I mean, it’s aggravating to see things you wrote and go, “But I SAID that! Was everyone just skimming over that part or what?”, but as the aphorism runs in the DI world, “If the learner hasn’t learned, the teacher hasn’t taught”, eh? :P
[And until one sees that aphorism as perfectly consistent with “logically faultless communication”, one must know that one still hasn’t understood the meaning of the technical term.]
I knew I’d make terribly stupid mistakes in miscommunicating this stuff when I started, so I figured it was time to let go of my fear of not having it be perfect in the first place and just start trying.
I should also make sure, when you say it was 1982, do you mean original publication, or that of the copy you got? The second (and most recent) edition is 1991.
Dunno offhand what’s different. Never saw the older one myself.
Yeah, no. I can see not providing examples of everything you talked about, and generally not following your own preferred method to the letter. But the picture Misha has given me of DI would have told you to provide clear positive and negative examples of something within about the first full screen of text. I think I looked at three screens’ worth before giving up.
The reason I did not, rightly or wrongly, was because you have to start off doing this by showing how it applies in the most basic context, like in the AthabascaU module.
This results in a very technical analysis of something that initially seems trivial and pointlessly detailed, and unrelated to the amazing-looking results from studies like Project Follow-Through (which, remember, the meta-analysis says are representative).
I remember glazing over that section in the AthabascaU module myself the first time I read it. And several times after that. Only my emotional experience with the Michel Thomas lessons made me keep focusing on it until it clicked. Way later.
Now, many people on LW surely have much quicker intelligences for such things than I do.
But see the last paragraph of this comment from prase, in which he, at least, is having the same ‘this seems trivial and pointlessly detailed’ reaction after reading the AthabascaU module.
Why was he sticking with it? I believe because he had heard my emotional enthusiasm, and wanted to find out if I was just a crank, or if there was actually a rational reason for all that gushing “this thing is important!”
I believe that in the future, when detailed knowledge of DI has become a common thing on LW among people who never read my original post, some of those people will go back and read it, and go, “Huh? Makes perfect sense to me!” making it an excellent case study of how someone can have read Eliezer’s “Expecting Short Inferential Distances”, marked it in their mind as very true and very useful, studied DI theory, and still had to go and run smack into the brick wall, knowing explicitly that that was what they were doing, before truly emotionally understanding that, yes, it actually does apply to them.
Anecdotally, this post interested me in direct instruction; none of yours did. Going back and looking, I finally found (16 paragraphs into the “quick sketch of the basic theory” section, and 7 pages of text into the post) a sentence that hinted at the intriguing description in this post: “This is why I say that a huge part of the basics of DI is ‘guided-induction’ (my term, not used in the field).”
Remember that, inductively, every sentence I read without knowing what I’m reading about or becoming interested lowers my belief that I will eventually find out what I’m reading about and become interested. The “show, don’t tell” maxim in writing helps to defend against results like 7 pages of sharing your enthusiasm before giving any clue as to what distinguishes the subject of your enthusiasm from the closest 100 enthusiasm-gathering subjects.
At this point, I have nothing more detailed to respond to that than, “I am now extremely aware of that, but thank you for telling me again, because the extra repetition couldn’t hurt my chances of remembering to thoroughly apply it in the future.”
Oh no, I know DAMN well I could’ve done WAY better if I’d been less stupid in the first place! Although if I had to communicate with my past self, I think the best thing I could have told him would be just to put a note at the beginning of the original post saying explicitly that it was a draft with many, many problems, but that I was pretty damn sure DI was a super-important topic to bring to the attention of LW, so if anyone would be so super-cool nice as to give me some feedback on how to make it more presentable...
There’s no way I could communicate the things I’ve learned so far to him more effectively than his resulting experience would teach him.
You’re right, writing concisely is definitely a learned skill.
I became pretty good at it, but that’s only through practice and helpful editors at my college student newspaper and a couple of newspaper internships. If you want to improve your professional writing skills, find a place where you can practice and people will point out your flaws so you can improve. LessWrong can definitely serve that function.
Glad you have a thick skin, glad you could start a useful conversation, and hope to see more of you in the future!
I’ve often lamented the fact that colleges so frequently assign papers with excessive minimum page limits when they would better serve their students by applying restrictive maximum page limits. Instead of learning to appreciate conciseness as a virtue and a skill, students come away with the association that a piece of writing must be long to be respectable, a lesson which many, it seems, go on to apply in their careers.
