I’ve now taken several online classes, with mostly positive experiences.

On Coursera, I took very useful classes in control of multiple robots and in image processing. I started a course in mathematical thinking, but found the prof quite annoying and dropped it (I had already studied this material, but took it because the prof is famous, to see what it would be like).

I’ve used Khan Academy several times, for freshening up some subjects I needed. In particular, the Linear Algebra I took in 1960 has changed a bit of its terminology and emphasis, and I needed updating for the robot control class.

There is one big practical difference between Coursera and Khan Academy. Coursera tries to force classes to be held on a particular schedule, while Khan Academy lets one work on any topic at any time, whenever you need it.

There are advantages to keeping the classes together–all the students are working on the same concepts and problems at the same time, so the Forum discussions when sorted by time also tend to be sorted by relevant topic. That means it’s easy to ask a question and find others who have just figured out the problem, who can help you understand where you’re going wrong.

But for people who can use Search to find what they need in the historical discussion archives, this synchronization isn’t that important.

Synchronization also helps with keeping exams and homework fresh, so that you work on them without knowing the answers until they are suddenly revealed and graded.

But when you just want to learn stuff, when you happen to need it, the Khan Academy approach is much more useful. If I had had to wait for the next class on Linear Algebra to start, I could not have gotten the info I needed in time to be useful for my robotics class.

Another great resource is WikiPedia, which amazes me how often it has an article that explains exactly what I need to know. What a gigantic, enormous, immense improvement this is over the printed encyclopedias of yesteryear!

**Attitudes toward teaching vary**

Some (few) people teach with the idea of making the subject as easy as possible to understand. This is very difficult, as it requires great effort to eliminate ambiguities and errors from the course text and problem sets. Such things seem trivial to the teacher or to anyone who already knows the material, but present enormous barriers to the student, who has to go to great effort to finally discover just what was in error. Humans normally work in environments with very high error rates (for example, people very often say literally the opposite of what they mean), and it works only because of the large shared understanding that forms the background against which everything is evaluated. Much of that background does not yet exist for the student.

Most teachers take only normal efforts to remove errors and ambiguities, and when such an error is pointed out their reaction is often to point out that the student has thus been forced to learn much more. The real world is full of errors and ambiguities, so the student has to learn to deal with them. An important goal for some teachers is to sort out the students, so that only the best go on to the best schools or the best advanced classes.

I think it’s true that a student who successfully understands material that is laced with errors does indeed have a deeper understanding at the end of the process. However, it is an enormous amount of work, and takes an enormous amount of time. The result is that many who would have been capable of learning the material simply can’t complete the job. They may finish the course, and even with a decent grade perhaps, but they haven’t had time to get everything sorted out, so they progress to the next class with a shaky foundation.

Here’s where I think the Khan Academy really has it right. Their passing grade is 100%. You don’t move on until you really understand what you’re currently learning. That greatly speeds progress over the long haul, because you have a reliable foundation on which to build.

What soured me on the mathematical thinking class was the prof’s tolerance of ambiguity. When ambiguities were pointed out, he had no interest in fixing them but blamed the students who chose the wrong interpretation. Seems a bizarre attitude for a mathematician!

Anyway, I’ve only had a few experiences with courses where the prof really tried hard enough to eliminate mistakes and confusions, and I found these courses far more satisfying and stimulating than the usual ones. There’s far more total learning, in my opinion, and far more students get equipped to go on to more advanced topics. I think it’s win-win. But it’s really, really hard work for the prof. Most egos won’t admit to enough possibility of errors to make this approach possible for them.

Khan tells of a class where one student stalled on a basic concept for a week or so. In a normal class, she would have been moved to a slower track, for less capable students, which would have lowered her whole future achievement level. But suddenly she got it, and then zoomed ahead, eventually finishing second in the class! It’s quite unlikely for good things like this to happen in traditional classes, where the most significant thing she would have learned is that she’s not good at the subject, something that isn’t even true.