Have things really changed that much? A letter to a friend.

You ask whether things have changed -- since math wasn't being taught well 40+ years ago either.   You're absolutely right on that, but I believe it's only gotten worse over the years, as more and more math phobic people have gone into the field of education.  These people never understood math well, so their teaching had to be based on rote following of procedures, etc.  Then came "new math", which was an effort to reinvent math and make it more accessible.  That bombed, and the efforts to reinvent continued. 

What happened is that eventually those bright, math-phobic folks took over the education establishment.  They reinvented math to be gentler, kinder, and more fun.  Some of the hallmarks are: Small group problem solving, with students figuring our their own solutions to challenging problems.  Visiting many topics for only a few weeks each year and moving on, regardless of whether any real mastery was attained. The thinking was/is that students will revisit the topics again in successive years, and will painlessly absorb the concepts.  As appealing as these ideas are, it turns out that they don't work reliably, as evidenced by ensuing decline in achievement scores, skyrocketing tutoring businesses, as well as skyrocketing rates of remedial math in our colleges. This also turns out to be an extremely inefficient way to teach math; in order to have enough time to do all these hands-on projects in groups, the explanation of the underlying structure of math and practice with standard algorithms have all been abandoned. 

It's been a grand experiment that has failed; the "discovery" books are confusing and inefficient.  Now, the vast majority of students feel irritated and demoralized about math.  Middle class whites can often afford tutoring, so they do better than minorities, but all are affected. It's been going on long enough so that we have statistics now to demonstrate that these "reform" books are making things worse than ever before. So, yes, things have changed.  We're not even trying to teach math, we're teaching "pretend math" and lo and behold, very few are developing math skills. What most students have learned is that they don't know how to do real math; instead of gaining skills and knowledge, they've internalized the belief that they can't learn it.

Where did we go wrong?  We never tackled the problem of teachers, particularly elementary teachers, who do not have a "profound understanding of fundamental mathematics." It turns out that teaching elementary math is really, really hard. Yet, teachers in China with way less education do it much better than we, primarily because they are carefully mentored by, and paired with, experts; this happens over years and years.

The reform approaches have added some very valuable elements to math education -- for example, use of physical objects ("manipulatives") in early grades to help students make the connection between concrete things and symbols. They've also introduced scads of wonderful problems.  But the traditional books had a lot of very good math context that needed to be explicitly presented, and not left for students to "discover" on their own -- what discoveries are made in modern classrooms would need to be organized and carefully studied in order to be understood, and there's no time left for that. Besides, that would be seen as "boring" and "not kid-friendly."

So, IMHO, we need to get solid texts back in our classrooms and set about the very, very challenging task of helping teachers to learn real, hard core math. For example, such skills as adding and dividing fractions are mysterious to huge numbers of elementary teachers, yet these skills are really helpful in daily life, and essential to mastering algebra, which is nowadays the "gateway into the American economy."

So, that's as much of it as I can cram into a few paragraphs.  Thanks for asking about this issue about which I'm so passionate.

Marty
P.S. The phrase “profound understanding of fundamental mathematics” comes from LiPing Ma's very enlightening book, Knowing and Teaching Elementary Mathematics. Robert Moses is the first person I know of who referred to Algebra as the “gateway into the American economy.” He wrote a book called, Radical Equations: Civil Rights From Mississippi to the Algebra Project. I found it completely riveting. Moses recalls his experiences in the civil rights movement and finds parallels with his championing math education for inner city students in Boston from the 80's to the present.