Interestingly, the day after I posted my review of the Udacity Statistics 101 class last week, Sebastian Thrun wrote a response on the Udacity blog site. In the response, Thrun agreed that the ST101 course "can be improved in more than one way... In the next weeks we will majorly update the content of this class, making it more coherent, fixing errors, and adding missing content".
First of all, I'll say kudos to Thrun for taking the time to read my blog and viewing the critique in the constructive spirit which it was intended (not everyone would do the same). If you consider the original review (here), then I'll say that this actually does address the final and overarching criticism, namely "Lack of Updates?". The fact that Udacity does intend to be fixing and re-recording lectures is undoubtedly a good sign. Personally, I think it would be ideal to have someone devoted to refining the course on a continuous basis, like a master teacher immersed in a class repeatedly every semester. Will Prof. Thrun personally have the time to make that happen (granted his other research endeavors)? Time will tell.
I'll be eager to see if the major specific content gaps are addressed in the planned updates. Among the missing topics: Probably "CLT Not Explained" (#6 on my list) is the easiest one to remedy -- taking maybe a single added lecture where it's clearly stated (and then hopefully moving the programming segment afterward so it serves as confirmation, symmetric with the other programming units). Somewhat harder would be "Normal Curve Calculations" (#5), which would require at least its own unit, alteration of how inferences are introduced, and maybe removal of the rather unhelpful derivation of the normal formula. Much harder would be "Population and Sample" (#4), which I think would require major alterations to the DNA of the course from the beginning to the end.
Now, Thrun also writes that "Statistics, to me, is a highly intuitive field... some [criticisms] are the result of... my dedication to get
rid of overly formal definitions". This is a spot where we here at MadMath (i.e., this writer) will remain philosophically in a different camp. I would say that we need both good intuition AND good attention to details -- the challenge to both myself and my students being to write things as clearly and carefully as possible AND to engage in quick decision-making and communication. Each is a force-multiplier on the other (my usual analogies being that a great musician can play both very fast and very slow; or a great programmer can make use of both a high-level abstraction and low-level assembly when the need arises).
Anecdote from this past week, starting a new semester of classes: On the very first day of any of my classes, I hand out a one-page sheet of all the definitions that will be introduced in the class, and say that the first -- and sometimes the hardest -- step in learning new math is to learn the meaning of the words involved. At the end of one of those sessions last week, I had one student approach me, profusely thanking me for just such a resource. "My last teacher," she said, "I begged him to define the words he was using, but he said, don't worry about that, just do the problems instead". Which just about broke my heart to hear. Although I've heard multiple voices recently call out for a reduction in formalism, I think that the end result is something like this: You (the instructor) risk putting yourself in a cul-de-sac where one day a student will ask you "why is that?" and you'll have to yell at them "just do it!" because you don't have the shared language to discuss the parts of the problem at hand.
Writing, the language-tool, is almost surely the most powerful thing humanity ever invented -- and math is fundamentally about communicating patterns in the most precise and unambiguous way possible -- so let's use the tool for the job it was intended.