(Again, thank you so much for working with me so patiently to get through such a big inferential distance!)
You said:
There is another suspect claim:
Q: If faultless instruction fails to result in appropriate learning: A: Faultless instruction, if truly faultless, does not need revision.
This is almost a tautology (with great potential for equivocation in appropriate, fail, faultless, need etc.), but can be also viewed as a claim that DI doesn’t need revision (the answer I chose, the instruction has a problem and needs revision, has been claimed incorrect) no matter what evidence we get. Do the DI proponents in general think that when DI fails, it’s never a sign of errors in theory, but rather imperfections in implementation of the method?
“Faultless communication” is the basis of the stimulus-locus analysis branch of the theory. If faultless communication fails with a particular learner, that gives you specific information about how the learner is not using the two-attribute learning mechanism. That tells you to shift to the response-locus analysis branch of the theory to figure out how to modify the learner so that they do use it (and the stimulus-locus analysis is more just an application of normal behavioural analysis to the situations encountered around the context of DI). For instance, it could quite possibly be that the learner is able respond, but there is a compliance issue (that’s usually relatively easy to diagnose and correct in one step). Or it could be that the learner is missing at least one logically necessary concept underlying the task, in which case the stim-loc tells you what to probe for, and the resp-loc tells you how. Once you find it, you shift back to the stim-loc to figure out how to teach the missing background bits and integrate them. Or if the learner simply can’t produce the response, you shape it (or apply context-shaping if they can produce it but in the wrong context).
Once a learner has been correctly placed in a full DI program, they’re in a context where the probability of compliance problems is drastically cut down, and continuously receiving positive reinforcement for compliance. And in the DI program the way in which later, more complex concepts logically depend on earlier, simpler concepts has already been accounted for, and students are brought to mastery on the logical pre-reqs before the dependent task is introduced, so that kind of problem is pretty much ruled-out. (Although understanding in detail how this is so requires more understanding of the knowledge-systems analysis portion of the stim-loc, and in the AthabascaU module you’ve only been shown how the communications-analysis applies to the first of the ‘basic form’ concepts in that hierarchy [that is, single-dimensional non-comparatives - ‘non-comparative’ meaning that the value of an example as positive or negative is absolute rather than relative to the preceding example])
Still, the two parts of the stim-loc and and resp-loc do interplay a lot in practice, of course.
“How do you teach algorithms (such as multiplication)? How do you teach history and geography? How do you teach calculus? How do you teach scientific method?”
You teach algorithms through ‘cognitive routines’ (a classification in the knowledge-systems analysis), if they can’t be sufficiently communicated as basic or… hold on, I should lay out a quick sketch of the hierarchy:
Basic forms:
single-dimensional non-comparatives
single-dimensional comparatives
multi-dimensional non-comparative (‘nouns’, and the reason why LW familiarity with “thingspace” should help with understanding DI)
[multi-dimensional comparatives seem to be implied to me, but Theory of Instruction doesn’t even mention them. I can see how they’d be a lot harder to construct sequences for, and would in practice be already ‘naturally’ generalized by the learner once they’ve got enough examples of basic forms of the other three types]
Joining forms:
transformations
correlated-features concepts
Joining forms are the two ways in which basic forms can be related to each other.
Transformations being generalizable systems of relating various examples of the same ‘type’ to corresponding regularities in the response [like grammar rules, spelling and reading, equivalent notations, and...I think I’m actually stipulating with those examples a much narrower range of variation in what transformations can cover than I should, but you know]
And correlated-features being communications about empirical relationships between two basic forms (“if the grade gets steeper, the stream runs faster” An example of a steeper grade is shown. “Did the stream run faster?” (not shown in the example, although they understand the verbal reference to the unshown sensory discrimination of ‘runs faster’ from a previous sequence). Learner: ‘yes’. “How do you know?” Learner: “Because the grade got steeper”).
Complex forms:
communications about events (‘fact-systems’)
cognitive routines
Complex forms being just that, complex systems of basic and joining forms.
Communications about events are kind of a systematic way of designing and teaching mind-maps (which applies to a lot of things from history and geography).
