What is the benefit of taking the AMC 8?
My DD13 has derived several benefits from getting involved in competitions (Mathcounts, AMC8/10) - not necessarily the test itself but the process and preparation.
1 - She is being challenged. She's in grade-accelerated honors math (has to walk across campus the the Intermediate HS each day to class) and has missed a single point the entire 1st grade period. Tests (100, 100, 100), quizzes, homework, etc., in total. But she's taking an AoPS AMC10 prep class and is solidly in the middle of her class. The homework stretches her to think, work hard, be creative, fail, try again, etc.
2 - She's learning outside the "normal" curriculum. While breezing through Algebra, Geometry, Algebra II in school she had also studied Number Theory, Probability, Game Theory, etc. Perhaps we'd do this anyway, but the various competitions put purpose, deadline, objective to the work.
3 - She's solving hard problems. Looking at problems 15-25 on these tests, they require creative problem solving and critical thinking. They don't require study of advanced topics - they only cover through standard grade 8/10 math - but require creativity and ingenuity. In the real world, it's the hard problems that need to be solved. Learning to solve hard problems with basic tools will make it easy when you need to solve hard problems with more advanced tools.
Of course, there needs to be an innate interest in the topics. Forcing a kid to take the test and study when the child isn't interested is not going to be beneficial. But the tests, especially when they are challenging and spark curiosity, can be a catalyst to new opportunities.
Speaking for myself - AoPS allowed me to finally hunt down the early 1980's AHSME (precursor to the AMC12) exam I took and find the solution to a problem that has been bugging me for 30+ years. I was high scorer in our school (still have my award), but that one problem I couldn't solve stuck with me all these years. That's the level of interest competitive math can instill in those with an interest.
