Very interesting. Upvoted, despite structural problems, but that has all been said already.
I have a minor interest in education (my mother is a teacher and I’m kinda her outside adviser), but I’m mostly interested in how to apply this to self-teaching. I can see how this would be awesome if you had a competent teacher to design a course for you, but how can I use DI if no such course exists?
As far as I can tell, one key idea is to construct a series of minimal examples to illustrate one (and only one) new concept. I’ve been using this for language learning very successfully so far (and it works even better combined with spaced repetition), but how do I use this for more abstract or complex concepts?
Mathematical proofs are something that I’m still struggling with in general (both constructing and understanding them). Let’s take the relatively simple proof that sqrt(2) is irrational. The presentation is fairly typical: it’s terse, no motivation for any step is provided, and the whole setup is confusing. Even worse, I don’t even see how I can apply the idea of example cases to this proof. It’s not a general property, so I can’t look at other cases. How do I now transform this into something not-confusing using DI? What would a DI teacher do here? (And ideally, how can I do this on my own without understanding it first?)
(As an aspiring polyglot, I also picked up the French Michel Thomas course and will test it this week. I had previously given up on French because of how awful the learning material for it was, compared to Japanese or Latin, and because it’s only a minor language for me, so I can’t be bothered to design my own material. Maybe this will work better.)
Cool, I look forward to discussing the French lessons with you (although honestly I’ve lately been practicing Spanish a lot more).
Remember to ask me for some small charts I made that will help you immensely in properly producing all the standard French phonemes that differ from the standard (American) English set at some point.
DI could probably be somewhat adapted to help in self-teaching, since it would at least give you a useful classification system for what possible logical structure the ideas you’re looking for might have… but that’s the possible structures of the most basic components, which for an advanced subject are arranged in relationships which make the whole thing exponentially more complex. Although different complex ideas can often differ in small ways, but...
Yeah, I dunno. It would have at least a little use I’m sure, but I would bet it couldn’t produce anywhere near the level of “magic”-seeming results that a good DI program designed by someone who already understands the material can.
But really, the basic answer is, “No. DI is simply the application of practical epistemology to teaching. When you are learning something on your own, you have to apply practical epistemology in the normal direction.”
Oh, and If you’re interested in Japanese but aren’t yet at a very high level, look for the book “Japanese Verbs & Essentials of Grammar” by Rita L. Lampkin. I took Japanese in high school, and the school only had a grade 11 class. I came into it below the level of the other students, but the teacher bumped me up to being the only grade 12 Japanese student in the school during that year. I believe that book was the single most significant factor in that, and any enabling traits I had on the side, I’m sure you already have too.
Actually, even though I still achieved a very weak grasp of the language at my peak and quickly lost most of that when I stopped practicing after grade 12, I think I would be able to apply DI theory to use that reference work to produce some great instruction on using the language expressively in a conversational context once I master the use of DI theory more.
(Essentially I would be using the book as a ‘prosthetic’ understanding of the material while I designed the instruction. I haven’t given it much thought, but I think this may not be possible in the same way with mathematical proofs [cuz that’s more cognitive routines than just transformation concepts, and cognitive routines are higher in the hierarchy of the knowledge-system analysis because they incorporate transformations as components.])
And that’s actually a project I’ve been thinking about how I might possibly do it eventually for a while.
You sound like you could make an awesome collaborator on something like that, if you got your hands on a copy of Theory of Instruction.
[Edit: note that language instruction will generally be much easier to design (for any student who already has a good adult grasp of their native language).
This is because it’s largely just subtype analysis of single- and double-transformations that you need to understand, which means you really don’t need the sections of Theory of Instruction that deal with cognitive routines, diagnosis and corrections, the response-locus analysis, and philosophical and research issues, and that’s the entire last half of the book!
Well, a bit of the response-locus analysis would be useful for teaching the production of new phonemes, but not that much theoretical detail.
The major practical difficulty would be tracking the schedule of the integrated review, simply because of the sheer number of distinct entires (vocabulary words and grammatical patterns), but it would be relatively easy to design a Computer Assisted Design program to help with that.
Oh, and the subtype analysis, which is the most complicated theoretical part, needed for ordering the introduction of the transformation concepts, is only needed for teaching all the basic grammatical structures of the language.
Once you’re done with that, all that’s left is just vocabulary and idioms, which pretty much just follow the same logical template over and over again.
(The only difference is that you’d start to be able to provide more and more of the definitions and directions of the instruction entirely within the target language.)]
Mathematical proofs are something that I’m still struggling with in general (both constructing and understanding them). Let’s take the relatively simple proof that sqrt(2) is irrational. The presentation is fairly typical: it’s terse, no motivation for any step is provided, and the whole setup is confusing. Even worse, I don’t even see how I can apply the idea of example cases to this proof. It’s not a general property, so I can’t look at other cases.
It’s a particular property, which you can apply to other cases by substituting some other particularity—for example, replace 2 by any other number throughout and see whether the proof still goes through. Doing this sort of thing will tell you how the proof works and why it works.
As an aspiring polyglot, I also picked up the French Michel Thomas course and will test it this week.
