When I was a kid, I loved digging through bricks to find something that I was looking for or, better yet, that I didn't know I was looking for and would inspire me to do something. Now that I can no longer be considered a kid (at least physically), it pains me to think about digging through random parts.
I don't have any kids myself, but in working with children on a LEGO League team and seeing the children of some of my friends, it seems like the ol' "Dig and Pray" method works well for them.
^ I coached an FLL team as an after-school group (I'm a 6th-grade teacher) for 6 years. I can tell you, @cheshirecat, that the money is needed for registration for the regional tournament, as well as for purchasing the mat and LEGO that apply to the challenge each year so that $375ish is a recurring cost on top of anything spent on Mindstorms elements and any additional LEGO pieces purchased to build the robot. About 8 teachers in my district were able to run teams through a grant from Motorola each year. There are dozens of other teams in the area made up of home-school students, students from other schools, friends whose parents were willing to run a team, or kids whose parents work for a company like Motorola.
There seems to be a lot of growing interest in FLL. For example, one of the regional tournaments that I went to had to split into two groups of 16 at the same middle school because of the number of teams that needed placement in that area.
For the most part, the kids on my teams wanted to do the program again the next year when they went from me to the junior high. Because of student interest at my school and limits on team size from FIRST (only 10 can be on an official team), I only took 6th-grade students on my teams, which meant I only worked with them for a year.
I think if a coach helps the kids take the research process seriously, there is academic growth. My kids would work on finding quality resources, gathering notes, developing their own ideas/solutions to problems, and gaining the confidence to e-mail or conduct in-person interviews of "experts" related to the research. They also gained knowledge of the science topic that season, which has included medical issues, natural disasters, and endangered species.
If you want some first-hand experience seeing these groups in action, I know one of my state-level tournaments (Illinois has two) is coming up on January 14th, so a lot of the larger tournaments will be occurring in the upcoming weekends. State- and country-level tournaments, I believe, are listed on the FLL site and free to the public.
I made time this weekend and built the bridge from book 3. As stated previously, I did make the actual bridge longer, but only 4 studs longer. That then required some other small changes, and I did make some adjustments on some of the tiling, but otherwise, this is what it should look like for everyone else. Unfortunately, with my expected schedule coming up, I won't be working on the hall until June/July. The boxes of pieces are calling to me from the basement...