Advertisers Can Learn From Montessori School Teachers
I believe there's a lot of work to be done on understanding mental engagement --as opposed to the physical kind. I like your reference to children and education. If you go back to the roots of the Montessori method, you'll find that it's all based on engaging the mind in the pre-computer age. They teach vocabulary, math, geography etc through a combination of interactive devices and socialization. (Full disclosure here: My wife is a Montessori teacher!)
The point is, when applying engagement to brands, we need to recognize that merely clicking on something or inviting consumer generated content is not going to create lasting experiences. The consumer needs to participate in the experience beyond clickthroughs. There may be no metrics for experiences --yet-- but it's time to stop measuring things just because we can measure them.
Interesting perspective! I went to Montessori school during the first years of my elementary education. It was a real, wholesome experience, something most advertiers don't understand with their hard-sell, cluttered, mass-marketing campaigns.