The standard view is that American kids aren't as good at math as kids in other countries and are learning less than we did "back in the day", but from my own experience I can say that our educational system currently expects more people to know more math than at any time in history. AP Calculus was pretty rare in my era, and expecting high school students to get through statistics or a beginning programming class was absolutely unheard of back before 1973 when the integrated circuit started the computer revolution. When I teach linear algebra at Berkeley City College, I can expect a lot of kids from Berkeley High School sitting in on what is still viewed as a sophomore level college class. Some material has been "dumbed down" without question, most notably reducing the emphasis on proof in geometry. As someone who was actually pretty good at it, I'm not exactly sure when we should ask students to sink or swim with the concepts of proof, but I think it's probably not something we should force on all kids at the age of sixteen with the threat of not graduating high school.
Friends send me links to articles about math and math education. My friend Ken sent me an interesting article from the New York Times quite a while back about the correlation between mathematical success in school and an early talent for estimation. As the article states, the skill of looking quickly at a picture and deciding if there are more blue dots or red dots is math brought down to the level where the test could be administered to lab rats, but people who show an early skill at this tend to do better in math than people who don't.
My friend Art sent a link to a paper done by some researchers from his alma mater Texas A&M that states American students somewhere in their early education are not grasping the concept of the equal sign as well as students from other countries. If the problem is stated as 3 + 4 + 2 = (____) + 2 for example, many students will add all the numbers from the left side and put a 9 in the blank, when the correct thing to do is just add the 3 and 4 to put 7 in the blank. I see things like this in my classes that appear to me to be about reading comprehension, especially on tests. If the instructions say "round to the nearest tenth of a percent", I will invariably have some students ask "Do you mean to the nearest tenth?" It's almost as if they run out of gas before they get to the end of the sentence.
It raises a question relevant to all education, not just math education. Most people who teach a subject decided to do this job because they are good at the subject, and with disciplines like math, music and athletics, innate talent means some people will be better than others even though they put in about the same amount of time in study or practice. It can be hard for the innately talented to get ideas across to people who don't have the same gifts, much in the same way as it would be for a person without colorblindness to explain green to someone who can't tell green from blue.
The struggle continues.