Tradeoffs will be necessary. For example, if your name was Philip of Macedon and you had unlimited resources, you would hire Aristotle to tutor your kid. However, most people don’t have unlimited resources, and there aren’t enough tutors to go around. So we will have to cut come corners.
On the other hand, as Knuth put it, premature optimization is the root of all evil. We don’t want to cut corners more than necessary. Consider the contrast:
| Doing things at scale imposes some limitations, because some things you would like to do simply can’t be done at scale. | If you are successful at scale, it releases some limitations, because you have more resources. You can do a lot more preparation. Any fixed costs can be amortized over a huge user base. |
- Certain things are needed by the student who is studying on his own, self-motivated, self-paced.
- Certain things are needed by the student who is part of a more-or-less conventional class, with a teacher present.
- Certain things are needed by the teacher. All too often,
people forget that the teacher is part of the team. See also
item 4. We want to empower the teachers. Letting the
student watch an online lesson frees up the teacher to do things
that only the teacher can do.
This is related to the trendy notion of “flipped classroom”. That is, the students can watch the video lectures on their own time – outside of class – and then classroom time can be devoted to discussion.
- I’m talking about serious misconceptions about the fundamental physics. The law of conservation of momentum is misstated. The second law of thermodynamics is misstated. Multiple inconsistent definitions of “gravity” are used. Et cetera.
- I’m also talking about the secondary laws and the not-so-fundamental rules of thumb. These have important provisos, i.e. limitations on their validity, which are not correctly stated. Example: Kirkhoff’s voltage law.
- I’m also talking about discussions where the bottom-line conclusion is more-or-less correct, but the derivation that leads up to it is completely bogus.
- There are some other things that are not completely wrong, but are 50 to 100 years out of date, sometimes more. This includes a pre-1898 approach to thermodynamics, a pre-1908 approach to special relativity, a pre-1924 notion of what “matter” is, a pre-1926 picture of what atoms look like, etc. – in cases where the modern approach would have been simpler and in every way better.
Remember, this is one of the better books!
Writing books is hard, far harder than most people imagine. This does not, however, mean that we should tolerate lousy books. Instead it means we need to apply sufficient resources to the problem. By way of analogy, suppose you want to build a fire:
- If you heat a bunch of oak chips to 100∘ C, you get nothing.
- If you heat a bunch of oak chips to 200∘ C, you get nothing.
- If you heat a bunch of oak chips to 300∘ C, you get nothing.
- If you heat a bunch of oak chips to 400∘ C, you get nothing.
- If you heat a bunch of oak chips to 500∘ C, you get a fire. You can use that to build a bigger fire, and so on.
The point is, if you apply insufficient resources, all the resources go to waste. On the other hand, if you arrange for sufficient resources, you achieve ignition, and the result is tremendously useful.
Rather than a large selection of lousy books and videos, we would be much better off with small number of really good books and videos. The task of organizing and focusing resources is a management task. The educational system and the publishing industry must be considered prime examples of managerial malpractice.
Let’s be clear: The teachers are a super-important part of the team. You neglect their needs at your peril.
Consider the example of PSSC. The book was clear, correct, and up-to-date when it was published in 1960. From a student’s point of view, it is probably the best physics text ever written. The course was supported by videos and by numerous “canned” experiments for students to carry out. However, it was failure in the marketplace. Anybody who wants to write a book had better understand PSSC failed.
My theory is that most teachers didn’t like it, because it was too radical. It was too unlike how they had been taught, and too unlike how they had been teaching.
It does not suffice to create a “teachers’ edition” that is basically just the students’ edition plus answers to the exercises. The teachers’ needs are different from the students’ needs. The teachers start out in a different place, and need to end up in a different place, different from the students.
- As always, the teachers need to know quite a bit more than the students. The level of proficiency sufficient to pass the course is nowhere sufficient to teach the course. That’s because for any given idea, there are about ten plausible ways of teaching it, only one of which is the optimal foundation for the next level of understanding. Therefore the teacher must have some acquaintance with the next level, maybe not in great detail, but enough to understand why we are handling the present level the way we are. In figure 1, the teachers’ goal G+ is different from the students’ goal G.
- If the new book is truly modern, the teachers will need to unlearn a lot of stuff. Unlearning is always hard. The teachers’ book will have to discuss misconceptions and out-of-date conceptions that would never occur to students, and should never be discussed in class or in the students’ book. In figure 1, the teachers’ path to the goal is wildly different from the students’ path.
