Big Kahunas
Who: The people and organizations with enough money to shape education nationally: billionaire philanthropists, big foundations, and think tanks ("institutes") that publish research and policy ideas.
Power: Money and ideas. Foundations fund pilot programs, research, and advocacy groups, and districts chase the grants. Starting around 2000, the Gates Foundation put more than $2 billion into remaking high schools, much of it into breaking big schools into small ones. In his 2009 annual letter, Bill Gates wrote that many of those small schools didn't improve achievement in any significant way, though many had better attendance and graduation rates (Gates Foundation). The foundation then moved on to teacher evaluation and to backing the Common Core, a set of standards for what students should learn in each grade. Common Core isn't a test; states choose their own tests.
What they care about: Big, measurable impact they can put in a report, and their own theory of how to fix schools. Priorities shift every few years.
How to work with them: You probably won't meet a billionaire, but there's money closer to home. Local community foundations give grants to schools and sometimes to student-led projects; find yours with the Community Foundation Locator. Many districts also have a local education foundation, and local businesses and service clubs fund school projects. Co-write the application with your principal or a teacher: they bring the school's credibility, you bring the idea. Before you copy a big-money initiative, check whether it actually worked.