Short Video Transcripts (September 2026)

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How to turn math into a superpower

Being really good at math, it’s kinda weird. Cause by itself, math is kinda underpowered. But when you combine it with some other area of expertise, it’s so overpowered Just ridiculously overpowered See, here’s the thing Most of the world does not care about pure math. But if you bring it as a power up to something else like coding, science, engineering, finance… or really any other deep domain obsession. Those serious math chops become a gigantic force multiplier. And that’s why learning math early is so valuable. The earlier those tools become automatic The more time you have to explore and find a field that you really care about and go deep. And that’s the thing, the goal is not to collect intellectual trophies. It is to become so technically skilled That you can solve real problems in ways that other people can’t even see.

Math trauma isn't really about math

Math trauma it really tends to be less about math itself and more about somebody asking you to perform advanced maneuvers before you’ve even mastered the basics. Imagine this. Imagine going to skating lessons ice skating lessons and your coach tells you to try skating backwards on one leg, and you can barely even skate forwards on two legs. But that’s what coach is telling you to do. So you try it and you fall, you get up, you try again, you fall again And I mean, deep down you know that this is hopeless ‘cause you can’t, you can’t even skate forwards. Like, how are you gonna skate backwards on one leg?! You can’t even skate forwards on two legs But your coach just keeps on telling you like, “Try harder, try harder.” And you’re just like, “I c- can’t do it.” And you’re just like crashing out ‘cause there’s this, you just know that there’s this huge prerequisite gap Between what you’re actually able to do and where your coach expects you to be. That’s the frustrating part when the coach is not recognizing that there’s this massive gap and helping you bridge that gap. They’re expecting you to just jump to the highest rung of the ladder in one go. And if you can’t do it, then it’s just ‘cause you’re lazy or you gotta try harder. Just try again, even though it’s just hopeless. That’s really what Math trauma is about. I mean, whether it’s math, skating, swimming, whatever That kind of experience would be traumatic for anybody.

The technical bar is skyrocketing

If you are a student who’s interested in tech, You need to be aware that you gotta graduate with serious technical skills. See, you used to be able to just learn a few basics, Make a few toy projects, And then get serious and skill up on the job. But those days are over The bar, the standard is just so much higher nowadays. So you gotta be able to hit the ground running. You have to be a net positive very early. You have to be more capable than an LLM. And that requires years of serious upskilling that most schools, even most top colleges, are not delivering on See, a degree is no longer proof of skill. An A in a course is no longer proof of skill. The bar for joining that technical workforce, it is skyrocketing And the bar for graduating school is cratering. That gap needs to close, and as of now, you are the only one who can close it for yourself.

The status quo isn't good enough

We can’t help people who don’t think that they need help. And the reality is that most students aren’t even at grade level in math. And a lot of schools have decided that they can just ignore the problem, that it’s okay if students are not prepared for the next grade Or that it’s an unsolvable problem Or that everybody has the same problem, so we don’t need to fix it. I mean, hey, if you’re fine with the results, then sure, keep doing what you’re doing. But If most kids reach high school unable to do basic algebra, then maybe the status quo isn’t good enough.

The limits of classroom teaching

Even a great teacher can’t easily implement mastery learning in a classroom. You know, where students only move on to a next topic after mastering its prerequisites. See, here’s the problem You’re a public school teacher. You got 4 classes, each with 20 to 30 kids That’s like 100 students that you’re having to manage all in parallel. And one single teacher can’t keep track of every single topic every kid knows or they don’t know Or just how well they learn it and what should they learn next It’s, it’s, it’s just too much work. And unless the teacher has some kind of technology to help them do that work, to manage the knowledge profiles and learning schedules of all these different students Unless they have that, the teacher just has to move the whole class at the same pace. And that means some kids just sit there bored waiting for everybody else to catch up while other kids are rushed through and they gotta move on before they’re actually ready. And because math is so brutally hierarchical, They just fall further and further behind with every new topic.

