Cognitive Load Theory is one of the most useful frameworks in education. It tells us that working memory is limited, that extraneous complexity impedes learning, that beginners and experts have different instructional needs.

All of that is true.

But it's only ¼ of the story.🧵 CLT is a theory of interference: it tells us what prevents learning.

What it doesn't tell us - and was never designed to tell us - is what produces learning in the first place.

These are different questions.

And the first tells us very little about the second.

In 𝘏𝘰𝘸 𝘞𝘦 𝘓𝘦𝘢𝘳𝘯, Stanislas Dehaene—one of the world’s leading cognitive neuroscientists and winner of the Nobel-equivalent Brain Prize—identifies the 4 Biological Pillars of Learning. Without all 4 of these pillars in place, learning is fragile and will not last: 🧵 Pillar #1: Attention

Dehaene identifies attention as the brain's gateway to learning; virtually no information reaches long-term memory without it. Attention amplifies the selected signal and suppresses everything else. Visual or verbal distractions inhibit learning at the neurological level. Dehaene is specific: overly illustrated textbooks and excessively decorated classrooms prevent children from concentrating. The learning environment must direct attention, not fragment it.

Okay, so I’ve been having a lot of trouble tweeting my thoughts lately…

My main interest in life other than my family is improving people’s lives through education, and I've searched for a method of teaching math that works for everyone for the past 30 years, going wherever that search led me.

Which was mostly nowhere.

Year after year in the earlier part of my career, most of my students came to me not knowing math, and 𝘭𝘦𝘧𝘵 me not knowing math, despite Herculean efforts on my part. It was heart-wrenching. I read every book on teaching math I could get my hands on. I tried every approach imaginable. I gave up - and then started over again - countless times.

And then I crashed and burned for a while. (Thinking I’d never achieve my main goal in life - and that I had been delusional to think it possible in the first place - was almost the end of me. Literally.)

And then, several years ago, and mostly out of the blue, I discovered the most effective method of teaching math imaginable.

I was thrilled, of course, and couldn’t wait to share it with other teachers! - but there was an enormous problem that came along with it, a problem I’ve avoided dealing with.

Here’s that story:

1/10 During the pandemic and remote learning several years back, and out of sheer desperation, I rigged up a system of teaching math to my students based on one-to-one pre-worked examples and practice problems, along with instant feedback. I figured it was the best I could do now that I could no longer teach them in person. I had no idea it would be 𝘣𝘦𝘵𝘵𝘦𝘳 than me teaching them in person - 𝘪𝘯𝘧𝘪𝘯𝘪𝘵𝘦𝘭𝘺 better.

Turns out, given sequential, example-based math materials, my students were fully capable of teaching 𝘵𝘩𝘦𝘮𝘴𝘦𝘭𝘷𝘦𝘴. This thought, I’m embarrassed to admit, had never occurred to me before - but now it consumed me.

2/10

One morning a number of years ago, I forgot to erase a completed problem on the whiteboard from the previous math class before my next group of 7th graders came in. To my surprise, instead of barreling in loudly as usual, the new class glanced at the left-over problem and quietly took their seats, evidently thinking this was a continuation of the “silent teaching” strategy I had been using with them recently. “I get this!” one of the students suddenly exclaimed, and others soon followed suit. A follow-up practice problem proved that they indeed 𝘥𝘪𝘥 get it - without me even saying a word.

I had accidentally discovered the power of pre-worked examples.

I had been working through examples with my students for a number of years by this point, both with commentary and silently, and I thought I had taken John Sweller’s concept of 𝘸𝘰𝘳𝘬𝘦𝘥 𝘦𝘹𝘢𝘮𝘱𝘭𝘦𝘴 as far as it could go. In an instant I found I had merely been scratching the surface; it had never occurred to me that the students could and would work through the examples on their own.

In the years since that day, I’ve incorporated pre-worked examples into practically everything I do as a math teacher - from classroom instruction to the creation of the 𝘠𝘰𝘶 𝘛𝘦𝘢𝘤𝘩 𝘠𝘰𝘶 book series - and I’ve had plenty of opportunities to reflect on what makes them so powerful and useful. Here are some of my conclusions:

1/13 Pre-worked examples focus attention instantly. Before students even have a chance to wonder what they’re supposed to be doing, a pre-worked example says “We’re doing 𝘵𝘩𝘪𝘴.”

2/13

Years ago, I had the unfortunate task of trying to teach a math class that simply could not stop talking. It didn’t matter if I was facing the dry erase board or the students themselves; if I said something, they said something, if I said something else, they said something else. All. period. long. Every. single. day. Threats of trips to the principal didn’t matter. Letters home didn’t matter. And these kids liked me too! Didn’t matter. The chatter continued incessantly.

One day, in a fit of frustration and dread as I was about to launch into another problem at the board, I blurted out, “Okay, nobody talks this time - 𝘯𝘰𝘵 𝘦𝘷𝘦𝘯 𝘮𝘦!”

And shockingly, as I worked my way through the problem, no one did.

And even more shockingly, when I asked them how I had just 𝘴𝘰𝘭𝘷𝘦𝘥 the problem, most of their hands shot into the air.

Thinking this may have just been a fluke, I launched into another problem the same way.

Same result.

Another problem.

Same result.

For the first time all year, we got through a whole class period without me wanting to pull my rapidly graying hair out in clumps the entire time.

Then came the biggest shock of all: when the students filtered into class the next day, they immediately asked, “Can you do that silent thing again today?”

I had discovered 𝘴𝘪𝘭𝘦𝘯𝘵 𝘵𝘦𝘢𝘤𝘩𝘪𝘯𝘨, which I subsequently learned is an actual thing.

Naturally, I used this strategy with all of my classes for the rest of that year. And I was literally astounded by the results - students now focused on the content and asked meaningful questions, and I was able to cover way more content, and maintain my personal sanity to boot.

Since that time, I’ve reflected on what makes this strategy so successful. My thoughts follow…

1/8 Silent teaching focuses attention like a laser beam. Students know precisely what they’re supposed to be focusing on, and have no distracting chatter preventing them from focusing on it.

2/8