- The teacher is already overworked, and simply does not have
enough time to learn a bunch of new stuff all at once. Therefore
there needs to be an introduction strategy, where the new stuff is
rolled out a little at a time, over a period of years.
We can also hope that by providing the teacher with valuable time-saving materials, we free up time that the teacher can use to get up to speed on the modern science.
Caveat: This is hard to set up. It requires exceptionally wise faculty and wise administration.
Rationale:
- Without real-world applications, the math is hoplessly dry and hard to motivate. Without the math, the science is impossible to understand.
- Mother Nature does not recognize any clear boundaries between disciplines.
- There is the classical on-campus class, with a few dozen students.
- There is the ordinary MOOC, with a few thousand students from around the world, all taking the course at the same time, phase-locked to the on-campus course.
- There is the set of online resources which can be
used and re-used in many ways, including:
- This includes organized group courses. The groups do not need to be huge; one could imagine a new group of 100 starting every week.
- This includes fully-individualized courses, such that a student could start any time, progress at any rate, and finish the course at any time.
- This includes using arbitrary subsets of the materials for independent study, without any notion of starting or finishing “the” course that gave rise to the materials.
- This includes incorporating arbitrary subsets of the materials into other courses, possibly similar, possibly very dissimilar.
It seems to me that item (3) – re-using the materials – represents a great deal of the value. That’s where most of the users are, if you integrate over time. Let’s be clear: We should think of the online materials as a valuable thing unto themselves. They exist partly as an offshoot of the original course, and partly as a resource in support of the future courses, but they also exist as a thing unto themselves. We cannot fully foresee – much less control – how they will be used.
We need to devote serious effort to optimizing the online materials. We should not think of them as a passive offshoot or by-product of the original course. Similarly, as noted in item 1, we don’t want to cut the wrong corners. There are some optimizations that are appropriate for the online materials that would be unnecessary in an on-campus course ... and vice versa. If the goal is to optimize the online resources, don’t be constrained by archaic classroom-scale thinking.
Rationale: Having lots of short segments gives the users more flexibility. I refuse to argue about the order of presentation of the various topics and sub-topics.
- For starters, the only thing that has ever made sense to me is the spiral approach. That is, briefly introduce a large number of topics, then spiral back and study each one in more detail, linking it to the other topics.
- Secondly, each teacher should have discretion as to the order of presenting each sub-topic. Indeed, each teacher and each student should have discretion to skip certain sub-topics, within limits.
- If the in-class presentation was bad, the Khan version might be better in relative terms, even if it is not good in absolute terms.
- Sometimes it helps to have two complimentary views on a subject.
- The videos are available on demand. The student can choose the time and place to watch the video.
- The student can pick and choose which videos to watch, based on personal interest and/or personal need. Maybe the student was absent from class when a particular topic was discussed. Maybe the student was present but distracted. Maybe the student needs background information on a particular topic, to a greater degree than other students. Maybe the student is motivated to pursue ramifications that were not covered in class.
I recently saw an hour-long video where one of the students asked a question, and the professor said, “That’s a good question. We will cover that in detail in about six weeks”. It would have been much nicer if the video contained a hyperlink from the question to the answer.
The whole course has been on the web for years, so there has been plenty of opportunity to go over it and do some nonlinear editing. It strikes me as penny-wise and pound-foolish to skip the editing step. It’s disrespectful to the viewers.
This is related to the idea that the online materials are a thing of value unto themselves, not merely a transcript of the classroom lecture, as discussed in item 6.
The real trick is to teach the other 99.9% of the population, the mass market, the ones who do not have a priori high motivation, strong study skills, and strong technical background.
We can use the Linux kernel as a reasonable standard of open-source professionalism unless/until we come up with something better. Salient features include:
- There is a formal document control system.
- There is an elaborate bug-tracker.
- Proposed changes are discussed amongst the stake-holders.
- Approved changes undergo an elaborate sign-off process before being committed to the repository. Here’s an an example of a patch committed to the Linux kernel.
Allowing free-for-all editing is not a good model ... especially if reform is one of the goals. Wikipedia articles on introductory physics concepts tend to have problems. Even if you fix them, they don’t stay fixed. Everybody who has ever taken the intro physics course thinks he knows the right answer, even if the course was 20 years ago and was 100 years out-of-date at the time. People who don’t know what they’re talking about vastly outnumber those who do, and tend to have a lot more time on their hands. Reform – more or less by definition – goes against the conventional wisdom. In accordance with Wikipedia rules, anybody who can find an “authoritative reference” for the unreformed approach is allowed to undo any reforms ... and there’s not much the reformers can do about it.