When homework isn't a good signal

A lot of homework in schools today is graded for completion, not accuracy. Did you turn something in? Did you upload it to Canvas? Did you check a box? But that’s, that’s useless as far as actual learning. It doesn’t tell you, like, does the student actually understand the concept? Did they actually do the problems correctly? Did they even do it themselves? Did they just outsource it to AI or Their older sibling, their smart friend…? Who knows? See, homework is supposed to be practice. And practice only helps if somebody is actually checking whether you’re practicing correctly and giving you feedback on the things that you gotta tweak so that you can improve on them. Otherwise, you can spend a whole hour doing homework and reinforce the exact mistakes that you were supposed to fix.

Learn faster, don't aim lower

Middle schoolers can learn all of high school math Yeah, algebra 1 all the way through calculus in just 3 years if they have the right setup. Now, I know that might seem kind of crazy, but here’s how to think about it. Think about driving 100 miles. In back roads, that might take like five hours. But on a highway, that only takes 2, maybe 1 and a half. See, the distance didn’t change, but the conditions did. You can go fast when the road is paved and there aren’t tons of bumps and potholes. And it’s the same thing with learning. The whole idea is you don’t have to bring the destination closer. You don’t have to decrease the distance from algebra to calculus. If you just improve the learning conditions: Make sure students know the prerequisites for each new thing you’re trying to get them to learn, scaffold each new thing so that they can learn it smoothly instead of constantly staring off into space, racking their brains about what the heck is going on. That is how you get students there faster.

The potholes of learning

The potholes of learning are when you find out that you have a knowledge gap that’s blocking you from learning the thing that you’re trying to learn. You try to learn this new thing and you’re like, “Oh, wait, this doesn’t make any sense. Why does it make sense?” And you have to kind of backtrack and figure out what’s the bottom of your foundation where things first are not really making sense? Then you gotta build all that up again. And if you are continually having to do that on every single topic that you learn, you waste a lot of time just figuring out what the heck is it that is confusing me that I have to learn before I learn this new thing? And often it’s really hard to figure that stuff out Cause you don’t have a great mental model of the subject. I mean, if you did, you’d already be an expert who knows a lot about it. And so that’s why it takes an expert to kinda help you chart a course that avoids all these potholes in your learning journey, so you can just step on the gas and go fast.

Learning debt compounds

Learning debt. It starts when adults stop correcting all these workarounds, these hacks to get by. Like, like you always use your forehand instead of your backhand, so You never develop your backhand. That’s a learning debt, and so is when you let a student keep on recalculating their multiplication tables Instead of actually memorizing them. Or you let them use a calculator instead of doing some simple mental arithmetic. I mean, I get it. Adults don’t want to nag, right? They don’t want conflict So they let these workarounds slide. But that skill gap, it, it doesn’t disappear, it just hides. And it compounds. And eventually it slows down progress. Students hit these ceilings that never even needed to exist. But the skill gap grows so big and so ingrained that everyone just assumes that it reflects innate ability or lack thereof. And if you scale that across millions of students, Then eventually you get a system That leaves millions of students without the skills to succeed.

Stop grading attendance

Attendance should not be a part of a student’s grade. I mean, your grade should answer one question, right? How well do you know the material? That’s it so if a student skips every lecture, teaches themselves from the textbook, and then aces the exam, they know the material, so give them an A. And if another student has perfect attendance, takes beautiful notes, and still can’t solve the problems, then they don’t know the material. So they shouldn’t get a grade that suggests that they do. So stop grading proxies for learning And don’t pretend that sitting in a chair is evidence of mastery.

When a workaround becomes a trap

Some alternative learning methods feel easier because they avoid the actual skill. I mean, take lattice multiplication, for example Kids often like it because it’s really pretty and visual and it’s fun to draw But it’s also slow And if they get attached to it, They just stop practicing the more efficient standard method. And if you let this continue, then eventually the alternative method becomes a workaround and the workaround becomes a trap, a crutch. The homework takes longer, More advanced problems get harder, And the student has to go back and relearn that method that they should have been practicing all along. I mean, it’s inefficient and leads to all sorts of frustration.

