On the proverbial nose, Wes. I've mentioned this elsewhere, but it bears repeating: Those who are working on building "intelligent apps" would benefit greatly from reading "Theory of Instruction" *and* "Inferred Functions of Performance and Learning."
Perhaps why the latest ideas of the human cognitive architecture is based on the similar predictive processes, statistical inference and building of generative models in the predictive processing / active inference theories are gaining such traction in most neuro related fields.... education being the laggard!
I struggled to engage with Engelmanns writing, but his textbooks and living the teaching gave me a really good feel for the principles in my training year. I've since seen so many examples of variation theory from Shanghai that have absolutely transformed my teaching - making pockets of these for lessons has made me a better teacher. Thank you for sharing this very readable summary as it captures the essence for me - I'll be sharing with my team on Monday.
"Diagnose missing prerequisites and teach those systematically. True adaptation goes backward to fill gaps, not forward to circumvent them. This approach requires diagnostic thinking about why students are struggling. Surface-level difficulties often mask deeper gaps that must be addressed before progress becomes possible. The goal is not to make tasks easier but to make students more capable of handling appropriate challenges."
You make this approach sound so student-friendly! Maybe because it is. I am super-sensitive to your phrases 'fill gaps' and 'mask deeper gaps' because I have found myself--yet again--having to defend against the accusation of displaying 'deficit thinking'--which is what many of us call by its more benign label: education. Denying that 'deficits' exist can lead to a professed compassion for our students that morphs into crippling pedagogy.
Great piece Carl, I’ve also been fascinated by Engelmann’s Theory of Instruction, especially when seen alongside variation theory and Ausubel’s ideas. For me, Predictive Processing / Active Inference provide a powerful theoretical underpinning. The brain’s natural learning system is extraordinary: it infers statistical patterns, building priors (schemas) of sameness and difference from repeated experience in noisy sensory environments to better predict what will come next. Teaching effectively hacks this system — we know what powerful, well-defined priors look like, so we design sequences of examples and contrasts that let students update their generative models far more quickly than raw experience would allow. These curated sensory experiences — whether listening, reading, speaking, writing, or active exploration — all engage the same predictive machinery, accelerating concept formation in exactly the way Engelmann describes.
Predictive Processing shows us that the brain constantly predicts using its stored priors, compares these to sensory input, and generates prediction errors. If the error cannot be resolved within current priors, it produces surprise — the signal for learning. Inference then works to update the generative model by asking: what was the same and what was different from past experience that caused this surprise? Updates are tested against new sensory input, but only those tagged as salient or useful are embedded. This is where Engelmann’s emphasis on practice, rehearsal, and retrieval becomes clear: designed practice strengthens the signal of salience, while spaced retrieval inhibits forgetting through Hebbian reinforcement. Again, teaching is a deliberate hack of the brain’s natural system for forgetting and updating, ensuring the right surprises and the right updates endure.
This is truly excellent, Carl. Sharing this with our team. It’s good to see a field that used to be considered ‘only for slow learners’, or only for ‘poor kids’ getting more recognition. Maybe we can even break the ‘rediscover every hundred years’ pattern.
Thank you! Much of this was well put by Willingham in Why Students Don't Like School. Some more examples for 4,5 and 6 would be useful. I love the line that 'students overcome our instructional failures through their own cognitive resources'. This does slightly contribute to a hegemonic tone in the article though that I am not entirely comfortable with, for example the implication that teachers should have 'faultless communication'.
I'd like to invite a bit of reframing: I really appreciate how your post honors the craft of teaching. What I keep circling back to, though, is that teaching and learning aren’t reciprocal forces in the way we often assume. We’ve inherited a powerful but misleading belief that good instruction leads to good learning. Yet the relationship is rarely that direct.
Learning is an act of readiness, not reception. The old saying isn’t “When the teacher is ready, the student will learn,” but “When the student is ready, the teacher will appear.” That distinction matters. It suggests that what counts most isn’t the quality of our instruction, but the conditions we help create for curiosity, need, and self-direction to surface.
When we focus primarily on instruction, we center the teacher’s performance. When we focus on learning, we center the learner’s growth—and that changes everything from how we design experiences to how we measure success. In that sense, instruction may be necessary, but it’s never sufficient.
I sometimes use mistakes I have made in applying these principles when I show other teachers how to create good writing examples and non examples. They can learn from my classroom non examples!
Great post. I read Theory of Instruction once but like you say it's dense and much of it didn't take, this is a great list of things to consider.
I'm curious what you make of "they generalize upon the foundation of the sameness of qualities" with respect to variation theory. I agree with all of the conclusions that Engelmann and Carnine draw, but I wonder if that isn't quite the right axiom to start with. Could you draw the same conclusions by beginning with "they generalize based on similarities and differences between examples and non-examples" or something else that gets at the importance of variation and boundaries, at the human capacity for noticing differences against a sea of sameness and learning from those differences.
Respectfully, I struggle to see how I can heed #9 and still honor the suggested wisdom of ideas like desirable difficulties, retrieval practice, pre-trieval (Carpenter), etc.-- all of which appear to be seeking out errors with a totally different presupposition of their value.
Wow! this is fascinating! I'm not a "teacher" in the traditional sense but this helps me organize how I want to communicate my ideas with clarity and retention
The amount of overlap this has with building effective training data for LLMs is astounding
And this is something I am working on. I'm fascinated by it all.
On the proverbial nose, Wes. I've mentioned this elsewhere, but it bears repeating: Those who are working on building "intelligent apps" would benefit greatly from reading "Theory of Instruction" *and* "Inferred Functions of Performance and Learning."
