<p>I think that there are two very different approaches to math that can explain this dichotomy.</p>
<p>First off, a lot of schools (I know mine does) stress rote memorization and completion of exercises in their math classes. What I mean by that is, for example: here are two lines on a plane, here are two particular methods to find where these two lines intersect, solve these 8 different but very similar systems of equations. Now, people who do well on these are just good at following algorithms, and often they can get 100% and think "Wow I'm good at math!" Ok. That's one approach.</p>
<p>The other approach is far more organic and interesting. Instead of following algorithms to solve Exercises (which test one's ability to use a mathematical tool, say, intersecting lines or chain rule or taylor series), people learn math by understanding the fundamentals, the symmetry, elegance, and ... 'tricks' behind the math. These are the people who succeed on the SAT, because when you near the end of the test, quite a few problems require this kind of thinking (and remember, 2-4 problems is the difference between 720 and 800). When people approach math like this, not only do they not have to memorize anything (everything is UNDERSTOOD), they have the ability to learn more math with much more appreciation and depth of understanding.</p>
<p>Another thing about the SAT is you have to be extremely careful. More often times than not a question is deceptively simple. If your sons have 5s on AP Calc they might be deceived into thinking that the questions are all simple exercises (as opposed to problems, which require more creative and intuitive thought). Some are not. There are a few that catch people off guard. I recommend, after the first 7-10 problems, that you devote an entire minute to each problem. Even if you get it in 20 seconds, spend another 40 seconds reading each word twice. That'll help a lot.</p>
<p>Of course, there are only like ... 3-4 questions that really require this kind of thinking (it's still only the SAT), but this attention needs to go for every problem to go from a good score to a great score.</p>
<p>Btw 800 on both SAT Math and SAT II Math II and 5 on AP Calc BC</p>
<p>But can you tell not an 800 on writing? LoL.</p>