Finally: The spacing effect gets its due!


Spaced repetition flashcards are my religion. Well: there's a problematically simple statement! (My actual religious views don't quite fit into a single, punchy sentence.) I'll put this a bit more straight-forwardly:

I have a collection of 5,972 flash cards. Each has been custom-made by me. Many of them are mind-changing quotes from various books and articles I've read:


That was the front — I've chosen two words to replace with [...]. When I see the card, I'm prompted to recall the crucial words that have been taken out:


I take the most exciting ideas from what I read, and put them into my personally-favorite spaced-repetition flashcard program  — Anki, which can be downloaded for free at

There are lots of ordinary flashcard programs out there. Many of them are pretty flashy, and easy to use: I'm looking at you, Quizlet!

They're all terrible. Or at least they're all terrible when it comes to the core purpose of learning: integrating knowledge into your mind for the long-term. 

Spaced-repetition flashcard programs use the spacing effect (the link is to the Wikipedia page) to give you maximal memory with minimal reviews.

To simplify some complicated math: after the first time I see a flashcard, the program waits 10 minutes to show it to me again.

Then it waits 1 day. Then 3 days. Then 1 week. Then 3 weeks. Then 2 months. Then 6 months. Then 1.5 years. Then 4 years. Then 12 years.

With only a handful of reviews, I can secure anything I want to remember, forever.

And then (and here's the religion part!) each day, I review the cards that Anki tells me to review. Amazingly, this only takes 5–10 minutes — but that's enough for Anki to preserve every flashcard in my long-term memory.

I've been doing this nearly every day for six or seven years now.

It's part of my quest to cultivate genius in myself.

For years, I've been scratching my head as to why more people haven't heard of the spacing effect. And just this morning, the brilliant (and always-worth-reading) educational reporter Annie Murphy Paul, touched on the spacing effect in her newsletter, The Brilliant Report.

Now, sometimes when I tell people about this, they scrunch their foreheads: Why on Earth would you want to just memorize this information? they seem to be saying. (I know that, because sometimes they actually say that aloud!)

Well, I don't just want to "memorize" the stuff! That would be stupid. I use Anki to plant ideas in my mind. I use it to put every amazing idea I read into my long-term memory, where it can blend together with every other thing that I learn.

People sometimes refer to me as "creative". Well: this is one of the secrets to my creativity.

Justine Musk, author and former wife of entrepreneur Elon Musk, wrote that the secret to innovation is to combine different worlds of knowledge:

bring them together in a way that will introduce hot ideas to each other, so they can have idea sex and make idea babies that no one has seen before...

That's what Anki is for me: an orgy of ideas! (My apologies for, um, that metaphor.)

I have so much more to write about Anki, and about spaced repetition more generally. For now, I'll hold back, and just ask a few questions:

  • How could a spaced-repetition flashcard program infuse every aspect of the curriculum?
  • What would it mean if we could guarantee students that everything they want to remember, could be remembered forever (with minimal work)?
  • Is it possible for a new kind of school to regularly help students cultivate genius?

I've previously pursued a few of these ideas in a bit more depth on this blog — especially in my posts about planting ideas, and about using "Leitner boxes" (which are a sort of physical flashcard system that uses a rudimentary spacing effect — now in use at the Island Academy of Hilton Head!).

Group math lessons AND personal math puzzles


A problem:

There's wonderful value in learning math as a group: students can help one another, and every day be reminded that everyone can understand math.

But there's wonderful value in learning math as an individual: each student can spend time struggling with whatever puzzles bamboozle him or her.

Each of these has its advantages and disadvantages — we need a synthesis.

The synthesis that many American schools choose often doesn't convince students that everyone can learn all of K-12 math, and also doesn't give every student a collection of math puzzles that bamboozle them.

Our basic plan:

We spend about an hour a day on corporate math lessons — in K-8, using the JUMP Math curriculum. (The JUMP approach excels at rapidly breaking down complex big ideas into understandable tiny ideas, and then helping students arrange these tiny ideas together.)

