Common Core includes memorization of tables. For instance, it explicitly calls for knowing from memory all products of two one-digit numbers by the end of Grade 3. By the time the students get to algebra, they'll be ready for simplifying 2x=4y.

What is covered in each grade is given here: http://www.corestandards.org/Math/

A lot of the criticism I've read of it seems to be from people who have been comparing grade X of CC (where X is the grade their kid is in) to what they remember learning in grade X when they were a kid, and conclude that CC does not teach the things they learned in grade X. In fact, it often does teach those things--just in a different grade, or later in the grade X year.

Note that I'm NOT saying CC is better than prior K-12 math programs. I'm just saying that comparisons should be done between CC and prior programs by comparing them as K-12 programs, not by comparing them for specific grades.

But I'm replying to all those who denounce rote memorization in whatever context, and claim this is not necessary to be good at math (or for a very large fraction of children, phonics, in order to later read well).

(It's something I've recently gotten really focused on, after a sister-in-law asked for help: one of her kids is great with numbers (even deduced negative numbers on his own, and asked her what they meant), but the eldest just cannot memorize the math tables, and we're despairing about what to do.)

The book A Mathematician's Lament really registered with me due to this experience.

So, while I don't know enough about educational theory or the Common Core mathematics curriculum specifically to say for sure that it is better than rote memorization, I can say my bias makes me think nothing could be worse.

The math practices I see elementary school kids doing under Common Core seems to be way more like "real" mathematics than what I did at that age.

I will say, I worry about the population of elementary school teachers who are asked to implement this, as a generalization they are the least likely to have taken advanced mathematics in university.

"Motivation" at a higher sense is something that's sorely lacking in US public school (free government school) math. Especially prior to real algebra, the teachers tend to be generalists who don't know to tell you "you need to learn X so you can learn Y which will allow you to solve problems like Z" and of course get you to understand why Z is neat and important. But that's a different sort of problem that just not making sure all students capable have the foundation they need.

Rote memorization of times tables doesn't lead to understanding. So, early in the learning process, you give children techniques that give correct answers, boost confidence and increase understanding of what is actually happening.

Thus when they see 4x = 2y they'll know that 4x means 4 xs and 2y means 2 ys.

If what we are trying to teach is this abstraction, then the rote table method is arbitrary* and a time sync. The students will still learn basic sums over time, it just won't be the focus of the practice.

*For instance, my education with the tables went up to 12s. Why in the world did we choose 12? 16 would have certainly helped me out more.

To solve your problem with the same technique as the article, you would have added 1 to 52, 73 - 53 = 20, then + 1 for the answer.

You would need to know ball park anyway to see if the calculator answer made sense.

You don't need arithmetic to learn pattern recognition.