Projects can help or harm

Projects can make math really fun, but only if the students actually have the prerequisites in place to do them. Cause if they don’t, if they don’t know the basics and you’re asking them to do this advanced project, then it is an awful experience. They’re sitting there confused like, “What am I even supposed to be doing?” How do I even start? So they just look over and copy what the smart kid does, right? And even if the project is something that they find intrinsically interesting, If they can’t actually do it, then they’re just being set up to fail. And that sends the exact wrong message. It sends the message, “I’m not cut out for this. There’s this thing that I think is really cool, intrinsically interesting, and I’m not cut out for it.”

Division of labor is division of learning

In a lot of classroom group projects, The strongest student does everything. They carry their entire group, and the weaker students just don’t really learn anything. And that’s not just some minor classroom inconvenience. That, uh, this is a structural failure mode of learning, of education. From the outside, it can look pretty collaborative, right? Makes for a good photo op, everyone’s discussing, engaged… or so it looks. But the thing is engagement does not imply learning. Learning requires direct contact with the work, pushing it forward yourself in a productive way. You gotta attempt to retrieve things that you’ve learned, do so successfully, Make a few mistakes, correct them, repeat again All right, I did it right this time. Now you’ve learned And somebody else cannot do that process for you. You don’t learn by watching somebody else do that process. You gotta do it yourself. So division of labor in a group project is, it’s ultimately division of learning. And concentrating that labor on one student, the smart kid who’s carrying their whole group, doing all the work for ‘em, That is a concentration of learning on that one student.

The anti-memorization movement

The anti- memorization movement has left millions of students unable to think because every little operation consumes their working memory. For instance, solving equations. It’s really smooth when basic arithmetic is automatic. It’s like moving puzzle pieces around. You just gotta figure out how they fit together. But if you are not automatic on your basic arithmetic, if you don’t know your times tables, if you’re always having to recalculate all that from scratch, then every puzzle piece that you try to move around when solving these equations, it’s like a heavy weight. It’s really hard to lift at all. So you can’t really move it around much, much less figure out where it should go. And it’s the same way all the way up that ladder of math from arithmetic to algebra to calculus to all sorts of university level math and beyond.

Taking notes isn't learning

You think that taking detailed notes in class means you’re actually learning? Think again See, learning doesn’t happen when you listen to a teacher and just copy down what they’re saying or just nod along and look studious. No, learning happens when you pull information from memory. That is what strengthens your knowledge: Retrieving information from your brain and bringing it out to the outside. And I mean, yeah, it’s gotta get inside your brain first, but if you just let it sit there without trying to exercise retrieving it from your brain to, to bring it out, then it’s just gonna kinda decay and dissipate and you’re just gonna forget it. It’s use it or lose it, right? Everybody knows that, but few people want to actually put it into practice. It’s the solving problems. That is where the learning happens.

Learning is memory

Everyone tells you not to memorize, but that’s backwards. At the end of the day, all learning, it comes down to memory. That’s what it is. That is the substrate of learning. Even deep understanding is memory. It’s deep ingrained memory. See, the difference between memorizing versus understanding is, it’s not about whether you use memory. It’s about how much memory you have stored and how well it’s connected. Facts connect onto concepts, procedures become skills, And all sorts of new ideas come from combining things that you already know. You can’t connect the dots if you got no dots. You can’t cook with ingredients that you don’t have. So you see, memory is not the enemy of understanding it’s the foundation of it.

