mostly stems from lack of reading comprehension, the 'new method' is more or less how I taught myself to do math in my head when I abandoned the clunky, overcomplicated, counterintuitive bullshit they taught me in school in favor of something that not only made more sense to me, but that was faster, more likely to be correct, and generally wrong by a smaller margin when I screwed up. Sure, the old way looks simple in those neat little lines the way that you write it out. But let's try a different problem. Let's say, 426 - 327.
First do it my way. We start by taking away three hundreds, 4 - 3 = 1, leaving us 126 - 27. Then we take away twenty, 2 - 2 = 0, leaving us 106 - 7. Then we take away seven: count back six to 100, then count back 1 more to 99. 426 - 327 = 99. This is an intuitive, left-to-right approach, like the way that we read, and it consists of two one-digit subtractions and one counting back: three operations, and as errors are more likely to compound the further into the problem we get, we're more likely to get an error in the 'ones' column than the 'tens' or 'hundreds'.
Now let's try it your way:
6 is less than 7 so we have to borrow:
16 minus 7 is 9, so:
So, 1 minus 2 ... whoops have to borrow again!
11 minus 2 is 9, so:
and three minus three is 0, so ...
Thus we have: two multi-digit subtractions, one single-digit subtraction, and two complicated borrowing operations, all going in a counterintuitive, right-left direction, with the hundreds column coming last, meaning that compounded errors will have a vastly greater effect on the magnitude of any wrong answer. Got all that, kids? In the real world, simplification is valued over complication---this might be why it takes you more than twice as long as me to do arithmetic. I certainly hope that wouldn't result in my termination, but if one of my engineers couldn't figure out a number line--or understand a word problem, or spot the difference between 306 and 316--it certainly would result in his!
Bemused English Major