Oct 16, 2023·edited Oct 16, 2023Liked by Brandon Hendrickson
I realize the SAT wasn't really your main focus here, but there's an argument I've heard occasionally within the rationalist community that goes something like this:
1. IQ is virtually impossible to train.
2. The SAT is basically an IQ test.
3. Ergo, we should expect SAT prep courses to be mostly ineffective. Very few people will be able to raise their score dramatically.
It sounds like you would disagree, right? Do you think most people are capable of getting a perfect score if they use your Deep Practice Book method?
Yeah! I used to be really into this research (the title of my TEDx talk was actually "Why Doesn't SAT Prep Work?"), I but haven't looked at it for years. Here's my memory of it: zillions of studies show that test-prep courses don't impressively raise scores, and this is incredibly damning of the $14-billion-a-year industry. However, studies show there's an outlier — I can't remember the name they gave it, but I remember someone else referring to it as "Asian test prep". Those classes routinely DID result in large score increases.
My time working with the East Asian immigrant community in Seattle opened my eyes to the often MASSIVE cultural difference in test prep. Some of the white kids took SAT studying seriously; others, much less so. (No judgment — I'm not an apologist for the test.) Most of the Chinese kids, however, took studying like training for the flippin' Olympics. For some of them, it was ASSUMED that you'd spend four+ hours each Saturday and Sunday taking cram classes for the year or so before your test.
The DPB method I came up with was an attempt to combine the benefits from "cramming" with the laziness of "shrugging off" — to get the most cognitive bang for the buck.
The thing that differentiates real IQ tests from the SAT is the role of long-term memory. Sticking just with the math section, there's so much math that people forget by the time they take the test: exponential growth and factoring trinomials and whatever. If you can get that to stick in their heads (even Anki would work for a lot of this), their scores will go up.
Are most people capable of getting a perfect score? (That would mean going from a 500 to an 800 on a section — three standard deviations.) I used to think so much about that; my current guess would be under near-ideal study conditions (with lots of motivation and time), a group of 500-ers could raise to 600 at least, and a 700 maybe.
Why not all the way? Because the tests do have some new-ish material on there: e.g. weird problems that are hard to train for. (Note that some parts of an IQ are more trainable — specifically, the parts that deal with long term ["crystallized"] memory.)
If anyone would like to find citations to any of these hazily-remembered studies, please share 'em (especially if they contradict my memories).
Math aesthetics are so funny. I made sure to tackle the problem before reading on, and was so surprised you'd written it as (pi - 2)/2 when it seemed obviously pi/2-1 to me!
One possible extra step for solving is thinking about how to "sanity check" your result. Once I did my geometric thinking, I wanted to make sure that pi/2-1 was in fact going to be between zero and 1!
Which reminds me of how I used to get math-nerdy students angry by telling them, "Look, π is just three." They'd (of course) respond "no, it's three-point-one-four-one-five-nine..." and I'd point out that we were BOTH approximating π, but I was doing it in a way that allowed for mental math, and (as you say) sanity checks.
Then I'd ask them WHY π was 3.14... (rather than, say, 3.13, or 3.02), and they'd have no idea what I was talking about. Very few of them had any idea that π is just the ratio of the distance around a circle and the distance across it. They had learned the high-level stuff, and missed the utter basics.
If there's an Eganian lesson underneath that, it might be something like "it can be useful to teach kids the mysticism of numbers, and π is transcendental and all, but we should be sure that when we do that we're not handicapping them."
"But that wasn’t the best part! Occasionally, while re-solving a problem for perhaps the fifth or sixth time, I’d realize that I had been an idiot. I had been solving a problem by doing a long series of steps — but if I just re-conceived the problem, looked at it from a different perspective, the entire thing would be easy, could be solved in one or two moves."