Learn math 4x faster

We increase math learning 4 times over a traditional classroom without even increasing the amount of time that students spend doing math. I know that sounds crazy, but the way you do it is you increase the learning efficiency. Have students work on exactly what they are ready to learn at every second. And they practice it until they master it. None of these false starts where a student kinda gets ahead of their skis cause they made a bunch of mistakes in the homework cause they don’t really know what’s going on, and then a week later they’re just totally lost and you have to rebuild their foundation. No, just, just make them master it to begin with, and then you don’t have to backtrack all the time. It’s just smooth forwards progress. And even after they establish some, some baseline mastery, you continually have them review it right before they’re about to forget it. That way they maintain their knowledge and you don’t look up a month later and ask them to build on foundations that have just decayed. That is how you do it. No wasted time on material that’s, that’s too easy or too hard. You meet the student where they’re at, and you fit their knowledge profile like a glove. And then you build upwards from there. Same amount of time, 4 times learning.

Silly mistakes are still mistakes

No, you did not make a silly mistake. You made a mistake. You dropped the negative sign. You forgot to carry. You didn’t flip the fraction before. Now, those mistakes might seem silly because you know how to avoid them But knowing how is not the same thing as actually doing it reliably. And if you keep making silly mistakes, then it means the skill is not actually automatic yet. And the solution isn’t to just shrug them off Nah, it’s more practice until getting it right becomes the default.

This will haunt you in math

This is the ghost of math that will come back to haunt you forever. It’s math facts, particularly times tables, multiplication tables. If you don’t memorize those early, then everything afterward, it gets much, much harder than it really needs to be. I mean, imagine solving a whole algebra problem while you’re spending a bunch of time trying to figure out, like, what is 9 times 6? That’s only one little part of the problem, and you got a whole bunch of other multiplications to figure out. So now every algebra problem is really an arithmetic problem, a handful of arithmetic problems, and you just can’t think about the algebra that’s going on ‘cause you’re so focused on these arithmetic problems ‘cause it’s a full brain problem ‘cause you never memorized your math facts! Every time one of those low-level things comes up, every time a multiplication fact comes up, you gotta stop, turn off your attention to everything that you were doing, and then focus on this one multiplication fact, work it out, and then pick your head up and be like, “What was I doing? Where am I? Oh, right, we’re doing this problem. This is where we left off. What are we trying to do?” It’s just totally disorienting And you can’t build fluency that way.

The wrong way to study

Here’s why you can study for hours and remember almost nothing: Thing is, a lot of students study like this. They study by reread the chapter, Highlight your notes, watch the lecture again… I mean, everything feels familiar, right? So you feel like you know it. But then you close the book, you’re trying to explain it back to yourself, And you’re just at a loss for words. Like nothing’s coming out. It’s like, it, it’s almost as like your, your mind got wiped And if that’s your study technique, then that’s a totally normal experience because that’s what happens when you’re just consuming information. You feel like you got a lot of it stored up there. You’re filling your brain with it, and then pff, just gets wiped You barely remember anything And the solution to this problem: If you want something to really stick in your brain, you gotta practice retrieving it. You gotta solve problems from memory. And if you really can’t, you can look back, and then close the book again and then try again, Just look back for a little hint, then close the book, go back to the problem, keep pushing it as far along as you can. Don’t just keep passing information over your brain. You gotta practice pulling it back out.

So you wanna be an ML engineer

So you wanna be a machine learning engineer Well, here’s just some of the math you’re gonna need: you’re gonna need linear algebra to represent data and model transformations, You need probability and statistics to reason about uncertainty And learn things from the data, like get your machine to learn things. And the way that the machine learns things, well, you’re gonna need multi-variable calculus to understand gradients and the way that models are trained. See, what you have to remember about these technical careers is that the really exciting stuff, the stuff that makes you feel alive Like, holy crap, it did this? I wrote a program to do that? I built a model that can do this? All this exciting stuff sits on top of this huge stack of math. I mean, if you wanna really build stuff yourself and extend it, really understand what’s going on well enough to extend it in super interesting and novel ways, you gotta know the math. It’s more than just importing some- somebody else’s API. Ultimately, if you wanna do novel things and, and provide it to everybody, you gotta know what you’re doing at a fundamental level Cause all that math is very hierarchical And if you wanna get to that top, you gotta build the foundation first.