Cognitive routines are algorithms, overtized so that they can be treated as physical operations. (You get any of the factors wrong in a physical operation like opening a door—unlocking it first if necessary, how you turn the handle, direction of applied force—and the environment gives you feedback: the door stays closed! But you try to read a word the wrong way and the environment does nothing to prevent you from saying the incorrect word! Independent practice on cognitive routines new to the learner is a logically insane idea, and experiments can prove it!)
Any concept that can be classified as joining can also be treated as basic, and anything that can be classified as complex can be treated through joining or basic, if the learner is already familiar. Like, you could do a non-comparative sequence “is this calculus? yes/no”, but you couldn’t teach the discrimination of ‘red’ through a cognitive routine or fact system or one of the joining forms.
But yeah, calculus as an unfamiliar topic could of course be largely approached as a body of inter-related cognitive routines (and their inter-relations mean the teaching of the whole body can be much simplified by applying single- and double-transformations).
Cognitive strategies like ‘scientific method’… well, read this comment. Like I say there, all the concepts represented by your brain on an idea like ‘reductionism’ must themselves by reducible somehow. We might not be practically able to reduce the whole huge thing in vaguely the same way we can’t calculate the exact aerodynamics of various shapes, but we can apply basic principles to do a lot better than just throwing something together (that analogy feels a bit looser than my other physics ones, but you get the point).
And I realize most of that was probably ridiculously hard to follow and pretty much most useful to me as practice reviewing the material, but unless you have some reason to think that the book Theory of Instruction is just 376 pages (not counting index and references) of crank techno-babble by two Ph.D.‘s (fine, Zig Engelmann’s is honorary from Western Michigan University, but whatever, he’s also a recipient of a Council of Scientific Society Presidents award) who are respected by multiple other Ph.D.’s they’ve collaborated with on books and papers and the DI programs themselves… and that the contents of the book have nothing to do with the reason that the DI programs they designed actually manage to achieve success in experiments like nothing else in the field of education has...
Just get your hands on the book! Because as much as I wish I could I’m not gonna be able to repost everything in it as a series of blog posts any time soon! Check a local university library, or just order it from ADI if you can’t find a copy! (It’s forty bucks, not exactly a huge expense!)
Again, thank you thank you thank you SO much for being patient and working with me so well through such a huge inferential distance!
{continued from last comment because of character limit}
(Again, thank you so much for working with me so patiently to get through such a big inferential distance!)
You said:
“Faultless communication” is the basis of the stimulus-locus analysis branch of the theory. If faultless communication fails with a particular learner, that gives you specific information about how the learner is not using the two-attribute learning mechanism. That tells you to shift to the response-locus analysis branch of the theory to figure out how to modify the learner so that they do use it (and the stimulus-locus analysis is more just an application of normal behavioural analysis to the situations encountered around the context of DI). For instance, it could quite possibly be that the learner is able respond, but there is a compliance issue (that’s usually relatively easy to diagnose and correct in one step). Or it could be that the learner is missing at least one logically necessary concept underlying the task, in which case the stim-loc tells you what to probe for, and the resp-loc tells you how. Once you find it, you shift back to the stim-loc to figure out how to teach the missing background bits and integrate them. Or if the learner simply can’t produce the response, you shape it (or apply context-shaping if they can produce it but in the wrong context).
Once a learner has been correctly placed in a full DI program, they’re in a context where the probability of compliance problems is drastically cut down, and continuously receiving positive reinforcement for compliance. And in the DI program the way in which later, more complex concepts logically depend on earlier, simpler concepts has already been accounted for, and students are brought to mastery on the logical pre-reqs before the dependent task is introduced, so that kind of problem is pretty much ruled-out. (Although understanding in detail how this is so requires more understanding of the knowledge-systems analysis portion of the stim-loc, and in the AthabascaU module you’ve only been shown how the communications-analysis applies to the first of the ‘basic form’ concepts in that hierarchy [that is, single-dimensional non-comparatives - ‘non-comparative’ meaning that the value of an example as positive or negative is absolute rather than relative to the preceding example])
Still, the two parts of the stim-loc and and resp-loc do interplay a lot in practice, of course.
