Few people have spent more time working through Engelmann and Carnine’s Theory of Instruction than Kristopher Boulton. Kris uses it to design math sequences for topics no DI program covers. In this episode he explains what a theory of instruction is, why the book is so famously hard to read, and how he and his wife Naveen each came to DI by very different paths.
In this Interview:
- The difference between a theory of learning and a theory of instruction, and why one can’t do the other’s job
- Why Theory of Instruction is so hard to read: according to Rob Dixon, its authors had to invent the language for a brand-new discipline
- To see a DI program’s design: you can’t see it in one lesson, only across lessons 30, 40 and 50
- Applying Engelmann’s ideas, and how Kris designs math sequences for topics no DI program covers
▸Show full transcript
[00:04] Welcome back, everyone, to the Direct Instruction Podcast. I’m here with my good friend and colleague, Kristopher Boulton. How are you doing, Kris?
[00:12] Hey Zach, doing really well today.
[00:14] It’s always great in Eugene at the National Direct Instruction Conference and Institutes that NIFDI — the National Institute for Direct Instruction — puts on. I’m super excited to ask you about something that’s come up. It was mentioned in the keynote by Carl Hendrick, who was also on the show. It’s these words: theory of instruction. And you have taken a lot of time to dig into what theory of instruction is. Can you tell us what theory of instruction is, and what it has to do with DI — capital DI, Direct Instruction?
[00:47] Well, think about it in terms of a theory of learning. There are lots of learning theories out there, and now there’s lots of talk about the science of learning, and that’s very important and can be very powerful. But you can have a robust and rigorous science or theory of learning, and still it won’t tell you anything about how to teach. It doesn’t tell you how to teach sequences on Monday, if that’s what I’m going to teach my kids, for example. That’s where you need a science or theory of instruction. And whatever that is, it needs to marry up with your theory of learning. Those two things need to be complementary, but they are distinct. It was in the ’80s that Zig Engelmann and Doug Carnine published a book they titled Theory of Instruction: Principles and Applications, and that’s exactly what it is. It’s the most extraordinary, comprehensive idea about how to teach almost anything.
[01:39] Yeah. And it’s famously—
[01:42] Unreadable.
[01:43] Unreadable, as some people say. And I think it comes down to the fact that when you’re designing these sequences, for any content, you need to get very abstract. How have you been able to take this abstraction and apply it to secondary math? There’s Essentials for Algebra as a DI program, but there are many different topics — there’s even physics adjacent to math. How have you been able to use theory of instruction to inform lessons and sequences that don’t have DI programs?
[02:18] I think, first, it’s okay to call it unreadable, because in the foreword to its own second edition, Rob Dixon says that since its publication, many things have been asked about the theory, and right up there is: why is it so difficult to read? And his answer to that question I find really interesting. He says what Doug Carnine and Zig Engelmann were trying to do was make sense of everything that was in their own heads — that they’d developed over the previous 20 years or more — and in so doing, they were giving birth to a brand-new discipline and a new field of inquiry. And because of that, they essentially had to invent language. So when you’re reading it, much of what they’re describing will be completely unfamiliar to you. It’s not a discipline you’ve already been inducted into. That makes it incredibly difficult to make sense of the first time around. The next problem is that they’re trying to articulate a general theory that could be applied to, as they say, nearly anything you want to teach. As a result, they’re taking examples here and there from programs they’ve developed. Some of them might be about how to teach the concept of equality in mathematics, other parts are about how to teach rhyming sounds in English and reading, other parts are about how to classify cars and motorbikes and trucks, and then another bit goes on for a little while about how to discriminate between different types of oak leaf. So they’ve taken a few different examples from all over the place. But most teachers — well, even an elementary or primary school teacher who works across subjects — in any one moment, they’re having to teach a subject. Now, the subjects all have distinct epistemologies. They’re all constructed from the same fundamental types of knowledge — you’ll get facts in there, you’ll get processes, you’ll get types of concepts — but the distribution of them varies a lot. Mathematics is very, very routine-heavy; biology and, say, history are very, very fact-heavy. And so how you apply it in aggregate changes quite a lot. I think it’s helped us to just really, really focus on mathematics. So now when we work with schools, teachers, chains of schools, we just work with them on mathematics for the time being, so we can really go deeper and help make sense of all these abstract ideas through lots and lots of concrete examples from across the whole mathematics curriculum, across all of the different year groups.