We also, though, have students individually play with off-curriculum math puzzles (starting with the puzzles of James Tanton), with the goal of finding puzzles that still stump them after (say) 10 minutes of focused struggle. We have them collect those problems in their personal Deep Practice Book, and help them make small-breakthrough after small-breakthrough. (We don't just tell them the answer.)

Because we understand that all memories deteriorate after time, we have students regularly re-solve (and re-approach) all the problems in their Deep Practice Books — perhaps once a week. As time goes on, and they re-solve a puzzle three, four, five, or more times, something wonderful can happen: problems that had once been unsolvable become easy, and even obvious. Puzzles that had been vexing and hateful become delightful and friendly.

And every once in a while, the student will realize that there's a much more beautiful way of unravelling the puzzle. This is a momentous discovery: it's as if the clouds roll back and a trumpet reveille sounds from the heavens! How often did moments like that happen in your K-12 math experience?

As students engrave these puzzles into their brains, they'll grow to love math more, and understand it much more deeply than is now possible in the conveyor-belt math approach that most schools use.

Our goals:

We think it's possible for all students to perfectly understand the K-12 math curriculum.

We think it's possible for all students to grow to love (at least in small part) the process of doing and understanding math.

We think math can become the place in the curriculum where students most develop their growth mindset — that they see math is something difficult that they can do. We can shatter the myth that only some people can understand math.

If you walk into our classrooms, you might see:

Walking into our classrooms, you might stumble upon one of our whole-group math lessons: expect to see the teacher posing a score of tiny questions to a focused group of students. During independent work time, you might see a student frowning intently as she tries yet another way to solve an especially diabolical puzzle. When she fails (again!), she goes through a problem-solving methodology, to better tease out any clues that could help her crack the riddle.

Some specific questions:

  • Are James Tanton's puzzles good to start in grade school?
  • What other good options are available for mathematical puzzles?
  • I mention here developing a single, standard problem-solving methodology. That would be great — if we could train the kids in just one, then performing it would become a habit, one that could extend what our kids are able to do throughout the rest of their lives. But: what problem-solving methodology should we try out? (I do have the beginnings of this, and will be working on it over the summer. Presumably, too, the kids in the classroom can slowly evolve an even better one!)
  • Lee, are the kids in your class too diverse in ages/math abilities to do any kind of group lessons with? Or are there enough little kids to jump into JUMP at the lowest levels? An alternative (that still uses JUMP) is just to have kids work through the workbooks themselves, with the teacher giving assists when needed. Corbett Charter School did something like this (though not with JUMP), and an amazing math teacher that both you and I know suggested that this "kids working by themselves" method might suffice to help kids learn the whole K-12 math curriculum (though she didn't think it was ideal).
  • Math circles haven't come into this description at all. They're magical. Where should they fit?

Leitner box


A problem:

We leak memories. In school, we stock up knowledge and understanding — but it evaporates. Forgetting is quick and brutal, and impedes future comprehension.

We leak memories even of things that we value. College, for me, was a never-ending series of wows! (It probably helped that I picked my classes mostly on whim, based on which struck my interest.) And yet I can hardly remember anything from my history degree. I learned this the hard way when I tried to teach a European history class, and couldn't remember any of the delightful little stories I had obsessed over in college. Sometimes, now,  I flip through my class books, and can't believe I've ever read them — there's just no memory there.

We're not even asked to value what we learnIn school we learn, and learn, and learn, but we're not given a chance to determine what things, specifically, we love.

Our basic plan:

Students keep, and regularly review, a collection of what they've found most valuable, or interesting, or wonderful, or important.

Each day each student adds to their collection, creating 1–2 flash cards that encapsulates what they've learned that they most love. Flash cards are made elegantly (however the student defines that) and are stored in a Leitner box.

Each day each students reviews their collection, using a spaced repetition system wherein newer cards get reviewed more frequently, and older cards get reviewed less frequently.

Over weeks and months, everything that students enter into their Leitner boxes gets engraved in their memories: they carry around their favorite knowledge wherever they go, and will for the rest of their lives.

The act of reviewing can be a delight: a chance to re-taste some tasty bits of knowledge and to re-visit their past selves ("Why did I ever think this was interesting?!"). It's also a chance to combine knowledge in new arrangements, making connections between information that was previously unrelated.

