At the level of the method as well, this study has a lot to teach us. The Future of Secondary School Geometry. The reader will find here an on-line version of his conference, with a lot of examples, even lively ones illustrating new theorems which de Villiers has coined using modern technology to support his intuition and explorations. I am not sure it's possible to evict drills altogether from the math classroom. But I hope, in time, more emphasis will be put on the abstract side of mathematics.
Drills contain no knowledge.
At best, after sweating on multiple variations of the same basic exercise, we may come up with some general notion of what the exercise is about. Moreover, if it's possible at all for a layman to acquire an appreciation of math, it's only possible through a consistent exposure to the beauty of math which, if anywhere, lies in the abstractedness and universality of mathematical concepts. Non-professionals may enjoy and appreciate both music and other arts without being apt to write music or paint a picture. There is no reason why more people couldn't be taught to enjoy and appreciate math beauty. Long-term building of mathematical ideas related to proof making.