I'm all for "math is cool," and "let's explore," but this guy seriously torques me off. My kids are currently suffering from the influence of people like him. They have taken the basics out of math and substituted this useless "math explorations" curriculum. Other folks have written better criticisms, but suffice it to say that the vast majority of kids don't benefit from all this "exploration" and "visualization" and the ones who do would have had those epiphanies anyway without any help whatsoever.
The BETTER way is to stick to the basics and train teachers to recognize kids who have a mathematically artistic talent and then remove them to an environment where it can flourish. That's tough for a couple of reasons. First, those kids might not actually get good grades. The author of TFA is entirely correct that the basics bore them which results in inattention and lack of motivation. Second, when they ARE good, removing them will lower the overall test scores of the class. Since teachers' pay and bonus structures are based on their students' test scores, there would be a strong monetary motivation to intentionally fail to recognize them.
Assuming that those two problems can be overcome (big assumption there), you continue to train the "artistic" kids in the basics, but only just enough to get by. The rest of the time, you motivate them in a way that would make the author of TFA happy.
The problem is, people have this wonderful but sadly mistaken belief that ALL kids can benefit from artistic mathematics when in fact most can't. Compounding the problem is the bizarre theory that teaching the artistic mathematics will somehow magically result in the basics becoming trivially easy. It doesn't. And unfortunately, our kids have to fail spectacularly in order to teach the education system this simple fact. "Luckily," that's what they're doing in droves.
There is no difference (other than media) between an ABP filterset and a set of pages custom-cut to fit over a particular edition of a newspaper or magazine and block the print of all advertisements therein, leaving non-advertisement text and pictures visible via cut-outs.
Let's say you obtain said magazine and page-by-age place the "PABP" (paper ad-block plus) "filters" such that you can read the entire magazine without ever setting eyes on a single advertisement. Is this illegal? Immoral? Unethical? I can't see how it is. Doesn't matter if the magazine is sold or given away for free. Once you get it, it's yours and you can look at any part of it you like.
In the paper publishing world, delivery of the "substrate" media (the magazine, newspaper, etc) is exactly equivalent to delivery of the advertising media. They cannot be separated. The advertiser, therefore, knows that his message has been delivered and counts on its positioning and his own unique presentation to make it eye-catching enough that the reader notices.
In the electronic publishing world, some genius decided to separate the advertisements from the content. Where previously it would have impossibly difficult to block the ads (who is patient enough to make a paper cut-out for every page of a magazine and carefully place it so that only the articles' text shows through?), now blocking is only a matter of applying a series of regular expressions. But the same principle applies. Once you've downloaded the "substrate" content (i.e. the pages hosting the advertisements), you are under no obligation follow any of the links. It's YOUR bandwidth, not the advertisers. If anything, the advertisers are stealing from YOU when they download commercial media without your consent.
The real problem is this: Advertisers are lazy. They are faced with a new type of media and are unwilling to invest the time and money to fully integrate the advertising with the "substrate." It's not impossible, and it doesn't have to be expensive. Look at the Hemmingway mock-prose competition that gets held every year. The contestants are required to incorporate the name of the sponsor in every submission, or the submission is disqualified. And for the price of a few trophies and a little PR, the sponsor of that contest gets amazing amounts of advertising.
Unfortunately, really integrating advertising with its "substrate" media takes a lot of thought and effort. So basically it boils down to a bunch of stupid lazy individuals who would rather point fingers at "evil users" than do their jobs. Sorry, fellas. The Whinery Tour starts every hour on the hour. Queue up under the sign with the picture of Sour Grapes.
"Inquiry is fatal to certainty." -- Will Durant