Eventually, we may transition the cards to a computerized spaced repetition system, like Anki.

Our goals:

Theologian James K. A. Smith writes:

our identity is shaped by what we ultimately love… what, at the end of the day, gives us a sense of meaning, purpose, understanding, and orientation to our being-in-the-world.

Our hope is that the Leitner boxes provide a chance for students to consciously ponder and freely choose those things, and to reflect on them more deeply (and ultimately build them into themselves).

Thus the goals for this really are that students experience more autonomy in school, see what they learn in school as an opportunity to build themselves, and ultimately care more deeply about what they learn.

If you walk into our classrooms, you might see:

Students slowly going through their day's reviews, smiling in reverie.

At the end of the day, the whole class pausing for ten minutes to reflect on what they've learned, and to carefully make two flash cards out of the choicest bits.

Some specific questions:

  • Each kid should get a specific box, but what sort of box that is, and how it looks (or is decorated) should be up to the individual student.
  • "Flashcard" connects soul-crushing tedium, but these flashcards are exactly the opposite! Should we avoid the word "flashcard"?
  • 1–2 cards per day — is that a good number?

Classrooms for brilliant innovation


How can we create a generation of brilliantly innovative kids?    And let's be clear: this is the purpose of our school. We're going to spend a lot of time learning about the past, and recapitulating its greatest accomplishments, but this is all toward the goal of doing new things in the future.

As the Renaissance reader, writer, and thinker Salutati wrote:

I have always believed that I must imitate antiquity not simply to reproduce it, but in order to produce something new.

So how do we create this generation of brilliantly innovative kids?

First, we have to understand the nature of creativity. Then, we need to build it into every piece of our school.


It's a professional nuisance, I suppose, that I end up hearing so much nonsense about creativity. Most educational innovators drivel on about "creativity", rarely defining the word (often it seems to mean anything to do with art) and trusting that creativity is natural.

The assumption seems to be that if you just "let out" the native forces of a child, creativity will result.

Well, sometimes. But not frequently.

At least, new, good ideas don't just spill out all by themselves. (Unless the kid is some kind of creative genius, in which case, why do we have them in a school at all?)


That's not to say that you force creativity. Typically, you don't — forcing doesn't get you innovation. Rather, new, good ideas take cultivation — they pop up in certain contexts, and not others. Get the environment right, and you'll get innovation.

What environment is that? 

Steven Johnson wrote the book on this: Where Good Ideas Come From: A Natural History of Innovation. His major idea:

Don't think of creativity as forging new ideas by yourself. Think of creativity, rather, as piecing together others' ideas to make something new.


We have a natural tendency to romanticize breakthrough innovations, imagining momentous ideas transcending their surroundings, a gifted mind somehow seeing over the detritus of old ideas and ossified tradition. 

But ideas are works of bricolage; they're built out of that detritus. We take the ideas we've inherited or that we've stumbled across, and we jigger them together into some new shape. (pp. 28–28, emphasis mine)

(Ooh — there's an RSA Animates for the book! Enjoy the next four minutes and six seconds of your life.) Johnson continues:

The trick to having good ideas is not to sit around in glorious isolation and try to think big thoughts. The trick is to get more parts on the tableA good idea is a network. (p. 42 & 45)

Creative students are network-builders. They take scads of other data, and combine them together in new ways. A limiting factor, then, is how many ideas they can stumble across! We need our school to be as idea-thick as possible. 

I hope it's apparent that we're planning to do just that — crowd our school with stories and thoughts and questions and images and facts and plenty of other abstract nouns I'm forgetting.

And those from as many disciplines as possible — chemistry and religion and art and math and music and biology and everything. Narrow disciplinary boundaries are the death of innovation (at least in K-12 classrooms).

Immerse our kids with wonderful and diverse content — one of the keys to prompting creativity.

But — if only ensuring creativity were so simple! Because here we run smack into a big problem; in fact, a fundamental cognitive limit.

