SAT math tries to trick students. You could say that the tricks relate directly to whether or not they really understand math. However, when you add in the time constraints, it really relates to preparation. Is preparation the same as mastery? Yes. Mastery of the test. Is this equivalent to mastery of math or whether you will do well in college math? Not necessarily. There are better ways of determining that than with the limited material included on the SAT. Why not just require students to take the Achievement Test? Look at the AP Calculus grade.and:
What is it about SAT-Math that is so important? They are trying to test something other than just math knowledge. They think that these tricky questions reflect on how well you think on your feet, but what it really does is test preparation and whether you have seen these questions before. The questions don't reflect on whether you have a wide body of knowledge and skills in math.
They create problems where you have to "see" the shortcut. You get problems with hidden 3-4-5 triangles. Add a time constraint and then what do you call those problems? It's not just about math knowledge and skills. The problem has to do with trying to determine the difference between aptitude and preparation. The tricks may have some basis in meaningful math, but that's not what they are trying to test.
It reminds me of questions companies like to ask at job interviews, like "Why is a manhole cover round", and "How many golf courses are there in the US.?" Preparation can make you look like you have a great aptitude. Preparation is directly related to math knowledge, and that is important, but identifying aptitude is an arms race for something like the SAT. That's causing the tricky problems, not any desire to test a breadth and depth of math knowledge.
In Dick Feynman's books, he talks about how he spent a lot of time in high school learning about all sorts of trick, lateral thinking problems. He would challenge people to ask him questions. There is nothing like preparation to make you look like a genius, although he really didn't need help with that. It really annoyed some of his colleagues.
My son will get to calculus in his junior year and he always gets A's. He still has to prepare for SAT-Math. He can't let others, with specific SAT-Math preparation, seem like they have a better aptitude than him.
They try to trick students in most questions....What bothers me the most are the shortcut problems where using standard math techniques cause you to take too much time. This is supposed to identify aptitude, but it really tests preparation for the test.
There are also the problems where using a brute force or direct counting technique works better than any applied math technique. In some cases, there is no math to apply. One question on a sample PSAT test asked for the number of positive integers less than 1000 which don't have a '7' as one of the digits. (notice - "don't have" and positive integer) This simply checks how well you work under time pressure. Nobody expects you to apply any fancy math to this problem. One of the answers was the "have" solution. This tests preparation and practice, not aptitude or math ability. There may be a correlation between the test and aptitude or math ability, but not to the resolution colleges use it to select students. At the top levels, it correlates to preparation. That's not necessarily a bad thing, but there are better ways of figuring that out.