This was my experience reading Euclid for the first time. I'd just aced calculus at university, but a really smart acquaintance put me onto Euclid's Elements. Easy, I thought. Basic geometry? A breeze! So I cracked open the book and tried the first four problems. I couldn't come up with a proof for any of them on my own. When I looked at Euclid's proofs, at first they looked like random steps that just happened luckily to solve the problems. But as I dug into the proofs, it suddenly hit me that Euclid was "looking" at the problems differently. The trick was to "see" the circles and lines in a certain way right from the start, and as soon as you saw them that way, you could solve the problem in just a few steps. The philosophers (I was a philosophy major at the time) call this "insight" or "intuitive cognition." It's why Plato thought Euclid's geometry was a pre-req for philosophy, since "insight" was precisely what it trained you to have.
By the way, I love the idea of "Deep Practice Book." I mentioned this idea earlier to my algebra students today, only I called it a "Math Monster Book." We do a math puzzle at the start of each class, and now I'm rethinking the ones I give them. Usually I throw softballs as a class starter, but what if we start out hard and then I tell them to add the problem to their Monster Book for future practice? If I try this, I'll report back with results. :)
Love it! At some point, I’ll have to write about how I Eganized our elementary program’s math curriculum (we used JUMP Math) with “Megaboss Problems”. In brief: before each new unit, I’d look at the final test, come up with my own versions of them, and tape them to the wall. Except: (1) they’d be much, MUCH harder, and (2) they’d be ridiculous. We gave incentives in class for any student who could solve ‘em. That gave a purpose to learning the math lessons.
We also did a “Boss Problems” thing, which was similar, but instead of being taped up before each unit, I’d put a super-hard problem at the start of each lesson (which was designed to only be solvable if you understood that particular lesson’s idea). I remember that the rule was: if kids could solve it, they didn’t need to do the lesson.
I found this really interesting. I just started homeschooling my 12yo son this fall and Math was never my best subject. Do you think this technique would be good to use for us? We currently do Khan Academy. I’m thinking we could just use the quiz/text questions he gets wrong and use this technique?
Worth a try! My recommendation would be to start as small as possible — with a single problem that he had a hard time with, but would like to be the master of.
It's best if he picks it, but you might want to scribble down a few contenders, and have him choose from among them — just give one of them to him after a few days or weeks, to help him see that human brains aren't designed to hold math in 'em.
After that (or maybe before it?) it's probably worth presenting the whole idea of a DPB to him (maybe by reading the main section of this post aloud?), talking about it, and getting his buy-in to try some.
The end goal is students copying down the problems themselves and all, but you both might benefit from your kick-starting the process by doing most of the work.
(Thanks — as the homeschooling father of a 13-year-old son, this is helpful for me to think about!)
Hi, Brandon! I am really, really hooked on your substack! My kids go to a Montessori school here in Brazil and I am very much in love with Maria Montessori vision - however, as her biographer, Rita Kramer, answered on an interview, she could have done much more if not for all the wars and dictatorships that got her moving around and having to start over again and again (Italy, Spain, the US, India). Besides, it's a known issue with the Montessori system the whole 12+ onwards. She had ideas, many interesting ones, but never really got to test them for enough time.
Egan seems to be a good match for Montessori, at least as far as I understood your points. I am still not so sure about the whole Ironic thing and the Somatic seems quite underestimated on the whole, but I can clearly see why you fell in love with his ideas. I am really, really, really interested in better understanding the whole thing - and I'm glad you wrote the ACX review and then, these posts! I am very fond of your way of writing, even the whole Q&A thing.
As for the point of this essay in particular:
1 - my mind was pleasantly blown by the alternate solution for the problem. I was trying to think of a different way of solving, got a blank, and when I saw the explanation, it felt great! That is why I love Mathematics, have always loved. It's elegant! I was thinking that there probably is a way to link this view with sets. If we take each quarter-circle to be A and B, then A + B - AintersectionB = AunionB. AintersectionB = A + B - AunionB. A and B are both pi/4, AunionB is the square, 1, so AintersectionB = pi/2 - 1. I am not actually really good with set theory, so maybe this does not generalize.
2 - I can see how this can work great for Maths, Physics, Chemistry. Now, what about less-problem based, more info-based subjects? You mentioned Anki for foreign language, clear usage, no questions. Do you think for studying Law, for an example, where students are required to remember articles, laws, jurisprudence and stuff like that, we should go for Anki too? Biology when it comes to knowing cells, organs, etc; Geography when it's about names and dates, etc? Anki + testing regularly to detect weak spots + get a feeling for the shape of the questions?