Thank you, although it’s not so much the writing per se as the analysis of the precise structure of the inferential gaps that needed to be bridged.
And you’ll see lots more of me in the future. I honestly think a big part of the reason I got over my fear of it not being perfect and posted it already was because I’m very lonely, and the case study of the NYC rationalist chapter was the biggest carrot ever.
It’s not that I’m socially inept. Quite the opposite, when I apply myself. It’s just that I get so damn tired of… well, you know, the second paragraph sums it up perfectly already, doesn’t it?
Being rational in an irrational world is incredibly lonely. Every interaction reveals that our thought processes differ widely from those around us, and I had accepted that such a divide would always exist. For the first time in my life I have dozens of people with whom I can act freely and revel in the joy of rationality without any social concern—hell, it’s actively rewarded! Until the NYC Less Wrong community formed, I didn’t realize that I was a forager lost without a tribe...
As to having a thick skin, I was actually pretty depressed the first day I got up and saw the first batch of comments, which seemed very negative, like Alicorn’s.
“Pretty depressed” as in not able to keep myself from wondering whether my failure to just commit a nice painless suicide already due to my self-preservation instinct was essentially a form of akrasia. (Obviously, past issues exist, and I’ve been using my informal understanding of REBT to keep myself together, although I think I am “naturally” a very optimistic person.)
But I forced myself to confront the question and admit, as I always do, that I do care, and am going to keep on fighting no matter how impossible success seems or how much it seems that I always just end up getting hurt over and over again, so I may as well stop whining to myself and get back to work! So I cheered myself up.
And then I got home and saw that the situation was actually pretty damn good (had like 20 upvotes, and a couple very positive messages from a few individuals), so...
I don’t think I’m going to have a crisis of faith in “the light in the world” ever again.
I mean, it’s aggravating to see things you wrote and go, “But I SAID that! Was everyone just skimming over that part or what?”
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”]
Is that useful? Anything in there unclear? Like how to learn task analysis?
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.
“I know I need to give you more information. Tell me where I should start.”
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.
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?
Ah! Sorry, I was thinking maybe you had understood some of the contents of that thread already before I mentioned it in this one.
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.
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?
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?
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
Some other thoughts: perhaps you could give me some examples of specific teaching goals you have, and specific problems you often encounter?
Sure, I can see that would be helpful. Right now I have a bunch of SAT prep students, and I teach college kids calculus when there’s a demand, but for the sake of argument let’s consider Algebra II. One of the goals in Algebra II is to get the student comfortable with polynomials: factoring, multiplying and dividing them, and understanding the relationship between those processes and things like zeroes and asymptotes of functions. So maybe we should talk about factoring?
Nearly all my students get the hang of factoring polynomials once I can convince them to sit down and practice for a while (which presents its own set of difficulties), but I’m sure I’m not teaching it optimally. Problems I run into: confusion about which term in a quadratic comes from what (“It’s supposed to multiply to this and add to this, right? Or is it the other way around?”); neglecting to look for common factors first; confusion/frustration when the leading coefficient isn’t 1; not recognizing special cases like difference of squares (only sort of a special case), higher degree polynomials in quadratic form, or sum/difference of cubes; not knowing when to use factoring by grouping. I have my own ad hoc ways of dealing with these problems, but I have no reason to believe they’re the best possible.
Maybe this is still too broad, or I’m assuming too much familiarity with the subject matter? I’m just tossing it out.
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
I like this idea. I do pretty much re-teach how to use fractions (and to a lesser extent exponents) whenever they come up, but much as I would like not having to do that, I’m not sure the problem is easily solved. Kids don’t learn how to use fractions partly because they don’t believe they need to; they decide in elementary or middle school that “decimals are way better and you can use a calculator,” and once they’re in high school they find out about “Ans=>Frac” on their graphing calculators. In my experience they really, really resent being drilled on fractions, and forget what they’ve learned very quickly because they refuse to use it for anything else. Maybe I’m being too cynical, though.
I do think it would be very useful to put together a “quit making stupid mistakes” program—if I could get kids to stop making sign errors, or doing the wrong operation because they didn’t think about it for half a second, their test scores would probably soar—and indeed I’ve seen this happen with at least one student before, so I should probably try to implement it systematically.