I’m interested in knowing how this goes. I’ve never got very far when learning other languages, although I have to say I’m not impressed by the Michel Thomas web site or the Amazon reviews. I suspect that his method would drive me up the wall.
Very interesting. Upvoted, despite structural problems, but that has all been said already.
I have a minor interest in education (my mother is a teacher and I’m kinda her outside adviser), but I’m mostly interested in how to apply this to self-teaching. I can see how this would be awesome if you had a competent teacher to design a course for you, but how can I use DI if no such course exists?
As far as I can tell, one key idea is to construct a series of minimal examples to illustrate one (and only one) new concept. I’ve been using this for language learning very successfully so far (and it works even better combined with spaced repetition), but how do I use this for more abstract or complex concepts?
Mathematical proofs are something that I’m still struggling with in general (both constructing and understanding them). Let’s take the relatively simple proof that sqrt(2) is irrational. The presentation is fairly typical: it’s terse, no motivation for any step is provided, and the whole setup is confusing. Even worse, I don’t even see how I can apply the idea of example cases to this proof. It’s not a general property, so I can’t look at other cases. How do I now transform this into something not-confusing using DI? What would a DI teacher do here? (And ideally, how can I do this on my own without understanding it first?)
(As an aspiring polyglot, I also picked up the French Michel Thomas course and will test it this week. I had previously given up on French because of how awful the learning material for it was, compared to Japanese or Latin, and because it’s only a minor language for me, so I can’t be bothered to design my own material. Maybe this will work better.)
Cool, I look forward to discussing the French lessons with you (although honestly I’ve lately been practicing Spanish a lot more).
Remember to ask me for some small charts I made that will help you immensely in properly producing all the standard French phonemes that differ from the standard (American) English set at some point.
DI could probably be somewhat adapted to help in self-teaching, since it would at least give you a useful classification system for what possible logical structure the ideas you’re looking for might have… but that’s the possible structures of the most basic components, which for an advanced subject are arranged in relationships which make the whole thing exponentially more complex. Although different complex ideas can often differ in small ways, but...
Yeah, I dunno. It would have at least a little use I’m sure, but I would bet it couldn’t produce anywhere near the level of “magic”-seeming results that a good DI program designed by someone who already understands the material can.
But really, the basic answer is, “No. DI is simply the application of practical epistemology to teaching. When you are learning something on your own, you have to apply practical epistemology in the normal direction.”
Oh, and If you’re interested in Japanese but aren’t yet at a very high level, look for the book “Japanese Verbs & Essentials of Grammar” by Rita L. Lampkin. I took Japanese in high school, and the school only had a grade 11 class. I came into it below the level of the other students, but the teacher bumped me up to being the only grade 12 Japanese student in the school during that year. I believe that book was the single most significant factor in that, and any enabling traits I had on the side, I’m sure you already have too.
Actually, even though I still achieved a very weak grasp of the language at my peak and quickly lost most of that when I stopped practicing after grade 12, I think I would be able to apply DI theory to use that reference work to produce some great instruction on using the language expressively in a conversational context once I master the use of DI theory more.
(Essentially I would be using the book as a ‘prosthetic’ understanding of the material while I designed the instruction. I haven’t given it much thought, but I think this may not be possible in the same way with mathematical proofs [cuz that’s more cognitive routines than just transformation concepts, and cognitive routines are higher in the hierarchy of the knowledge-system analysis because they incorporate transformations as components.])
And that’s actually a project I’ve been thinking about how I might possibly do it eventually for a while.
You sound like you could make an awesome collaborator on something like that, if you got your hands on a copy of Theory of Instruction.
[Edit: note that language instruction will generally be much easier to design (for any student who already has a good adult grasp of their native language).
This is because it’s largely just subtype analysis of single- and double-transformations that you need to understand, which means you really don’t need the sections of Theory of Instruction that deal with cognitive routines, diagnosis and corrections, the response-locus analysis, and philosophical and research issues, and that’s the entire last half of the book!
Well, a bit of the response-locus analysis would be useful for teaching the production of new phonemes, but not that much theoretical detail.
The major practical difficulty would be tracking the schedule of the integrated review, simply because of the sheer number of distinct entires (vocabulary words and grammatical patterns), but it would be relatively easy to design a Computer Assisted Design program to help with that.
Oh, and the subtype analysis, which is the most complicated theoretical part, needed for ordering the introduction of the transformation concepts, is only needed for teaching all the basic grammatical structures of the language.
Once you’re done with that, all that’s left is just vocabulary and idioms, which pretty much just follow the same logical template over and over again.
(The only difference is that you’d start to be able to provide more and more of the definitions and directions of the instruction entirely within the target language.)]
It’s a particular property, which you can apply to other cases by substituting some other particularity—for example, replace 2 by any other number throughout and see whether the proof still goes through. Doing this sort of thing will tell you how the proof works and why it works.
I’m interested in knowing how this goes. I’ve never got very far when learning other languages, although I have to say I’m not impressed by the Michel Thomas web site or the Amazon reviews. I suspect that his method would drive me up the wall.