Taking the problem in the illustration, subtracting 12 from 42, the four-step process is ridiculous. The way an adult would look at it in a real-world situation is to recognize that the 12 neatly coincides with part of the 42. The relevant concept is units of 10 and of less than 10. One might use a somewhat different concept for a different question.

I'm not sure of the best way to teach the concepts - cover base 10 and places first, I guess, and then talk about how and why adults who are good at math perceive problems in certain ways. "Common core" looks like about what I would expect when the USG takes a basically good idea and mashes it thru a bureaucracy.

This really doesn't have anything to do with common core. Different curriculums that the school districts choose to purchase and implement go about achieving the goals of common core quite differently. Everyday Math is mentioned in another comment and is mostly awful. It's pretty widely used though. We are actually moving to a house in my wife's school district this summer so that our son doesn't go to school where we currently live to avoid both Everyday Math and an equally awful reading curriculum.

If you can't just look at something like 2x = 4y and instantly simply it....

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.

If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.

You are not a six year old child learning arithmatic. You have missed the point.

> The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”

Mental methods are taught so that children do understand numbers, which gives them a better grounding for future learning.

Waving a hand and saying the "old way" is simply an algorithm and a poor method because it glosses over the details is like saying teaching someone how to use a calculator will make them forget how math works.

That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.

That was a point I made elsewhere on this thread. When helping my second-grader with her homework, it sometimes seems that they are just changing what the student is required to memorize (and also increasing the volume), without necessarily imparting additional understanding.

That problem relies on what they call the "Add it Up" method, and it is specifically a technique with which I've helped my daughter. I observed that kids can completely learn the method and ace a test without understanding the concepts behind it.

> That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.

You do not understand what it is trying to teach. It is teaching children that taking one number from another can be done using columns, but it can also be done in your head by breaking big numbers down into small numbers and counting up.

It's like asking why ever read a book, with a level of english past the level of a memo asking if you have completed a task. This article also seems to suggest that people don't understand how to preform basic mental arithmetic.

In the states there also seems to be this insane way of thinking that you should learn an algorithm to do things in a particular way, if you can do it one way you should understand it and all the other methods should just fall into place.

This is a pretty good explanation of the problem. https://www.youtube.com/watch?v=5ZED4gITL28

(hey I took double maths for A-level and enjoyed every minute of it)

    12 = 2 + 10
    32 - 2 = 30 
    30 - 10 = 20

http://brightbacon.com/blog/work/how-count-back-change-begin...