Hmmm, there could be lots to reply to in that post, but I’ll try to keep it brief...
Can you give me a few specific examples of actual tasks that your students have problems with most commonly? Like, show me exactly what the students are presented with.
With that, I might be able to do a transformed task analysis, and develop an example cognitive routine.
Actually, factoring is used as one illustration of a cognitive routine in Theory of Instruction. I’ll scan that section when I get time.
Ok. Well, we were talking about factoring. Here’s a factoring problem I would not expect most of my students to get:
Edit: Sorry, I guess you wanted more than one example? Not sure whether these are supposed to all be examples of the same basic type of problem, or different, or what, but I added a couple more factoring problems.
The last one might throw me off if I didn’t remember off hand that a^3+b^3 has a factoring—is there a reason one should be especially likely to mistake the others?
These are not intended to be hard factoring problems for LessWrong, as if there were such a thing. They’re hard factoring problems for most high school algebra students because none of them have a leading coefficient of 1, and because on all but the first you have to remember to look for common factors before they even look like something you can cope with. The first is mainly hard because most kids, when they even remember how to deal with the 4 at all, will try to factor it as (2x+c)(2x+c) and then give up.
These are not intended to be hard factoring problems for LessWrong, as if there were such a thing.
Successfully factor inferential distance into how hard it will be to convince people in your life of the following:
Probability is subjective
Science and its method are a social model for humans to avoid believing in untrue things, not a logically correct way to discover what is most likely true.
Absence of evidence is evidence of absence (only applies for those who were or will be in college)
Maybe the “completely” is inappropriate here? In my defense, that’s what textbooks at this level usually say when they mean “factor as far as possible using real, integer coefficients”.
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.]
My edition is 1982 (the library didn’t have any others). It doesn’t seem too different—in particular, page 143 in my edition is identical to the page 143 that you scanned and posted (which means, among other things, that there wasn’t anything added or removed to the first 143 pages; at most, there are changes in wording). Perhaps it’s just a reprint.
That makes lots of sense. I know that the original publisher folded and that’s why they had to switch to publishing it through the Association for Direct Instruction directly, but I didn’t know whether they updated it at all beyond the preface at the same time.
The book is honestly full of little typos, so I doubted they’d edited it again anyway. I’ve been taking notes of things I think belong on an errata sheet myself.
Misha, you are spectacularly awesome. =D
I mean, it’s aggravating to see things you wrote and go, “But I SAID that! Was everyone just skimming over that part or what?”, but as the aphorism runs in the DI world, “If the learner hasn’t learned, the teacher hasn’t taught”, eh? :P
[And until one sees that aphorism as perfectly consistent with “logically faultless communication”, one must know that one still hasn’t understood the meaning of the technical term.]
I knew I’d make terribly stupid mistakes in miscommunicating this stuff when I started, so I figured it was time to let go of my fear of not having it be perfect in the first place and just start trying.
I should also make sure, when you say it was 1982, do you mean original publication, or that of the copy you got? The second (and most recent) edition is 1991.
Dunno offhand what’s different. Never saw the older one myself.
You should have given some examples of things that are direct instruction and some that are not, and let us figure out what it was for ourselves! :p
Ha ha. See here.
Yeah, no. I can see not providing examples of everything you talked about, and generally not following your own preferred method to the letter. But the picture Misha has given me of DI would have told you to provide clear positive and negative examples of something within about the first full screen of text. I think I looked at three screens’ worth before giving up.
Indeed.
The reason I did not, rightly or wrongly, was because you have to start off doing this by showing how it applies in the most basic context, like in the AthabascaU module.
This results in a very technical analysis of something that initially seems trivial and pointlessly detailed, and unrelated to the amazing-looking results from studies like Project Follow-Through (which, remember, the meta-analysis says are representative).
I remember glazing over that section in the AthabascaU module myself the first time I read it. And several times after that. Only my emotional experience with the Michel Thomas lessons made me keep focusing on it until it clicked. Way later.
Now, many people on LW surely have much quicker intelligences for such things than I do.
But see the last paragraph of this comment from prase, in which he, at least, is having the same ‘this seems trivial and pointlessly detailed’ reaction after reading the AthabascaU module.
Why was he sticking with it? I believe because he had heard my emotional enthusiasm, and wanted to find out if I was just a crank, or if there was actually a rational reason for all that gushing “this thing is important!”