What about the other subjects? Say, Literature/Language when it's about learning to write and interpret texts and use the language? Coding, maybe? Economics, when it's about understanding the whole dynamics, not memorizing formula or particular names?
Your notion of another alternate method for that circle–square problem has got me thinking about the Pythagorean Theorem, whose fame is such that it's attracted (according to some quick Googling) 371+ independent proofs, and from such luminaries as da Vinci, a 12-year-old Einstein, and U.S. President Garfield.
(Well, I'm not sure I'd call Garfield a "luminary". I have a degree in history, and other than that one fact, I'm not sure I can tell you anything interesting he accomplished at all. "His name was Garfield" and "he was assassinated by an anarchist" don't count, because he didn't have much of a choice in either...)
It's interesting to me that MANY things kids do in math could attract this same kind of love and care. (If anyone is interested in this, the book "The Teaching Gap" shows how, in Japan, math class is based on this notion.)
I'd say that the power of a Deep Practice Book is that it helps match spaced repetition (even if one doesn't perfectly follow an exponential forgetting curve, as Hermann Ebbinghaus would bid us do) with analytical problem-solving. I'd say that for most of the fields you mentioned — law, geography, biology, and literature — would be better served with Anki decks.
(Which isn't, of course, to say that Anki should take over ALL or even MOST of the learning in those domains — there are bigger-picture ideas to be grokked, and Anki excels at small-picture stuff.)
Coding and economics, I'm not sure!
If anyone who loves Anki is interested in seeing the Anki decks I make my students, lemme know; I'm happy to share.
Yes, I'm being ambitious here and trying to better understand how the ideal model of school/community center for interaction and learning for all ages (my current idea for replacement of this "school" thing we are attached to) would work. The DPB is great for some subjects, and Anki would certainly improve several subjects that rely on memorization. However, there are still certain concepts that need to be discussed in a broader sense and through a greater lens - here the myths, the stories behind the discoveries and ideas, the evaluation of different views, these take some time and I don't think optimizing for time should be at the core. Even if our students only grapple with half a dozen of these ideas each year, these should be deep dives and less ocupied with teaching them the content, I reckon we should be focusing on teaching them skills and tools for thinking, learning, grappling with these. Not to teach them how to sail from Rio to Novgorod, but to sail.
Brandon, I know you have lots and lots and lots of things to say, to explain, and I think you could run ~two~ three parallel series: one on the big ideas of Egan, one on how Egan's ideas interact with other great thinkers on education, and one on the practical aspects, the teaching of subjects, the development of students' knowledge, skills and tools. Welp, you probably have 100+ posts to write and 1000+ possible posts on which to ponder!
I'm so glad that you mentioned Anki at the end. The whole idea of a DPB seems incredibly compatible with spaced-repetition. I kept thinking that you could just chuck those questions onto Anki flashcards and it would be great. Do you think a regular review of all problems in the same session (as described in the post) is likely to deliver better results?
Man, I used to spend SO MUCH TIME thinking about this!
I think there's a different curve (in effect) for problem-solving than for straight-up memory. Basically, you want to repeat solving a problem far more often than you would memorizing a single piece of information.
Why? A couple reasons.
First, the problem involves lots of pieces of information — one repetition ain't enough. Second (and more importantly), each time you re-solve a hard problem, you see more good stuff in it than you did before — so you want to maximize your opportunities to do that.
When I was using a lot of DPBs with students, though, I did create rules of thumb for their practice, to build more "forgetting curve" into it — something like "once a week, re-solve ALL the problems, but each day, spend a minute looking at each of the problems marked "HARD".
That said, for those of us who swear by Anki, having an Anki deck of cards for problems we've gotten to "Automatic" would be a great idea — we could just snap photos (or take screenshots) of the pages.
This is an amazing piece and I am so glad to come across it.
Thank you for this especially since you honestly showed its limits in tutoring vs classroom.
