Admittedly I was in school multiple decades ago, but our teachers wanted us to memorize addition and multiplication tables. Which of course made anything outside the tables hard to do. I (and others apparently) thought it would be a great idea to use shortcuts like this.

So many failed tests. So many. When teachers saw us write down that we took the 21 apples multiplied by 7 bushels and just did 2x7, and tack a 7 on the end, they broke out the red pen.

Yup, this is what parents are complaining about when they say math has changed. Before, math was primarily about rote memorization. You just memorized that 9+7 is 16. There were multiplication tables you were expected to memorize and regurgitate ad nauseam. Sure you could count it out on your fingers, but that only works for numbers under 11. For anything above that, you just referred to your memorized addition, subtraction, multiplication, or division tables. But this also meant that numbers outside of those tables were really difficult to do in your head, because you were poorly equipped to actually calculate them out.

Common core math is attempting to make math easier to do in your head, by teaching the concepts (rather than promoting rote memorization) and helping students learn shortcuts to avoid getting lost. 9+7 is 16, but it’s also 10+6 or 8*2, which are much easier to visualize in your head without counting on your fingers.