I believe that in the future, when detailed knowledge of DI has become a common thing on LW among people who never read my original post, some of those people will go back and read it, and go, “Huh? Makes perfect sense to me!” making it an excellent case study of how someone can have read Eliezer’s “Expecting Short Inferential Distances”, marked it in their mind as very true and very useful, studied DI theory, and still had to go and run smack into the brick wall, knowing explicitly that that was what they were doing, before truly emotionally understanding that, yes, it actually does apply to them.
Anecdotally, this post interested me in direct instruction; none of yours did. Going back and looking, I finally found (16 paragraphs into the “quick sketch of the basic theory” section, and 7 pages of text into the post) a sentence that hinted at the intriguing description in this post: “This is why I say that a huge part of the basics of DI is ‘guided-induction’ (my term, not used in the field).”
Remember that, inductively, every sentence I read without knowing what I’m reading about or becoming interested lowers my belief that I will eventually find out what I’m reading about and become interested. The “show, don’t tell” maxim in writing helps to defend against results like 7 pages of sharing your enthusiasm before giving any clue as to what distinguishes the subject of your enthusiasm from the closest 100 enthusiasm-gathering subjects.
At this point, I have nothing more detailed to respond to that than, “I am now extremely aware of that, but thank you for telling me again, because the extra repetition couldn’t hurt my chances of remembering to thoroughly apply it in the future.”
Sorry to f5 it, then—I just got the impression you were thinking inferential distance was the main problem.
Oh no, I know DAMN well I could’ve done WAY better if I’d been less stupid in the first place! Although if I had to communicate with my past self, I think the best thing I could have told him would be just to put a note at the beginning of the original post saying explicitly that it was a draft with many, many problems, but that I was pretty damn sure DI was a super-important topic to bring to the attention of LW, so if anyone would be so super-cool nice as to give me some feedback on how to make it more presentable...
There’s no way I could communicate the things I’ve learned so far to him more effectively than his resulting experience would teach him.
Uh, does this seem like an interesting idea?
You’re right, writing concisely is definitely a learned skill.
I became pretty good at it, but that’s only through practice and helpful editors at my college student newspaper and a couple of newspaper internships. If you want to improve your professional writing skills, find a place where you can practice and people will point out your flaws so you can improve. LessWrong can definitely serve that function.
Glad you have a thick skin, glad you could start a useful conversation, and hope to see more of you in the future!
I’ve often lamented the fact that colleges so frequently assign papers with excessive minimum page limits when they would better serve their students by applying restrictive maximum page limits. Instead of learning to appreciate conciseness as a virtue and a skill, students come away with the association that a piece of writing must be long to be respectable, a lesson which many, it seems, go on to apply in their careers.
Thank you, although it’s not so much the writing per se as the analysis of the precise structure of the inferential gaps that needed to be bridged.
And you’ll see lots more of me in the future. I honestly think a big part of the reason I got over my fear of it not being perfect and posted it already was because I’m very lonely, and the case study of the NYC rationalist chapter was the biggest carrot ever.
It’s not that I’m socially inept. Quite the opposite, when I apply myself. It’s just that I get so damn tired of… well, you know, the second paragraph sums it up perfectly already, doesn’t it?
As to having a thick skin, I was actually pretty depressed the first day I got up and saw the first batch of comments, which seemed very negative, like Alicorn’s.
“Pretty depressed” as in not able to keep myself from wondering whether my failure to just commit a nice painless suicide already due to my self-preservation instinct was essentially a form of akrasia. (Obviously, past issues exist, and I’ve been using my informal understanding of REBT to keep myself together, although I think I am “naturally” a very optimistic person.)
But I forced myself to confront the question and admit, as I always do, that I do care, and am going to keep on fighting no matter how impossible success seems or how much it seems that I always just end up getting hurt over and over again, so I may as well stop whining to myself and get back to work! So I cheered myself up.
And then I got home and saw that the situation was actually pretty damn good (had like 20 upvotes, and a couple very positive messages from a few individuals), so...
I don’t think I’m going to have a crisis of faith in “the light in the world” ever again.
