The good:It was inspiring to see 300-400 kids all competing together and very excited about Math. This competition was hosted and mostly run by the high school math club at Newport H.S. which was also kind of cool. Despite my worries the night before, everyone who signed up showed up and I didn't have to scramble around. I also kept tabs on everyone and didn't lose any kids in the crowd. (It turns out this was my main worry during the event)
This competition was very focused on computation and speed. There was a 45 minute individual section with 40 questions. See http://www.newportmathclub.org/kpmt/archive.aspx for some examples. Then there was a speed math section and then a mental math piece on top of that. It reminded me of another blog post I read recently: http://mathbabe.org/2011/07/17/math-contests-kind-of-suck/.
I felt that the relationship between what was being rewarded here and interesting mathematics was a bit warped. Basically, if you were serious about earning medals then you'd focus on speed drills, review a few advanced concepts like probability and permutations, exponents, geometry perhaps solving some beginning linear systems or factoring a polynomial and focus on test strategies.
Some samples I happened to see and my thoughts.
Evaluate 14641^1/4. Most of my kids haven't seen the definition for fractional exponents being n-roots which is what half this problem comes down to. For me I took a glance and divisibility rules popped into my head. Palindrome numbers are often multiples of 11 so I did the quick test (https://www.math.hmc.edu/funfacts/ffiles/10013.5.shtml) and yes it was. If 11 is a factor of number to the fourth then 11^4 must also be. A mental estimate and then a quick check showed that yes that was the answer. On reflection if you checked an easy benchmark like 10^4 = 10000 you'd realize that it must be very close to there and you could guess and check your way also quite quickly to the answer.
However, this is a really mechanical problem. It's not really tricky so much as facilitated by experience. You could just try every number starting from 1 and get there fairly quickly. A little number theory about which digits raised to fourth end in one would speed this up. Which is all to say I don't think this bridges much to more advanced math.
Another one asked what percentage of all numbers between 1 and 10 when plugged into x^3 - x are divisible by 6? For anyone with a little algebra and number theory you immediately see this factors into x(x-1)(x+1) and therefore is always divisible by both 2 and 3 and by extension 6. I think again the kids probably just plugged some numbers in and after observing the pattern worked could just assume the answer. Which for me misses the kernel of interest here.
Also as you might imagine with this type of focus, the demographics were a bit skewed among the contestants. If you're interesting in encouraging more widespread passion for math this format doesn't seem promising. On the other hand, I left thinking there's no need to hand wring over math performance in countries like South Korea, China or Japan. We're importing and assimilating that culture. Hopefully we'll arrive at a happy medium over the years.
So the big question is whether I'd go back again. I think the answer is yes despite my previous paragraph. There aren't many fall events and this fills a hole. Its high energy and I don't think it did any harm. I did have one kid bring home a very large trophy after all. That said, I'm not interested in focusing on preparation for this style of contest. Next year if I continue I think I will outline how to prepare at the beginning when signing up kids and leave it up to them whether they want to spend their time doing so. I'm happy to supply worksheets and mentor if requested.