I could say I'm a test prep coach for Caribbean high-stakes tests, for Biology specifically. I would love to try this with both my one-on-one clients and online classes. I do have an idea of where I can find tough questions, but any suggestions for the online classes? I only see them once a week and many are busy working adults.
Love the notion of this in golf! Have you read Daniel Coyle (he, the author of “The Talent Code” mentioned above)? He wrote a follow-up — “The Little Book of Talent” — that applies some of his ideas to golf. (Oh, and he recorded this video — you’ll want to watch to the end: https://youtu.be/dY7QNxXbziA?si=9AgLBguxJW1uxg-d )
I haven't. Watched the vid, thank you. not sure if you have same quirk, but when I watch New Person, and they overstate a detail that i know, then i banish them to Don't Trust List.
in this case, Dan says "Deep Practice is 10x better than Regular Practice." yeah yeah but that's twisting the empirical findings, this guy is Selling, fine, I'm tuning out.
BUT I often remove someone from Don't Trust List if someone else (you) says "No no persist, this guy is good."
I'm a fan of Dan Coyle; there was a moment in the Aughts when I hoped his popularization of K. Anders Ericsson's work (emphasizing deliberate practice) would triumph over Malcolm Gladwell's (emphasizing the 10,000 rule). That hope was dashed! So yeah, you're definitely correct to interpret Coyle as a popularizer, and to not give his precise words your full trust: that said, he's one of the GOOD popularizers.
As an aside, I might actually agree that deliberate practice (which is just Coyle's term for "deliberate practice", which is a mouthful) really IS 10x better than "regular practice"... but that's because I'm including in "regular practice" a whole lot of stuff that people do that's virtually valueless (and occasionally anti-helpful). But if there's evidence to the contrary, please set me straight.
well heck wish i'd you. allergic kid so mom kept me home when furnace started up because i'
d sniffle. never got that daily habit of math. in college finally had abcomyter math class that worked with my brain. lots of hands on visualizatin of ratiis and such.
I realize the SAT wasn't really your main focus here, but there's an argument I've heard occasionally within the rationalist community that goes something like this:
1. IQ is virtually impossible to train.
2. The SAT is basically an IQ test.
3. Ergo, we should expect SAT prep courses to be mostly ineffective. Very few people will be able to raise their score dramatically.
It sounds like you would disagree, right? Do you think most people are capable of getting a perfect score if they use your Deep Practice Book method?
Yeah! I used to be really into this research (the title of my TEDx talk was actually "Why Doesn't SAT Prep Work?"), I but haven't looked at it for years. Here's my memory of it: zillions of studies show that test-prep courses don't impressively raise scores, and this is incredibly damning of the $14-billion-a-year industry. However, studies show there's an outlier — I can't remember the name they gave it, but I remember someone else referring to it as "Asian test prep". Those classes routinely DID result in large score increases.
My time working with the East Asian immigrant community in Seattle opened my eyes to the often MASSIVE cultural difference in test prep. Some of the white kids took SAT studying seriously; others, much less so. (No judgment — I'm not an apologist for the test.) Most of the Chinese kids, however, took studying like training for the flippin' Olympics. For some of them, it was ASSUMED that you'd spend four+ hours each Saturday and Sunday taking cram classes for the year or so before your test.
The DPB method I came up with was an attempt to combine the benefits from "cramming" with the laziness of "shrugging off" — to get the most cognitive bang for the buck.
The thing that differentiates real IQ tests from the SAT is the role of long-term memory. Sticking just with the math section, there's so much math that people forget by the time they take the test: exponential growth and factoring trinomials and whatever. If you can get that to stick in their heads (even Anki would work for a lot of this), their scores will go up.
Are most people capable of getting a perfect score? (That would mean going from a 500 to an 800 on a section — three standard deviations.) I used to think so much about that; my current guess would be under near-ideal study conditions (with lots of motivation and time), a group of 500-ers could raise to 600 at least, and a 700 maybe.
Why not all the way? Because the tests do have some new-ish material on there: e.g. weird problems that are hard to train for. (Note that some parts of an IQ are more trainable — specifically, the parts that deal with long term ["crystallized"] memory.)
