Another treatment of Direct Instruction getting more into the technical details of the theory

Thank you very much for the IM convo you had with me resolving all those confusions I had about how I had miscommunicated various points. I just thought I should post this comment before I go and use what you gave me to write a much better clarification post for discussion, since the comment was almost done when you IM'd me.

I hope that report doesn't read too similarly to my posts! I only did the quickest skim of the "what is DI" section, but it seems to be like an abridgement of "Rubric for Identifying Authentic Direct Instruction Programs" (prologue here ) that's even more abridged than my treatment of Theory of Instruction.

I wouldn't even try to communicate DI theory across a large inferential distance (unless the audience already had a positive impression of it from personal experiences teaching from DI programs after failing with low performing kids, to make them patient).

But with LW, I figured that after showing the experimental evidence of effectiveness (in the way teachers who had previously been failures became successful after they started using DI programs), to convince some LW people to study the theory themselves, they would find it much easier to understand because of their prior understanding of concepts like extensional/intensional definitions, 'looking into the dark', and thingspace.

For instance, when studying the theory behind the design of templates for teaching 'noun' concepts (or 'multi-dimensional non-comparatives'), any LWer should go, “Ohhh, this is taking the basics of what Eliezer was talking about with the example of the 'bird-cluster' in 'thingspace', and applying it make sure you're giving enough information to someone else who doesn't already know what the label 'bird' refers to that they can find the cluster!”

And of course as we discussed by IM, the way that “logically faultless communication” relates to the “2-4-6 game” and is "logically faultless" in the same way Bayes is the logically faultless way of doing induction yourself, but that doesn't guarantee that a particular user won't misapply it. But if they do misapply it, someone who knows how to apply it correctly can figure out exactly how the mistake-maker must change to become correct.

But yeah, I'll go get on that clarification post for discussion now.

Thanks again!

If you can't instruct someone as to what DI is, it might not be living up to claims its a ground-breaking instructional process.

The main difficulties in giving an accurate and brief statement of what physics is for someone who's never seen anything like it are (1) that physics is a very big subject and (2) that your stipulation about the audience seems to be intended to assume they don't know any mathematics to speak of either.

Are you claiming that DI is a hugely varied subject like physics? (If so: How is that even possible, given how recent it apparently is?)

Are you claiming that DI depends on a large and conceptually very difficult substrate, as physics does with mathematics? (If so: What is that substrate?)

If the answers are both "no", then I'll adjust your question to fix those two mismatches, and attempt to give a brief summary of (not all of physics, but) Newtonian particle mechanics for (not someone completely ignorant of mathematics, but) someone who has college-level mathematics but has somehow managed not to hear that it can be applied to understanding the physical world.

"This is a theory about the motion of small rigid objects such as rocks. The same theory can actually handle large objects by considering them as aggregates of smaller ones, but for the moment we'll only consider objects that are very small. So, suppose we have a bunch of small objects. At any instant we can describe the state of the universe by saying (1) where these objects are -- we specify this by giving three coordinates for each object -- and (2) how fast and in what direction each object is moving -- we specify this by another set of three coordinates, which collectively we call the velocity. And the only other thing there is to know about each object is its mass, a single positive number that in some sense describes how much of it there is; it's closely related to how heavy it feels when you hold it.

"Now the basic rules are as follows. First: the derivative of position with respect to time is the velocity. Second: the derivative of velocity with respect to time, which we call the acceleration, is completely determined by a set of rules that care only about the positions, velocities, and masses of the objects. (As long as they don't actually crash into one another. We'll talk about that in a moment.)

"Third: the rule for finding the acceleration is as follows. The acceleration of each object is a sum of vectors, one for each other object. What's happening here is that all the objects are pulling on one another; objects with more mass pull harder. More precisely, the formula goes like this: the acceleration of an object with mass m is the sum over all the other objects of Mr/|r|^3 where r is the vector from our object to the other object and M is the mass of the other object. So the further away the other object is, the less effect it has; in practice this means we can mostly ignore objects very far away.

"Here's an exercise, to give you a feeling for what the theory lets you do. Define the momentum of an object to be the mass times the velocity. Then prove that the sum of all the momenta in the system never changes.

"This system takes some getting used to, although basically it's just fairly elementary mathematics. Let me mention a few of the things that follow from it. We just saw a "conservation law": the total momentum is constant. There are a whole lot of other conservation laws, and in many cases one can make detailed predictions using only those. If you have one object whose mass is very large and all other nearby objects have much smaller mass and don't get too close to one another, then you can pretend that the first object stays fixed in place, and that the others' motions are affected only by it, and in that case it turns out that their paths are always conic sections. In particular, our solar system is like this, and the planets move in near-perfect ellipses. If you do the calculations more carefully, taking into account the planets' influence on one another, you can get very accurate results, and in fact someone once found a previously unknown planet by noticing that another already known planet wasn't moving quite as expected and working out where another planet would have to be to produce the observed deviations.

"That'll do for now. If you want a more difficult challenge, try to prove the statement I made about conic sections."

But physics and DI are different in this important way: physics is a classification of knowledge, and DI is a technique for communicating knowledge. It's reasonable to ask for a functional description of a technique, even though it wouldn't be reasonable to ask for a functional description of a classification of knowledge. I don't think your analogy works.

You're claiming that DI is a way of teaching people things. You'd like to teach us what DI is (or, at least, we're giving you the benefit of the doubt in assuming that this is your goal). However, you've currently been successful in teaching (as near as I can tell) exactly zero of us what DI is. If you've succeeded in teaching zero people the thing you're trying to teach, I suggest this is evidence that you don't have a good teaching method.

Here are some things I don't yet care about, and can't care about until I know what DI is. If your response addresses these non-concerns, my doubts about your stated goal will increase:

• I don't care if DI is effective.
• I don't care if DI is well thought-of by others.
• I don't care if DI is the result of a new paradigm or an old one.

Here are two things that I do care about:

• I'd like to know what DI is.
• I'd like to know if you, personally, are a member of the Church of Scientology.

Sorry I have to include that last one, but your behavior so far absolutely mimics a common CoS MO of introducing a new program which is vague on details but turns out, in practice, to be Scientology (see, for example, Narconon).

Those givens seem to provide information all by themselves.