Creativity is connecting, and the easiest place to connect ideas is inside your own head. We pull information — ideas, stories, facts, questions, images, whatever — out of our long-term memory, and connect it with whatever new thing we're looking at.

The trouble is that it's easy — scandalously easy! — to misplace the memories in your long-term memory.

We all know this, of course. You've learned far, far more about (say) the Civil War than you're aware of right now. Much of that knowledge is still inside your skull, somewhere. If you heard it again, you'd recall that, yes, you'd heard it before. But you couldn't have said what it was. The knowledge was more or less useless to you.

This is the Tragedy of Long-Term Memory. (Well, it's one of the tragedies. The other is that you just plum forget things. More on that, and how to overcome it, in a later post.)

And some people fall prey to this tragedy more than others. Some people are simply worse at making these connections — they can't access their long-term memories as quickly, can't hold as much data in their working memories (more on this later) to juggle the ideas around.

So we're in danger of privileging some of our students over others. To some extent, this is unavoidable — but we should look for tools that will equalize the playing field.

Delightfully, there's a fix! And this fix revolutionized human society: write ideas down. 

Paper is the original creativity-extender. (Well, clay tablets, but nuts to the Sumerians!) Writing things down offloads the memory. We can think just by leafing through a notebook. Of course, there is the occasional glitch:

Professor Henry Jones: Well, he who finds the Grail must face the final challenge. Indiana Jones: What final challenge? Professor Henry Jones: Three devices of such lethal cunning. Indiana Jones: Booby traps? Professor Henry Jones: Oh, yes. But I found the clues that will safely take us through them in the Chronicles of St. Anselm. Indiana Jones: [pleased] Well, what are they? Indiana Jones: [annoyed] Can't you remember? Professor Henry Jones: I wrote them down in my diary so that I wouldn't have to remember.

But that trouble seems more limited to international adventurers than to K-12 students.

Except maybe it's not. 


I want to point out that I'm not just blasting conventional schools, here. I'm rather tickled that schools make use of one of humanity's most time-tested cognitive tools! But why don't school notebooks, as they're popularly used, increase creativity?

Three reasons, I think.

First, creativity isn't part of the curriculum. Many classes don't ask students to think new thoughts — and when they do (English essays, for example), they don't train students in how to cobble together old ideas to make new ones.

Second, the notebooks aren't used for creativity. Notebooks are seen as places to dump data, and maybe review it before a test — not places to access again and again to get new insight.

Third, when was the last time you looked through your school notebooks? You can cheat for this one, and include your college notebook. Did you leaf through them in the last month? Less than a year ago? I didn't think so. (And neither did I — and I kept mine!) We dump data in, and then let it moulder there.


There's a solution to this. Well, actually there are a number of solutions to this — but I want to outline just one today:

Externalize knowledge. Splay it on the walls.

One major purpose of classroom walls is to store information. Interesting information. Beautiful information. Information that students value, and which can help them think new thoughts in the future.

The walls can take on some of the role of long-term memory.

Information on the walls can be casually referenced in class. Students can browse the walls when they're stuck for an idea.

Of course, we can't fit all of the information students learn on the walls — only the most meager sliver of it. But that's all we need: we can fill the walls with triggers for what the class has already learned.

Triggers for what they've already learned: that seems a crucial piece. It's not that we'll put new information on the walls. That'd be stupid. New knowledge is best learned through other people (and experience, and books, and any number of other things). It's not best learned through truncated bits of information hung on a wall.

But the walls can display bits of information that students have already learned — bits that trigger complex recollections.

At the beginning of the year, much of the wall-space of a classroom, therefore, will be empty. As the classes move on, we'll gradually fill the walls until the room becomes an index of what's their heads.

I say "index" — but it can be thought of as a sort of machine, with students the moving parts. They'll walk around, connecting an idea here (next to the wind0w) with a question there (above the sink), comparing it all to a story there (behind the plants).

Students must play a hand in construction of this — they can deliberate as to what to put on the wall. It's an externalization of their knowledge, after all.


But I have to apologize: this probably seems entirely abstract. Next, I'll hope to give an example of one type of information we can put up — a "wall of talking dead people" — and what we can do with it — practice moral creativity.