If anyone would like to find citations to any of these hazily-remembered studies, please share 'em (especially if they contradict my memories).
Math aesthetics are so funny. I made sure to tackle the problem before reading on, and was so surprised you'd written it as (pi - 2)/2 when it seemed obviously pi/2-1 to me!
One possible extra step for solving is thinking about how to "sanity check" your result. Once I did my geometric thinking, I wanted to make sure that pi/2-1 was in fact going to be between zero and 1!
Sanity checks: undervalued in math classes!
Which reminds me of how I used to get math-nerdy students angry by telling them, "Look, π is just three." They'd (of course) respond "no, it's three-point-one-four-one-five-nine..." and I'd point out that we were BOTH approximating π, but I was doing it in a way that allowed for mental math, and (as you say) sanity checks.
Then I'd ask them WHY π was 3.14... (rather than, say, 3.13, or 3.02), and they'd have no idea what I was talking about. Very few of them had any idea that π is just the ratio of the distance around a circle and the distance across it. They had learned the high-level stuff, and missed the utter basics.
If there's an Eganian lesson underneath that, it might be something like "it can be useful to teach kids the mysticism of numbers, and π is transcendental and all, but we should be sure that when we do that we're not handicapping them."
"But that wasn’t the best part! Occasionally, while re-solving a problem for perhaps the fifth or sixth time, I’d realize that I had been an idiot. I had been solving a problem by doing a long series of steps — but if I just re-conceived the problem, looked at it from a different perspective, the entire thing would be easy, could be solved in one or two moves."
This was my experience reading Euclid for the first time. I'd just aced calculus at university, but a really smart acquaintance put me onto Euclid's Elements. Easy, I thought. Basic geometry? A breeze! So I cracked open the book and tried the first four problems. I couldn't come up with a proof for any of them on my own. When I looked at Euclid's proofs, at first they looked like random steps that just happened luckily to solve the problems. But as I dug into the proofs, it suddenly hit me that Euclid was "looking" at the problems differently. The trick was to "see" the circles and lines in a certain way right from the start, and as soon as you saw them that way, you could solve the problem in just a few steps. The philosophers (I was a philosophy major at the time) call this "insight" or "intuitive cognition." It's why Plato thought Euclid's geometry was a pre-req for philosophy, since "insight" was precisely what it trained you to have.
By the way, I love the idea of "Deep Practice Book." I mentioned this idea earlier to my algebra students today, only I called it a "Math Monster Book." We do a math puzzle at the start of each class, and now I'm rethinking the ones I give them. Usually I throw softballs as a class starter, but what if we start out hard and then I tell them to add the problem to their Monster Book for future practice? If I try this, I'll report back with results. :)
Love it! At some point, I’ll have to write about how I Eganized our elementary program’s math curriculum (we used JUMP Math) with “Megaboss Problems”. In brief: before each new unit, I’d look at the final test, come up with my own versions of them, and tape them to the wall. Except: (1) they’d be much, MUCH harder, and (2) they’d be ridiculous. We gave incentives in class for any student who could solve ‘em. That gave a purpose to learning the math lessons.
We also did a “Boss Problems” thing, which was similar, but instead of being taped up before each unit, I’d put a super-hard problem at the start of each lesson (which was designed to only be solvable if you understood that particular lesson’s idea). I remember that the rule was: if kids could solve it, they didn’t need to do the lesson.
Very motivating!
I found this really interesting. I just started homeschooling my 12yo son this fall and Math was never my best subject. Do you think this technique would be good to use for us? We currently do Khan Academy. I’m thinking we could just use the quiz/text questions he gets wrong and use this technique?
Worth a try! My recommendation would be to start as small as possible — with a single problem that he had a hard time with, but would like to be the master of.
It's best if he picks it, but you might want to scribble down a few contenders, and have him choose from among them — just give one of them to him after a few days or weeks, to help him see that human brains aren't designed to hold math in 'em.
After that (or maybe before it?) it's probably worth presenting the whole idea of a DPB to him (maybe by reading the main section of this post aloud?), talking about it, and getting his buy-in to try some.
