I have no idea why "libertarians" would support this idea at all; especially not Jim Henley, who ought to know better. Briefly, "Direct Instruction" suggests that teachers should be given prepared scripts to use in class and instructed to follow them exactly, with classes streamed by ability and repeating courses until passed.
First of all, this is of course wildly managerialist and authoritarian; who precisely gets to decide what goes in the script? What happens to local, democratic accountability? The examples given refer to big school systems (>20 kilostudents), which implies that the sort of parish-meeting board of governors folk like Henley romanticise would maybe have some influence over paperclips.
And, of course, the entire history of brilliant centralising education schemes shows that brilliant centralising education schemes don't work. This is one, so it almost certainly won't. So how the hell did libertarians, subtype North American, come to like it?
My explanation is that it's purely the politics of ressentiment: school teachers and their trade unions are a traditional rightwing enemy image in the US, as in the UK through the 1980s, and this appeals simply because it would piss them off. It's worth remembering that even Henley and Co are actually very right-wing people indeed; in an alternate time line, they'd be on the other side.
Hence the neato anti-trade union ads; from the "Center for Union Facts", indeed. Further reading is here; apparently the Center consists of a bunch of Wal-Mart money and a well-known tobacco industry lobbyist. I think the phrase is "nice mates you got there".
This is one of the reasons I don't have ads on this blog; you either have to filter them, in which case you are in a sense taking responsibility for their content and could be accused of a conflict of interest, or else if you disclaim any control and make it clear that it's entirely up to the BlogAds or Google computers, you run the risk of something really horrible turning up. And then, if you decide to censor it, you've got to answer why you don't censor X, Y, or Z.