Want to improve your creativity?

Everybody wants to think creatively, but nobody really wants to build their knowledge base. See, the thing is creativity It doesn’t come from nothing. Almost never can you discover a clever proof if you don’t know any theorems. You know that saying, A writer is the sum of their experiences. Well, that applies in math too. And math is really, really hierarchical So you can’t really even collect experiences at the top if you’re just sitting there at the bottom. You need to climb your way up into the level of skill and domain expertise That all those symbols and theorems And clever tricks at the top actually mean something to you beyond just generating a pretty picture on a YouTube video. Ultimately, creativity comes from taking things that you actually know and combining them in new ways. It’s a, it’s a combinatorial explosion. So if you wanna be more creative and really expand the possibility space of all the ideas, perspectives, all the insights that your mind is capable of coming up with, Then build a bigger knowledge base. Give your brain more to work with.

What can you learn after calculus?

What can you learn after calculus? Well, there is a whole world of math afterwards. If you go down the applied math path, You might find yourself taking differential equations where you model really complicated real-world systems. And you’ll use a lot of probability and statistics Where you study randomness and uncertainty and distributions. And by the way, that’s calculus-based probability and statistics I’m talking about. It gets really, really complicated And when you go far enough, you actually end up using tools from calculus, not just algebra, but calculus integrals, derivatives to model all that complexity. And you also need bunches of tools from linear algebra: vectors, matrices, eigenvalues, eigenvectors… see, the thing is calculus is not the end of math at all. It’s really the starting point where you get to choose your own adventure.

Unserious edtech is rotting your brain

Your brain gets really soft when you avoid hard thinking. And that’s so common now, right? I mean, a lot of mainstream ed tech tries to make math feel really fun and effortless. All you gotta do is, is watch a little video and answer 1 or 2 conceptual questions. And if you get them wrong, ah, that’s okay. As long as you’re having fun, kid It’s just so much fluff and so little actual thinking, actual working out problems, actual retaining what you learned And being made to demonstrate it again the next day, the next week, the next month… actually being held accountable for all that.

You gotta build mental strength

See, the thing is math is cognitive athletics. That’s basically what it is. You wanna make progress? Well, you gotta build up your sub-skills, practice them really well So they’re just automatic And you can pull them together and practice close to the edge of what you know, where things are tricky, Where you make a mistake every now and then, and you get feedback on it, And you have to try again And again And you gotta really demonstrate the skill Prove that you can actually do it before you keep moving on. You need to retrieve it from your head. You can’t just consume stuff And then do projects where you outsource every difficult step to a calculator or to AI. If the tool is doing the hard part, then you aren’t really getting the rep. And without reps, you you don’t get stronger.

Why math hits people differently

The bigger factor controlling how difficult math feels for most students in classrooms is that they’re not all starting from the same place. The kids who seem the brightest Sometimes they are, but a lot of the time It’s really coming from the fact that they have mastered the prerequisites. So they’re really prepared for what it is that they’re being asked to learn. When they’re learning algebra, their arithmetic is automatic, rock solid. They know their times tables. They can factor numbers like nobody’s business. They don’t need to finger count. They got no baggage slowing them down from learning algebra. Same thing in calculus: They’re automatic on not just their arithmetic, but also their algebra. They have no issues solving equations, Manipulating expressions, they can do it in their sleep. And that’s why, you know, natural talent, it is a thing, but what looks like natural talent is often largely the result of being better prepared.