You teach algorithms through ‘cognitive routines’ (a classification in the knowledge-systems analysis), if they can’t be sufficiently communicated as basic or… hold on, I should lay out a quick sketch of the hierarchy:
Basic forms:
single-dimensional non-comparatives
single-dimensional comparatives
multi-dimensional non-comparative (‘nouns’, and the reason why LW familiarity with “thingspace” should help with understanding DI)
[multi-dimensional comparatives seem to be implied to me, but Theory of Instruction doesn’t even mention them. I can see how they’d be a lot harder to construct sequences for, and would in practice be already ‘naturally’ generalized by the learner once they’ve got enough examples of basic forms of the other three types]
Joining forms:
transformations
correlated-features concepts
Joining forms are the two ways in which basic forms can be related to each other.
Transformations being generalizable systems of relating various examples of the same ‘type’ to corresponding regularities in the response [like grammar rules, spelling and reading, equivalent notations, and...I think I’m actually stipulating with those examples a much narrower range of variation in what transformations can cover than I should, but you know]
And correlated-features being communications about empirical relationships between two basic forms (“if the grade gets steeper, the stream runs faster” An example of a steeper grade is shown. “Did the stream run faster?” (not shown in the example, although they understand the verbal reference to the unshown sensory discrimination of ‘runs faster’ from a previous sequence). Learner: ‘yes’. “How do you know?” Learner: “Because the grade got steeper”).
Complex forms:
communications about events (‘fact-systems’)
cognitive routines
Complex forms being just that, complex systems of basic and joining forms.
Communications about events are kind of a systematic way of designing and teaching mind-maps (which applies to a lot of things from history and geography).
Cognitive routines are algorithms, overtized so that they can be treated as physical operations. (You get any of the factors wrong in a physical operation like opening a door—unlocking it first if necessary, how you turn the handle, direction of applied force—and the environment gives you feedback: the door stays closed! But you try to read a word the wrong way and the environment does nothing to prevent you from saying the incorrect word! Independent practice on cognitive routines new to the learner is a logically insane idea, and experiments can prove it!)
Any concept that can be classified as joining can also be treated as basic, and anything that can be classified as complex can be treated through joining or basic, if the learner is already familiar. Like, you could do a non-comparative sequence “is this calculus? yes/no”, but you couldn’t teach the discrimination of ‘red’ through a cognitive routine or fact system or one of the joining forms.
But yeah, calculus as an unfamiliar topic could of course be largely approached as a body of inter-related cognitive routines (and their inter-relations mean the teaching of the whole body can be much simplified by applying single- and double-transformations).
Cognitive strategies like ‘scientific method’… well, read this comment. Like I say there, all the concepts represented by your brain on an idea like ‘reductionism’ must themselves by reducible somehow. We might not be practically able to reduce the whole huge thing in vaguely the same way we can’t calculate the exact aerodynamics of various shapes, but we can apply basic principles to do a lot better than just throwing something together (that analogy feels a bit looser than my other physics ones, but you get the point).
And I realize most of that was probably ridiculously hard to follow and pretty much most useful to me as practice reviewing the material, but unless you have some reason to think that the book Theory of Instruction is just 376 pages (not counting index and references) of crank techno-babble by two Ph.D.‘s (fine, Zig Engelmann’s is honorary from Western Michigan University, but whatever, he’s also a recipient of a Council of Scientific Society Presidents award) who are respected by multiple other Ph.D.’s they’ve collaborated with on books and papers and the DI programs themselves… and that the contents of the book have nothing to do with the reason that the DI programs they designed actually manage to achieve success in experiments like nothing else in the field of education has...
Just get your hands on the book! Because as much as I wish I could I’m not gonna be able to repost everything in it as a series of blog posts any time soon! Check a local university library, or just order it from ADI if you can’t find a copy! (It’s forty bucks, not exactly a huge expense!)
Again, thank you thank you thank you SO much for being patient and working with me so well through such a huge inferential distance!