The end goal is students copying down the problems themselves and all, but you both might benefit from your kick-starting the process by doing most of the work.
(Thanks — as the homeschooling father of a 13-year-old son, this is helpful for me to think about!)
Hi, Brandon! I am really, really hooked on your substack! My kids go to a Montessori school here in Brazil and I am very much in love with Maria Montessori vision - however, as her biographer, Rita Kramer, answered on an interview, she could have done much more if not for all the wars and dictatorships that got her moving around and having to start over again and again (Italy, Spain, the US, India). Besides, it's a known issue with the Montessori system the whole 12+ onwards. She had ideas, many interesting ones, but never really got to test them for enough time.
Egan seems to be a good match for Montessori, at least as far as I understood your points. I am still not so sure about the whole Ironic thing and the Somatic seems quite underestimated on the whole, but I can clearly see why you fell in love with his ideas. I am really, really, really interested in better understanding the whole thing - and I'm glad you wrote the ACX review and then, these posts! I am very fond of your way of writing, even the whole Q&A thing.
As for the point of this essay in particular:
1 - my mind was pleasantly blown by the alternate solution for the problem. I was trying to think of a different way of solving, got a blank, and when I saw the explanation, it felt great! That is why I love Mathematics, have always loved. It's elegant! I was thinking that there probably is a way to link this view with sets. If we take each quarter-circle to be A and B, then A + B - AintersectionB = AunionB. AintersectionB = A + B - AunionB. A and B are both pi/4, AunionB is the square, 1, so AintersectionB = pi/2 - 1. I am not actually really good with set theory, so maybe this does not generalize.
2 - I can see how this can work great for Maths, Physics, Chemistry. Now, what about less-problem based, more info-based subjects? You mentioned Anki for foreign language, clear usage, no questions. Do you think for studying Law, for an example, where students are required to remember articles, laws, jurisprudence and stuff like that, we should go for Anki too? Biology when it comes to knowing cells, organs, etc; Geography when it's about names and dates, etc? Anki + testing regularly to detect weak spots + get a feeling for the shape of the questions?
What about the other subjects? Say, Literature/Language when it's about learning to write and interpret texts and use the language? Coding, maybe? Economics, when it's about understanding the whole dynamics, not memorizing formula or particular names?
Your notion of another alternate method for that circle–square problem has got me thinking about the Pythagorean Theorem, whose fame is such that it's attracted (according to some quick Googling) 371+ independent proofs, and from such luminaries as da Vinci, a 12-year-old Einstein, and U.S. President Garfield.
(Well, I'm not sure I'd call Garfield a "luminary". I have a degree in history, and other than that one fact, I'm not sure I can tell you anything interesting he accomplished at all. "His name was Garfield" and "he was assassinated by an anarchist" don't count, because he didn't have much of a choice in either...)
It's interesting to me that MANY things kids do in math could attract this same kind of love and care. (If anyone is interested in this, the book "The Teaching Gap" shows how, in Japan, math class is based on this notion.)
I'd say that the power of a Deep Practice Book is that it helps match spaced repetition (even if one doesn't perfectly follow an exponential forgetting curve, as Hermann Ebbinghaus would bid us do) with analytical problem-solving. I'd say that for most of the fields you mentioned — law, geography, biology, and literature — would be better served with Anki decks.
(Which isn't, of course, to say that Anki should take over ALL or even MOST of the learning in those domains — there are bigger-picture ideas to be grokked, and Anki excels at small-picture stuff.)
Coding and economics, I'm not sure!
If anyone who loves Anki is interested in seeing the Anki decks I make my students, lemme know; I'm happy to share.
Yes, I'm being ambitious here and trying to better understand how the ideal model of school/community center for interaction and learning for all ages (my current idea for replacement of this "school" thing we are attached to) would work. The DPB is great for some subjects, and Anki would certainly improve several subjects that rely on memorization. However, there are still certain concepts that need to be discussed in a broader sense and through a greater lens - here the myths, the stories behind the discoveries and ideas, the evaluation of different views, these take some time and I don't think optimizing for time should be at the core. Even if our students only grapple with half a dozen of these ideas each year, these should be deep dives and less ocupied with teaching them the content, I reckon we should be focusing on teaching them skills and tools for thinking, learning, grappling with these. Not to teach them how to sail from Rio to Novgorod, but to sail.
