With Interactive Exploration of a Dynamical System earlier this month and today's Scrubbing Calculator, Bret Victor is doing some of the most provocative work in math education right now. As much as I'm curious how STEM educators perceive his work, I admit I'm much more interested in the perceptions of educators in the humanities and of people who, at one point or another, were totally put off by the abstract symbology of mathematics.
I'm also strongly inclined toward P.J. Karafiol's critique:
If our goal is to empower students to do more and more interesting mathematics, we can't just hand them simulators and tell them to go play: we need to teach them how to create those simulators. Doing that requires a lot of math and a lot of programming. So Victor's "simulation" model of doing math ultimately requires teaching kids a lot of traditional mathematics.
Of course, replace "simulators" with "calculators" and we have another familiar argument. Obviously, I'm of two very different minds about this.