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The fact that this whole story culminates in the punchline, "The answer is Udacity!" is kind of a sick joke. Udacity, from what I've seen of it, is comically awful. Sebastian Thrun seems to be mostly a carnival shyster from what I can tell. Their original premise was to offer a full college education (and "disrupt", run existing colleges out of existence), and they've long since retreated from that goal. Their attempt at solving the remedial-math problem was an epic disaster (link). I haven't really heard anyone hype Udacity in a few years now.

Review of Thrun's Udacity statistics course, from a statistics professor (me), on my blog:http://www.madmath.com/2012/09/udacity-statistics-101.html

Previously featured on Slashdot: https://news.slashdot.org/story/12/09/10/129231/the-problems-with-online-math-classes

The fact that this whole story culminates in the punchline, "The answer is Udacity!" is kind of a sick joke. Udacity, from what I've seen of it, is comically awful. Sebastian Thrun seems to be mostly a carnival shyster from what I can tell. Their original premise was to offer a full college education (and "disrupt", run existing colleges out of existence), and they've long since retreated from that goal. Their attempt at solving the remedial-math problem was an epic disaster (link). I haven't really heard anyone hype Udacity in a few years now.

Review of Thrun's Udacity statistics course, from a statistics professor (me), on my blog:http://www.madmath.com/2012/09/udacity-statistics-101.html

Previously featured on Slashdot: https://news.slashdot.org/story/12/09/10/129231/the-problems-with-online-math-classes

I have a good friend, who is himself German, with a full-time faculty position at a top U.S. university in CS. Last summer he taught in Germany as part of an exchange program. He himself came back basically blown away by the different level of preparation and maturity of the German students.

My take is that German universities actually maintain legitimate entrance standards. All college costs are paid by the government, there isn't a free-market race to the bottom, and the only people accepted are high-quality and expected to actually take responsibility and succeed at the work. Vocational programs exist for other types of jobs. Different schools are attended after the age of 10 based on whether someone is headed for college or not (contrast with the U.S. where "tracking" is anathema in education since about 25 years ago).

http://www.history.didaktik.mathematik.uni-wuerzburg.de/meg/weidiga1.html

In addition, I must point out that German math educators, even K-6 equivalent, are highly prepared (like maybe 8 years of training), respected, well-compensated, and tenured by the government. This is in contrast to math in the U.S. which is taught from K-6 by non-experts who are actually the least capable of math, least knowledgeable, poorly trained, have the highest levels of math anxiety (which has been shown to rub off on students), little support, and high turnover in a typical American meat-grinder context. As a community-college math teacher, I suspect that this rotten foundation in math from K-6 is the single biggest problem with American education.

In Germany: http://www.history.didaktik.mathematik.uni-wuerzburg.de/meg/matheda4.html
In the U.S.: http://www.madmath.com/2016/02/hembree-on-math-anxiety.html

Likewise: One of my last interviews in my gaming career, an interviewer (producer) asked me to convert a string of ASCII digits to an integer value. I did happen to remember the algorithm directly from my machine architecture class (which I feel is quite memorable). Didn't believe me when I said it's actually more efficient to walk in the forwards direction through the string and multiply by 10 at each step (he maintained you had to search to the end of the string for the lowest place-value, the walk back right-to-left). I even walked through an example to show him correct result and total operations -- still didn't believe me. No job offer, left the industry.

http://www.madmath.com/2015/12/that-time-i-didnt-get-job.html

A major problem is that practically no teachers in U.S. elementary schools actually understand math (and so they teach the emergency fall-back of remember this nonsense). Education majors in the U.S. have perennially had the lowest qualifications of anyone entering college, and the highest rating for math dislike/anxiety. They're effectively self-selected for lack of mathematical understanding. I talked to a guy who used to run a middle school, and he said that he had no hope or even desire of getting math experts into the system, because they couldn't possibly be good with young kids.

There was an excellent article by Patricia Clark Kenschaft in the Notices of AMS (2005), on how she observed this functioning at both poor and wealthy schools, and concluded that most people who got math in elementary school must have some outside/home resource to make that happen. (Link)

Close -- as far as I know (and I research this), high school teachers in most states still need a specialized bachelor's degree in math education, plus the general teaching certification.

The undeniable problem is that teachers at the elementary-school level definitely don't need any such skill, and in fact are perennially the weakest and most hateful about math of our entire college-going population. Then they teach broken math to our children from K-6 and in many cases there's no recovery after that. I agree that we need math specialists at all level of education, like every other modernized country.

More specifically: U.S. elementary-school teachers are the weakest at math, and the most hateful about math, of our entire college-going population. This suggests that we really need math-specialist elementary teachers like every other modernized country.

MadMath: Who Has the Math Anxiety?

Hacker is a professor emeritus from CUNY in Political Science. He has a new book coming out right now, his second on the subject. He personally gets a lot of publicity for the "Man Bites Dog" headlines that can be written about the professor-who's-against math. (Also, he's a regular book reviewer for the New York Times, who usually start off his PR tours by publishing an op-ed from him.) On the other hand, CUNY administrators have plans to get rid of even the most basic math requirements (7th-grade level) for any of their degrees, so as to boost retention/graduation rates in the face of a tidal wave of unqualified open-admissions students from NYC high schools. Hacker gives them political cover for that project by writing stuff like this. Journalists don't know any better... heck, the writer of the Slate article actually thinks that pi is 3.14!

Counterargument from the mathematics side -- MadMath: Lower Standards are a Conspiracy Against the Poor
Counterargument from the political science side -- Gin and Tacos: A Very Stupid Argument Gets the FJM Treatment

I agree with this comment 100%.

http://www.madmath.com/2012/07/teach-logic.html