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
Sure, I can see that would be helpful. Right now I have a bunch of SAT prep students, and I teach college kids calculus when there’s a demand, but for the sake of argument let’s consider Algebra II. One of the goals in Algebra II is to get the student comfortable with polynomials: factoring, multiplying and dividing them, and understanding the relationship between those processes and things like zeroes and asymptotes of functions. So maybe we should talk about factoring?
Nearly all my students get the hang of factoring polynomials once I can convince them to sit down and practice for a while (which presents its own set of difficulties), but I’m sure I’m not teaching it optimally. Problems I run into: confusion about which term in a quadratic comes from what (“It’s supposed to multiply to this and add to this, right? Or is it the other way around?”); neglecting to look for common factors first; confusion/frustration when the leading coefficient isn’t 1; not recognizing special cases like difference of squares (only sort of a special case), higher degree polynomials in quadratic form, or sum/difference of cubes; not knowing when to use factoring by grouping. I have my own ad hoc ways of dealing with these problems, but I have no reason to believe they’re the best possible.
Maybe this is still too broad, or I’m assuming too much familiarity with the subject matter? I’m just tossing it out.
I like this idea. I do pretty much re-teach how to use fractions (and to a lesser extent exponents) whenever they come up, but much as I would like not having to do that, I’m not sure the problem is easily solved. Kids don’t learn how to use fractions partly because they don’t believe they need to; they decide in elementary or middle school that “decimals are way better and you can use a calculator,” and once they’re in high school they find out about “Ans=>Frac” on their graphing calculators. In my experience they really, really resent being drilled on fractions, and forget what they’ve learned very quickly because they refuse to use it for anything else. Maybe I’m being too cynical, though.
I do think it would be very useful to put together a “quit making stupid mistakes” program—if I could get kids to stop making sign errors, or doing the wrong operation because they didn’t think about it for half a second, their test scores would probably soar—and indeed I’ve seen this happen with at least one student before, so I should probably try to implement it systematically.
Hmmm, there could be lots to reply to in that post, but I’ll try to keep it brief...
Can you give me a few specific examples of actual tasks that your students have problems with most commonly? Like, show me exactly what the students are presented with.
With that, I might be able to do a transformed task analysis, and develop an example cognitive routine.
Actually, factoring is used as one illustration of a cognitive routine in Theory of Instruction. I’ll scan that section when I get time.
Ok. Well, we were talking about factoring. Here’s a factoring problem I would not expect most of my students to get:
Edit: Sorry, I guess you wanted more than one example? Not sure whether these are supposed to all be examples of the same basic type of problem, or different, or what, but I added a couple more factoring problems.
Factor completely.
4x^2+11x-3
3x^3-13x^2-10x
3x^5-3x
2z^3+16
blinks
The last one might throw me off if I didn’t remember off hand that a^3+b^3 has a factoring—is there a reason one should be especially likely to mistake the others?
These are not intended to be hard factoring problems for LessWrong, as if there were such a thing. They’re hard factoring problems for most high school algebra students because none of them have a leading coefficient of 1, and because on all but the first you have to remember to look for common factors before they even look like something you can cope with. The first is mainly hard because most kids, when they even remember how to deal with the 4 at all, will try to factor it as (2x+c)(2x+c) and then give up.
Successfully factor inferential distance into how hard it will be to convince people in your life of the following:
Probability is subjective
Science and its method are a social model for humans to avoid believing in untrue things, not a logically correct way to discover what is most likely true.
Absence of evidence is evidence of absence (only applies for those who were or will be in college)
Good luck!
Its roots will be multiples of the three complex cube roots of unity, so it can’t be factored in the reals.
Maybe the “completely” is inappropriate here? In my defense, that’s what textbooks at this level usually say when they mean “factor as far as possible using real, integer coefficients”.
All I was looking for was 2(z+2)(z^2-2z+4).
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.]
My edition is 1982 (the library didn’t have any others). It doesn’t seem too different—in particular, page 143 in my edition is identical to the page 143 that you scanned and posted (which means, among other things, that there wasn’t anything added or removed to the first 143 pages; at most, there are changes in wording). Perhaps it’s just a reprint.
That makes lots of sense. I know that the original publisher folded and that’s why they had to switch to publishing it through the Association for Direct Instruction directly, but I didn’t know whether they updated it at all beyond the preface at the same time.
The book is honestly full of little typos, so I doubted they’d edited it again anyway. I’ve been taking notes of things I think belong on an errata sheet myself.