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Molybdenumblue comments on What Direct Instruction is - Less Wrong Discussion
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If it makes you feel any better, I did read that part with considerable interest, and I understood how it related to your example of teaching the numbers 1-100, but I felt like it was touched on only briefly and the rest of the article was really long and pretty scattered, so I was left unsure whether the set of rules for choosing examples was DI, or one of the main things about DI, or just an example of why DI was awesome, or what.
I do think I might be able to make use of this. When I'm teaching a (usually high school-age) kid how to do math problems, I tend to use a series if examples like this:
Here's a simple example of how to do this technique. Each step is mathematically valid using these rules you already know, and the point of doing it this way is that it gets you to your answer like this. Want to see another one? Ok, then let me switch it up...
Here are some trickier problems. If the problem looks weird in these particular ways, you can still use the technique by doing this. Otherwise, it's basically like the first example.
If you're going to screw it up, it'll probably be like this or this. Please notice that this is not the same as the right way to do the problem. Also, a lot of people make this careless error. Make a checklist of these mistakes to look for in your work.
I guess DI would tell me to use positive examples that are as diverse as possible, and to avoid confusing examples where you can get a right answer by doing something other than the right process? Would you suggest anything else?
The first obvious thing that comes to mind is to learn to use task analysis. If you're going to be working in an environment where the instruction hasn't been designed to contradict misrules before the students develop them, you're going to need to do lots of correction.
Remember that unless you actually get one of the DI programs like "Connecting Math Concepts", anything you do will be just little chunks of big-DI fading off into little-DI at the edges. Doesn't mean it won't help you do better than average, but it'll be way below what's really possible.
Is that useful? Anything in there unclear? Like how to learn task analysis?
[Edit: sorry, you said "usually a high school age kid". There's no high school level "Connecting Math Concepts"]
Well, it would have been considerate if you'd told me what is meant by "task analysis" here, with an eye to enlightening me as to why I will want to use it. I can only infer from context that it will somehow make doing correction better or easier.
Oh no, I didn't mean "Is that all you need?" as in "subtext: I've given you enough, go away". :P
I meant: "I know I need to give you more information. Tell me where I should start."
I linked to a scanned page of Theory of Instruction here in this comment thread
Please start by providing a definition--like, the kind you might find in a glossary--of "task analysis" as you are using the phrase in the above comment.
Ah! Sorry, I was thinking maybe you had understood some of the contents of that thread already before I mentioned it in this one.
Anyway, sorry this reply took so long. I was having scanner issues.
Here's the first page of Chapter 12 in ToI, "Programs Derived from Tasks" [edit: fixed from accidental link to section of the AthabascaU module]. A definition of "Task Analysis" is, of course, under that heading.
There are details in the definition that rely on knowledge of concepts covered earlier in the book, but as a whole, does it help?
I just realized that page starts the heading "Strict Task Analysis" but I didn't scan "Transformed Task Analysis" since that's on the next page, and that's what you need.
But honestly, it is reasonable of me to direct you to the book yourself, right? Rather than trying to write a " Complete Guide to Task Analysis for Beginners!" right now?
Well, you didn't define it in that thread either, as far as I can see, so I am confused by this statement.
In case this needs to be said: you really shouldn't use jargon without defining it if you aim to write for beginners.
It is reasonable to quit whenever you decide it's in your best interests to quit, of course. I'm sorry if you found my request for a definition onerous. I hope nothing I said seemed like a demand for a complete guide to anything; I didn't intend it that way.
I may or may not ever get around to checking out the book from the UCF library. I was looking for more concrete and actionable pieces of advice on how to improve my teaching process, partly because they might be immediately useful, and partly because I am still undecided about whether DI has much to offer me and the quality/novelty of the advice would be significant evidence.
Anyway, thanks for your time.
ETA: The definition on the scanned page is sufficient, if not entirely transparent, so I upvoted you for answering my question. Thanks!
No no no! Please don't mistake my tone! I am so happy that you're asking me for detailed help with this! Responding to you is not onerous, but joyful!
Writing a "Complete Guide to Task Analysis for Beginners!" is something I'd love to do! I just know it won't get done very soon.
I'm sorry I keep forgetting to examine my jargon that seems intuitively transparent to me and try to over-estimate how much explanation it needs. From now on I will start compiling a glossary of terms.
But yes, you raise a very important question:
"How much practical use can I get out of DI theory without actually studying it in depth?"
It is true that it is not like a magic item you can just put in your inventory and thereby receive extra points to your teaching ability, but an entire complex, well, theory, for engineering complex educational machines, which you have to understand and master the use of to create such machines yourself.
But still, there must be at least a few quick equivalents to things like pulleys and levers that I could distill for you.
The hardest part of that will be simply noticing what's not already obvious to you...
How about if I submit the question to the DI community for you?
That is a doubleplus good idea.
Sure, sounds great.
Some other thoughts: perhaps you could give me some examples of specific teaching goals you have, and specific problems you often encounter?
Honestly, I suspect most of the problems high-school students have are due to lack of mastery of the basics. That they are weak enough on such things as adding/subtracting/multiplying/dividing fractions and working with exponents that they are likely to make mistakes on those even if they aren't having their cognitive resources split between trying to track that shaky foundation and learn the details of the new thing you're presenting to them.
If we could develop some systematic diagnoses, corrections, and practice materials (practice to mastery!) for just fractions and exponents, I think we might be able to hugely improve any tutoring you [or anyone else!] attempt.
ETA: If the lowest hanging fruit in improving your own skills is to "stop doing stupid shit", then it follows that the lowest hanging fruit in improving your teaching is to figure out how to get your students to "stop doing stupid shit". :P
Problem is that the DI world, in terms of the actual experts on the theory rather than just people who deliver programs, is very small, and most of those experts work together in person rather than communicating online.
So it might take a while to get a response.
Heh, I actually just realized that I've been using some non-transparent LessWrong jargon in some of my communications with the DI community, like "inferential distance".
The problem is that, once you understand the concepts common both on LW and in DI theory, there is so much overlap in meaning that it takes a little bit of conscious thought to remember which way of expressing an idea is appropriate in which context.
[I mean getting the context of LW and DI people confused, of course. In the context of individual sentences, it's obvious which is most apt, hence why I need to stop myself from switching back and forth without thinking about it.]