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patchwork collection of online courses that's difficult for students to navigate.

they can improve their online-education efforts to help students find streamlined, affordable pathways to a degree.

Let’s start with what Khan Academy is. Khan Academy is a collection of video lectures that give demonstrations of mechanical processes. When it comes to this purpose, KA videos are, on the average, pretty good. Sal Khan is the main reason; he is approachable and has a knack for making mechanical processes seem understandable. Of course, his videos are not perfect. He tends to ramble a lot and get sidetracked; he doesn’t use visuals as effectively as he could; he’s often sloppy and sometimes downright wrong with his math; and he sometimes omits topics from his subjects that really need to be there (LU decomposition in linear algebra, for example). But on balance, KA is a great resource for the niche in which it was designed to work: giving demonstrations of mechanical processes.

But let’s also be honest about what Khan Academy is not. Khan Academy is not a substitute for an actual course of study in mathematics. It is not a substitute for a live teacher. And it is not a coherent curriculum of study that engages students at all the cognitive levels at which they need to be engaged. It’s OK that it’s not these things. We don’t walk into a Mexican restaurant and fault it for not serving spaghetti. I don’t fault Khan Academy for not being a complete educational resource, because it wasn’t designed for that purpose. Again, Khan Academy is a great resource for the niche in which it was designed to work. But when you try to extend it out of that niche — as Bill Gates and others would very much like to do — all kinds of things go wrong.

When we say that someone has “learned” a subject, we typically mean that they have shown evidence of mastery not only of basic cognitive processes like factual recall and working mechanical exercises but also higher-level tasks like applying concepts to new problems and judging between two equivalent concepts. A student learning calculus, for instance, needs to demonstrate that s/he can do things like take derivatives of polynomials and use the Chain Rule. But if this is all they can demonstrate, then it’s stretching it to say that the student has “learned calculus”, because calculus is a lot more than just executing mechanical processes correctly and quickly. To say that it is not — that knowledge of calculus consists in the ability to perform algorithmic processes quickly and accurately — is to adopt an impoverished definition of the subject that renders a great intellectual pursuit into a collection of party tricks.

Propose what grade they deserve for class participation thus far, and Defend their proposed grade with evidence from the classroom.

Last May Brian shared how he grades students' class participation.

The assignment sheet for these classes is simple: on it I've printed the class participation policy from the syllabus. I ask students to write a one-page essay in which they:

20 slides at 20 seconds per slide, a Pecha Kucha is, as Jason writes, necessarily “SHORT, INFORMAL, and CREATIVE.”

In addition to the time constraint of the Pecha Kucha, your presentation must also follow the 1/1/5 rule. That is, you must have at least one image per slide, you can use each exact image only once, and you should add no more than five words per slide. The formal constraints of this rigid format call for discipline, focus, practice, and paradoxically, creativity.