I'm not a math teacher, and my children aren't school age yet, so I have no real experience with CC.

..and it leads me to believe that CC is largely the answer to made-up problems.

DAD22, I'm going to put it to you that if your kids aren't in school yet, you probably aren't aware of the full horror of US math "education." It's a disaster from start to finish. To summarize, there are two basic paths to teaching math in this country:

1.

Memorize and Regurgitate. See most big-publisher textbooks (e.g. Sadlier-Oxford). These programs teach nothing about concepts in mathematics. They present algorithms to be memorized and provide worksheets with 35+ identical problems. 35+64= 48+89=

Again and again and again. And more of the same tomorrow night!

2.

Reform math. See Everyday Mathematics or EnVision math (there are many options on this menu, however). Reform systems use gimmicks, faddish approaches, and calculators in a largely botched attempt to teach concepts. The people who made them were right about students not learning concepts, but their solution is as bad as the problem it purports to solve. In these systems, standard algorithms are b-a-d and we need to teach several different approaches to [insert operation], no matter how kooky or mathematically incorrect. Look up partial products as one egregious example. Partial quotients is another.

Guess-and-check assumes that you have all day to solve a single division problem.

They want me to believe that understanding similar triangles is a prerequisite for understanding the slope of a line? I don't buy that. I don't believe that everyone comes to an understanding of the slope of a line in the same way.

A huge problem in math education in this country is that there are way, way, WAY too many approaches to teaching an idea. Most of them are created (and taught) by people who don't understand mathematics. You, as an intelligent engineer, may be able to see different correct ways to teach the slope of a line, but what you probably don't understand (YET) is that the vast majority of current curricula botch it completely.

I should mention in passing that CCMS makes the effort to teach similarity in grade 8 not just for making sense of the concept of

slope. It also serves the larger purpose of laying the groundwork

for high school geometry.

This is part of CCMS's overall eort to maintain grade-to-grade continuity.

IMO, his points about the slope of a line show the beauty of mathematics. Look kids! This stuff is part of algebra! And it's part of geometry! It all fits together.

Let's consider a line with a slope of 0, or infinite slope. Where are their triangles now?

There is no slope in the former case. And you can't calculate it in the second one. You could still use right triangles, though, if you really wanted to.

What goes on in their heads is their own business, and their ability to relate that to others is an issue wholly distinct from mathematical mastery.

On the contrary. Being able to explain something is critical, if for no other reason than because it teaches you how to explain something in a logical way. This skill is critical in the workplace and elsewhere.

But explaining it also proves that you understand it. Richard Feynman used to say that if physicists couldn't explain an idea to freshmen physics students, they didn't really understand it to begin with. This was taken as a sign to keep trying to figure it out.

Again, if your kids aren't in school yet, you probably haven't plumbed the depths of how bad our math education system truly is. It's kind of hard to believe it when you haven't witnessed it. I have a 13-year-old, and I'm still discovering new layers of horror below the ones I've already found. Just when you think they've hit rock bottom, someone comes along with something insane and you discover a whole new system of caverns of badness.

If your kids are lucky, the CC may save them. But it's more likely that they'll come home with 35 examples of the same problem to do, or will be using boxes or lattices or calendar-like-constructions to do basic arithmetic. And with each passing year, you will try many different reasonable approaches at advocacy, and all or nearly all of them will fail. You will tear more of your hair out until, like KADmom (and me, and HowlerKarma, and most others here), you will begin to feel that gut-wrenching desperation-resignation that results when you finally realize that how bad the schools truly are, public or private, with very few exceptions.

No, I am not making this up.