Perhaps why the latest ideas of the human cognitive architecture is based on the similar predictive processes, statistical inference and building of generative models in the predictive processing / active inference theories are gaining such traction in most neuro related fields.... education being the laggard!
That's because some of us like to confuse people with machines.
I struggled to engage with Engelmanns writing, but his textbooks and living the teaching gave me a really good feel for the principles in my training year. I've since seen so many examples of variation theory from Shanghai that have absolutely transformed my teaching - making pockets of these for lessons has made me a better teacher. Thank you for sharing this very readable summary as it captures the essence for me - I'll be sharing with my team on Monday.
"Diagnose missing prerequisites and teach those systematically. True adaptation goes backward to fill gaps, not forward to circumvent them. This approach requires diagnostic thinking about why students are struggling. Surface-level difficulties often mask deeper gaps that must be addressed before progress becomes possible. The goal is not to make tasks easier but to make students more capable of handling appropriate challenges."
You make this approach sound so student-friendly! Maybe because it is. I am super-sensitive to your phrases 'fill gaps' and 'mask deeper gaps' because I have found myself--yet again--having to defend against the accusation of displaying 'deficit thinking'--which is what many of us call by its more benign label: education. Denying that 'deficits' exist can lead to a professed compassion for our students that morphs into crippling pedagogy.
Keep this stuff coming! It really helps.
Oh my goodness, thank you for this. 100% agree on the real scandal…
Great piece Carl, I’ve also been fascinated by Engelmann’s Theory of Instruction, especially when seen alongside variation theory and Ausubel’s ideas. For me, Predictive Processing / Active Inference provide a powerful theoretical underpinning. The brain’s natural learning system is extraordinary: it infers statistical patterns, building priors (schemas) of sameness and difference from repeated experience in noisy sensory environments to better predict what will come next. Teaching effectively hacks this system — we know what powerful, well-defined priors look like, so we design sequences of examples and contrasts that let students update their generative models far more quickly than raw experience would allow. These curated sensory experiences — whether listening, reading, speaking, writing, or active exploration — all engage the same predictive machinery, accelerating concept formation in exactly the way Engelmann describes.
Predictive Processing shows us that the brain constantly predicts using its stored priors, compares these to sensory input, and generates prediction errors. If the error cannot be resolved within current priors, it produces surprise — the signal for learning. Inference then works to update the generative model by asking: what was the same and what was different from past experience that caused this surprise? Updates are tested against new sensory input, but only those tagged as salient or useful are embedded. This is where Engelmann’s emphasis on practice, rehearsal, and retrieval becomes clear: designed practice strengthens the signal of salience, while spaced retrieval inhibits forgetting through Hebbian reinforcement. Again, teaching is a deliberate hack of the brain’s natural system for forgetting and updating, ensuring the right surprises and the right updates endure.
( To get background/ more on Predictive Processing see my blog: https://predictablycorrect.substack.com/)
This is truly excellent, Carl. Sharing this with our team. It’s good to see a field that used to be considered ‘only for slow learners’, or only for ‘poor kids’ getting more recognition. Maybe we can even break the ‘rediscover every hundred years’ pattern.
Thank you! Much of this was well put by Willingham in Why Students Don't Like School. Some more examples for 4,5 and 6 would be useful. I love the line that 'students overcome our instructional failures through their own cognitive resources'. This does slightly contribute to a hegemonic tone in the article though that I am not entirely comfortable with, for example the implication that teachers should have 'faultless communication'.
I'd like to invite a bit of reframing: I really appreciate how your post honors the craft of teaching. What I keep circling back to, though, is that teaching and learning aren’t reciprocal forces in the way we often assume. We’ve inherited a powerful but misleading belief that good instruction leads to good learning. Yet the relationship is rarely that direct.
Learning is an act of readiness, not reception. The old saying isn’t “When the teacher is ready, the student will learn,” but “When the student is ready, the teacher will appear.” That distinction matters. It suggests that what counts most isn’t the quality of our instruction, but the conditions we help create for curiosity, need, and self-direction to surface.
When we focus primarily on instruction, we center the teacher’s performance. When we focus on learning, we center the learner’s growth—and that changes everything from how we design experiences to how we measure success. In that sense, instruction may be necessary, but it’s never sufficient.
Thank you for this great article. I would add that we also need to consider the affective and motivation perspectives.
Thank you Carl Hendrick. Applause!
I sometimes use mistakes I have made in applying these principles when I show other teachers how to create good writing examples and non examples. They can learn from my classroom non examples!
Great post. I read Theory of Instruction once but like you say it's dense and much of it didn't take, this is a great list of things to consider.
I'm curious what you make of "they generalize upon the foundation of the sameness of qualities" with respect to variation theory. I agree with all of the conclusions that Engelmann and Carnine draw, but I wonder if that isn't quite the right axiom to start with. Could you draw the same conclusions by beginning with "they generalize based on similarities and differences between examples and non-examples" or something else that gets at the importance of variation and boundaries, at the human capacity for noticing differences against a sea of sameness and learning from those differences.
Respectfully, I struggle to see how I can heed #9 and still honor the suggested wisdom of ideas like desirable difficulties, retrieval practice, pre-trieval (Carpenter), etc.-- all of which appear to be seeking out errors with a totally different presupposition of their value.
Thank you for summarizing this important information!
Wow! this is fascinating! I'm not a "teacher" in the traditional sense but this helps me organize how I want to communicate my ideas with clarity and retention
As always Carl causes our learning with his post!