"Beauty and Future Philosophers" is about a program that the U of Nottingham runs in which philosophers design workshops to teach philosophy to primary school students. What I find most interesting about the video is when the speaker. Jonathan Tallant, describes what it's like to tackle problems with primary school students, first-year undergraduate students, and philosophy professors. Undergraduate student have recently come from high school in which they are taught to think and write in very structured ways. Primary school students have none of this training; what they come up with are wild ideas from all sorts of directions, most of which don't work (but some of which do). Philosophy professors also have the structure born of training, but at the same time they have trained to ignore the training sometimes and just focus on the problem. Faculty are like a mix of undergraduate students and primary school students (and, implicitly, this is the aim of studying a discipline, the play of the structured and the spontaneous, the orthodox and the unorthodox, the methodical and the creative).
One thing I notice about the program that Tallant doesn't discuss directly is that they focus on problems, not philosophers or schools of philosophy. They go into a classroom and start an exercise in which the students are asked to make decisions and then justify those decisions--in the video's example, they ask the students to rank a number of images according to how beautiful they are, and then the students must justify their ranking. I'm not quite sure what to say about this, but it seems the right way to go about teaching philosophy at that level, rather like teaching math by getting students to solve problems rather than solve equations.