[04:49] It sounds complex because it is. And I guess the big question for many people is: how can I learn about this? I do want to plug this for you — you didn’t even say it — but I think people should check out your Substack. Especially if you’re teaching math, going onto your Substack allows you to get involved in chats with people who are trying this out. You’ve created a very teacher-ready, accessible process that you can go through to do the analysis, right? So I think checking out your Substack would be the place to go — and of course checking out the original work to see what we’re talking about, and knowing that if you’re a DI teacher, this process of analysis is what’s underpinning the design, right? I do want to cue you up on one more thing. You’re most famous for being the husband of the famous Naveen, who was on this podcast as well. She got an award and gave the best speech of this generation in front of all the OGs of DI. Tell me about how you both have navigated this landscape and DI together. I think it’s just so cool.
[06:06] Yeah, it’s complementary and somewhat distinct. As Naveen said in the speech, I introduced her to it really early on in our relationship. And then Naveen got access to it firsthand at one of the schools she worked at. They implemented Connecting Math Concepts, I think it was — might have been Corrective Math, one or the other. She had essentially no training whatsoever; she was just given these scripts to read from. Even a few years into teaching mathematics already, she realized just how much care and detail had gone into the production of this. It doesn’t happen immediately, because you can’t see it in one lesson, but as she was teaching it over weeks and months, she started to see how things in lessons 30, 40, 50 were all linking together with the previous lessons that had come through. And that started an ongoing love affair with the DI programs and DI implementation. She’s brought them into lots of different schools and multi-academy trusts in England, and she has a very strong working relationship with the people at NIFDI on implementation, training, coaching and development. My experience was completely different. I had to teach a group at one of the — in fact, at one point it was the number one non-selective school in England — a group of six kids who were essentially a very high-SEN nurture group. Unlike Naveen, I didn’t have access to these materials, I had no idea what I was doing, and the whole thing was a bit of a train wreck. And you know what? Nobody cares. They sort of care, but they don’t care institutionally, because those kids are never going to sit the exam; they’re never going to show up in any of the performance metrics. So, very sadly, I don’t think those kids had a great experience of mathematics at all. Naveen had a very different experience. She had the DI program, and she saw what a difference it made to children exactly like that. That’s what inspired her. I came to it through the theory of instruction route. I learned to speak other languages, like French, via a program, and then there was an analysis of that program by somebody else, and that person drew parallels between the program and theory of instruction. That led me to Theory of Instruction. And that was very difficult to read — I failed at first, and then came back and tried again. There are other books they have that sometimes explain the ideas a little more easily, like Teaching Needy Kids in Our Backward System, Could John Stuart Mill Have Saved Our Schools?, and War Against the Schools’ Academic Child Abuse. These are much easier books to read, and they expand on the ideas. There are some rudimentary analyses you can find online, which again are a little easier to make sense of. And slowly but surely, over years of reading that, connecting it with ideas from cognitive science and other behavioral sciences and variation theory, and just trying it out in the mathematics classroom, I started to piece it all together until all the bits clicked into place. But they clicked into place in a way where I devised and created it myself, based on everything I’d read, as opposed to delivering a pre-existing DI program. That’s really helpful, because there are no pre-existing DI programs for most of higher-level mathematics.
[09:26] Yeah, it’s been fun to follow you in all these things and have you on the podcast — and just honoring and respecting the folks who came before us. As your wife said, standing on the shoulders of giants this week. And listeners, this is the National Direct Instruction Conference and Institutes by NIFDI. You should come next year — I want to see you here. Kris has come multiple times; I’ve come multiple times. It’s sort of a pilgrimage. Come and join the pilgrimage, come learn about DI, and check out nifdi.org for implementation support. Thank you for tuning in.
