Technique will follow

I've started to think that perhaps the right, responsible way to approach the teaching of mathematics is to willfully place skills and techniques, always, in a position subservient to concepts.

What is Algebra? I've become convinced that it is not the manipulation of variables-- the "arithmetic with unknowns" that I've previously described-- but rather, that Algebra (in despite of it's etymolgical roots?) is the *idea* of the variable, the All-Number, the dice in hand. If this is well understood, in all it's richness, the solutions to equations are trivial practice-- technique and form that flow easily, just as the artist, with a rich understanding of light and shadow, creates the image fluidly.

Add to this a rich and powerful sense of proportion, built upon the scaffold that is born into us, in the way that intuition understands logrithms better than linear systems, and you're a long way towards the entirety of the typical high school math curriculum.