SAT math and high school math are very different animals. In high school, students study one concept at a time, from one area of math. For example, most students take a year of geometry. During that year they might study angles, then triangles, then polygons, then circles. After studying a concept for a couple of weeks, they're tested on that concept. For the test, they mainly have to recall the information learned over the prior few weeks and apply it over and over again in slightly different ways.
The SAT tests dozens of concepts from different areas of math. What's more, many problems test multiple concepts within one problem! Students can't simply regurgitate the same information again and again. They have to use their critical thinking skills to evaluate the information provided and determine the concepts, equations, or strategies necessary to solve the problem.
Student who do well on the SAT are not necessarily the ones who receive the highest scores on their classroom tests. But they are the ones who understand how math works. They are the ones who can reason out an answer even without a handy-dandy formula.
So how can you help prepare your child? Here are some tips:
Know the Facts
The SAT is a timed test and every minute counts. So having basic math facts memorized obviously helps. Yes, students can use calculators, but calculators are easy to confuse. Hit plus instead of minus or add an unnecessary decimal and your answer is thrown off. I've seen many many students multiply 36 x 9 and get 4 without realizing that something strange is going on. I love the free site XtraMath for memorizing facts. It's simple, graphic free, and kind of boring, but it gets the job done!
Work the Word Problems
The SAT is the wordiest math test you'll ever see. Many students can't even figure out what the problem is asking them to do, much less how to solve it. Public schools do spend more time on word problems than they used to, but it's still not enough. Particularly at higher levels. Two useful resources are Singapore's Challenge Word Problems workbooks and The Art of Problem Solving curriculum.
Don't Give Partial Credit
Teacher's often give students partial credit if they solve the problem the right way but make a calculation error. The SAT does not, and for good reason! I remember watching my husband and father-in-law build radiator covers for our old house. They knew how to do the calculations, but kept making minor mistakes. Much cursing ensued when the resulting radiator covers didn't fit over the radiators. There's not such thing as a "partially correct" answer to a math problem!
Mix It Up
While new concepts clearly need to be taught one at a time, it doesn't mean students should only work on one type of problem at a time. Every lesson should end with review problems from several different areas. And as students get older, problems should be multi-step and multi-concept. For example, the SAT often gives students the area of a square inscribed in a circle, then asks for the circumference of the circle. Students must use their knowledge of area to find the length of the square's sides. Then they must use their knowledge of right triangles and squares' diagonals to find the length of the diagonal. This in turn is used to find the circle's radius, which is then (finally!) used to calculate circumference. See why your teenager's head is spinning?
Don't Wait to Get Help
If your son or daughter is struggling with math, don't delay getting help or hire a "homework tutor." I have frequently been asked by parents to tutor their children by helping them with their homework each day. I see two problems with this. First, it's just treading water. Students who are struggling generally need to go back to the basics and move slowly forward from there, filling in gaps in knowledge and skills as they go. Second, it teaches the student to be dependent on outside help. Tutors should help students master concepts so that they can do homework problems (which are designed as practice) on their own. Math continues to build each year, so getting your child help with pre-algebra will be much more useful then trying to diagnose what she's missed when she's in algebra II.
I hope these ideas help! If you have other ideas or resources, let me know and I'll try to add them in.