I've given thought to topics like this as well. Unfortunately, I don't have very many new and innovative ideas to offer. If my mind ever stumbles upon something worthy of sharing, I'll let you know

There's tremendous competition for time these days - at least compared to the 60's and 70's when I was a kid with plenty of free time. I would have jumped on a math team or club if I'd had the opportunity. My kids have much more homework from public schools than I did. They're also involved in many more activities. Their lack of free time is almost scary.

The potential market for serious problem solving might extend to the top 1% (possibly 5%) of students. That's a lot of potential, mostly untapped. Reaching the market in the way you envision will take a lot of marketing - problem solving will need to be "cool" at least among the top students and respected among others.

I'd suggest spending some money on marketing efforts, especially those that might lead to additional unpaid publicity. Newspapers and TV stations tend to pay attention to advertised events. Changing the negative perceptions associated with math in the U.S. won't be easy but I'm not sure that there are any realistic alternatives to marketing in our society.

Some of the marketing needs to be directed to teachers who control most of the time that students now have. Building problem solving into curricula in a meaningful way would really help. This is done in a few places but not nearly enough. A serious shortage of capable teachers is a big impediment in many areas. Maybe some problem solvers from local industry / colleges could be enticed to teach such classes.

It's interesting that many relatively mediocre high school athletic events get some newspaper coverage even though attendence is much lower than a typical MathCounts chapter/state/national competition that garners little or no publicity. This could change as more and more students participate in academic competitions. Unfortunately, many of these contests are not problem solving oriented and don't really develop problem solving skillsets.

The other missing element is a talented pool of coaches/teachers/problem solvers willing to donate time to the cause at the local level. Perhaps marketing would solve that problem as well. There's no shortage of coaches for athletic teams and they're willing to work for next to nothing.

Good luck.

I generally strongly agree that publicity is one of the biggest problems all the notable extracurricular programs face. I'm very happy to hear more ideas about how to reach more people. Marketing in general is a tough problem, particularly in an area that has scarce resources to begin with. (Though effective marketing may help change that!)

Reach teachers!

I think we need a lot more teachers who are willing to commit to building a successful math program. We had one of the best mathcounts coaches forever and then he just decided to quit my 7th grade year because the last of an "elite" math family (they always won state and their youngest won the national competition a few years ago) had gone through the program and I guess he didn't feel we would win anymore :/.

I also think that there should be something like mathcounts at the high school level. Something which promotes strong individual achievement, but has enough of a team element so that students will focus on working together and helping each other improve. We have AMC but that is 100% individual which..plainly..is no fun (or at least not as much).

Ive found that with some schools there is simply no internal impetus for such programs. for example many of the most affluent schools in my area are typically already taking a direction, and are minimally receptive to such programs. However there does seem to be a large drive in up and coming schools. For example there is a school called Southwest highschool in i think el centro. although they rank lowest in academics (as far as national test scores and what not) they excel in things such as Academic DEcathlong and Buzzers. It seems that within those schools there is a strong subculture which is yearning to excel. And typically they only have these isolated outlets (I say ac-dec and buzzers is isolated because from personal experience it teaches little about logic and intuition , mostly just studying a random collection of unconnected facts.) However in such cases, because inevitably with the way education is there is bound to be a collection of such schools, a program which teaches both studyuing skills and problem solving would, i believe, provide an exceptional outlet.
Now from what i can see, such schools "attach" themselves to such programs. Although they are the among the poorest schools in the nation the subcultures which cherish academics go to extreme lengths (Ive seen them raise enough money for 30 kids to go on a weekend trip to new york) to keep it strong.
I think this would be a good place for such programs.

I have to say that this is a very interesting topic to me and I actually am about to write an essay about a similar topic. First, I want to give you my story about my experience in math, then some ideas about how to attract people.
My essay topic is: Why do I do math? If somebody had told my younger self that I would eventually enjoy math, I would be shocked. But lo and behold I enjoy doing math now and spend a fair amount of time problem solving. But of course on the topic of discussion,
1. What got me interested?
2. What keeps me going?

1. Before 9th grade, I was never really that exceptional in math. In Junior High, I was above average in math, but I was not that great. Ex. I did not make the advanced placement program program in my school. But during 9th grade when I took the AMC 10, that sparked my interest. I remember a specific problem:
Find the average of all 5-digit numbers that can be made with 1,3,5, 7, and 8. (maybe not those exactly, but you get the idea).
Anyway, I had figured out the clever way of how each digit appears in each place value an equal number of times. This solution not only was satisfying, but this problem was much more clever than any other things I had done. Later that night, I decided to go on the AMC website, and I did some sample problems. Again, it was fun to do these types of problems. I got a sense of satisfaction for seeing the clever insight. Later, I believe that I found the link to this site, and I decided to get the AoPS books. I have been problem solving ever since .

2. I still maintain the satisfaction for solving a good problem, but more advantages have arisen. First of all, the math gives me something to really excell in. It would be a nice thing to say to colleges that you are really exceptional in math. But the other (main) reason is that it feels good to be so good in something. Ex. In the league that my math team participates in (NSML), I am first in the sophomore division out of everybody in the league (55 schools). It just feels great to do so well.

Overall, I really enjoy solving a clever problem, and I continue to do math because it gives me self-esteem. It is hard to say how you could advertise this to other people. It seems to be a very acquired taste to enjoy doing math problems. But I think that the people that will be open to these things have to be introduced to the concept of more interesting problems. All the time in school, the math we do is so boring. All the problems that we do are just following a process, with no creativity whatsoever. (Don't even get me started about how I hate school math). I can understand why people find these problems so boring. It would be good to introduce kids to more unique and interesting problems. There would be many kids that would not care, but at the same time, you could attract some of the select few students to problem solving. Perhaps there would be some other way to get it so more kids could see a few more clever math problems.

It is also a difficult balance between too difficult, and clever. At one end, the problem has to be clever enough so people can solve it, but on the other hand, it cannot be so difficult that it is discouraging and the child gives up. One problem that I liked a lot was like when I was 7 or 8 and my dad was reading to me about Gauss, and how his teacher gave Gauss (as a child) the problem to add 1+2+3+...100. This was intended to be a tedious exercise, but he discovered the trick to pair terms. I thought this was a cool story, and I actually figured out the same method as little Gauss did.

Anyway good luck with your advertising! I hope that my story could give you some insight as what to do.

Thanks for the story. I'll be seeing the man who is in charge of the AMC 10 in a few weeks. I'll be sure to pass it on; he'll love it.