Brandon, I know you have lots and lots and lots of things to say, to explain, and I think you could run ~two~ three parallel series: one on the big ideas of Egan, one on how Egan's ideas interact with other great thinkers on education, and one on the practical aspects, the teaching of subjects, the development of students' knowledge, skills and tools. Welp, you probably have 100+ posts to write and 1000+ possible posts on which to ponder!
I'm so glad that you mentioned Anki at the end. The whole idea of a DPB seems incredibly compatible with spaced-repetition. I kept thinking that you could just chuck those questions onto Anki flashcards and it would be great. Do you think a regular review of all problems in the same session (as described in the post) is likely to deliver better results?
Man, I used to spend SO MUCH TIME thinking about this!
I think there's a different curve (in effect) for problem-solving than for straight-up memory. Basically, you want to repeat solving a problem far more often than you would memorizing a single piece of information.
Why? A couple reasons.
First, the problem involves lots of pieces of information — one repetition ain't enough. Second (and more importantly), each time you re-solve a hard problem, you see more good stuff in it than you did before — so you want to maximize your opportunities to do that.
When I was using a lot of DPBs with students, though, I did create rules of thumb for their practice, to build more "forgetting curve" into it — something like "once a week, re-solve ALL the problems, but each day, spend a minute looking at each of the problems marked "HARD".
That said, for those of us who swear by Anki, having an Anki deck of cards for problems we've gotten to "Automatic" would be a great idea — we could just snap photos (or take screenshots) of the pages.
This is an amazing piece and I am so glad to come across it.
Thank you for this especially since you honestly showed its limits in tutoring vs classroom.
I could say I'm a test prep coach for Caribbean high-stakes tests, for Biology specifically. I would love to try this with both my one-on-one clients and online classes. I do have an idea of where I can find tough questions, but any suggestions for the online classes? I only see them once a week and many are busy working adults.
Loved the detail in this blog. You're a fantastic writer.
I wonder if your point here is broadly true, not just for math learning.
I've been toying with a related idea in golf, helping players improve with their own customized deep practice books.
Love the notion of this in golf! Have you read Daniel Coyle (he, the author of “The Talent Code” mentioned above)? He wrote a follow-up — “The Little Book of Talent” — that applies some of his ideas to golf. (Oh, and he recorded this video — you’ll want to watch to the end: https://youtu.be/dY7QNxXbziA?si=9AgLBguxJW1uxg-d )
I haven't. Watched the vid, thank you. not sure if you have same quirk, but when I watch New Person, and they overstate a detail that i know, then i banish them to Don't Trust List.
in this case, Dan says "Deep Practice is 10x better than Regular Practice." yeah yeah but that's twisting the empirical findings, this guy is Selling, fine, I'm tuning out.
BUT I often remove someone from Don't Trust List if someone else (you) says "No no persist, this guy is good."
No, no, persist — this guy is good!
;)
I'm a fan of Dan Coyle; there was a moment in the Aughts when I hoped his popularization of K. Anders Ericsson's work (emphasizing deliberate practice) would triumph over Malcolm Gladwell's (emphasizing the 10,000 rule). That hope was dashed! So yeah, you're definitely correct to interpret Coyle as a popularizer, and to not give his precise words your full trust: that said, he's one of the GOOD popularizers.
As an aside, I might actually agree that deliberate practice (which is just Coyle's term for "deliberate practice", which is a mouthful) really IS 10x better than "regular practice"... but that's because I'm including in "regular practice" a whole lot of stuff that people do that's virtually valueless (and occasionally anti-helpful). But if there's evidence to the contrary, please set me straight.
well heck wish i'd you. allergic kid so mom kept me home when furnace started up because i'
d sniffle. never got that daily habit of math. in college finally had abcomyter math class that worked with my brain. lots of hands on visualizatin of ratiis and such.