It's not talent, it's better preparation

Here is why some students seem naturally gifted at math And they learn new concepts instantly while everybody else is really struggling. The kids who seem the brightest Sometimes they are, but a lot of the time It’s really coming from the fact that they have mastered the prerequisites. So they’re really prepared for what it is that they’re being asked to learn. And when you’re in that situation, whatever new concept you’re being asked to learn, well, that’s the only thing that you really have to think about. It’s just the new thing. You don’t have to worry about that huge swath, the mountain of prerequisite skills that this is sitting upon. If you got those skills on lockdown, then it’s just, it’s no big deal. But if you don’t know your foundational skills, then oof. Being asked to learn one new concept can bring along so much baggage that you might as well be asked to learn an entire semester of math in a day. And that’s why, you know, natural talent, it is a thing, but what looks like natural talent is often largely the result of being better prepared.

The ghost of learning gaps past

This is the ghost of math that will come back to haunt you forever. It’s math facts, particularly times tables, multiplication tables. If you don’t memorize those early, then everything afterward, it gets much, much harder than it really needs to be. So now every algebra problem is really an arithmetic problem, a handful of arithmetic problems, and you just can’t think about the algebra that’s going on ‘cause you’re so focused on these arithmetic problems ‘cause it’s a full brain problem ‘cause you never memorized your math facts! And you can’t build fluency that way. See, that’s why gaps in your fundamentals are so costly. They don’t stay behind you. They just keep on following you forever and ever and ever Like a stalker Just trying to sabotage your every move as you climb up this ladder of math slowing down your progress, weighing you down, and the higher you climb, the heavier they become.

This sets students up to fail in math

Putting a student in the wrong math class doesn’t make them more advanced. It doesn’t make them smarter. It just makes them crash and burn. They might wanna be an engineer, and then they get thrown into a math class that’s just way above where they are currently. Maybe just ‘cause they were never held accountable for learning the prerequisite material. And then they crash and burn and come out thinking “I’m not cut out for engineering” when really They very well may be, And a placement exam would have identified like, Listen, kid We need you here, and here’s where you are, and here’s all the skills that you gotta fill in Which might look daunting at first But if you start the student in the right place, then they can start making progress, and progress produces motivation.

Why placement matters

Student signs up for calculus and the transcript says that they passed pre-calc. They got an A in the class, right? So they should be prepared. And then the first quiz has a problem with fractions in it, and everything falls apart. Not the calculus, the fractions. See, this situation is why placement exams matter. You can’t really guess math readiness by vibes or a padded inflated grade from last year. At some point, somebody’s gotta ask the question: Can you actually do the prerequisite work? Now, my question might feel rude. It might feel like an interrogation, an audit, and Well, it is But it’s necessary because putting a student in the wrong math class doesn’t make them more advanced. It doesn’t make them smarter. It just makes them crash and burn while simultaneously making it harder to diagnose what even happened.

Why automaticity matters

People sometimes talk about multiplication facts like they’re some kind of old-fashioned tiny little detail that doesn’t matter But understand That they do matter a lot And if they’re not automatic, then every algebra problem gets way heavier. See, when a student isn’t automatic on arithmetic and they’re trying to do algebra, They’re not just thinking about variables, equations, or structure. They’re also spending a lot of mental energy on that basic arithmetic. And that mental energy, that working memory, all the stuff they can hold in their brain at once, it’s pretty limited. So now the algebra problem is competing with the multiplication problem inside the student’s head, Each vying for attention. That’s why automaticity matters cause it frees up the student’s brain to actually think and pay attention to the harder thing. Just like a basketball player thinking strategy while simultaneously dribbling the ball and passing to teammates, cause that’s all so automatic that they don’t even have to think about it. They can just think about the game.

Sometimes a push is what opens the door

The most mathematically gifted student I ever worked with, he was still kind of resistant to learning calculus. He liked math that felt interesting, which to him often meant familiar. Kind of like a gifted basketball player who learned a bunch of cool moves and now loves playing at the park, showing off sometimes, having a good time But kind of starting to stagnate, not really developing their game. And the same thing happened with this kid. He was having a good time, but he was just kind of stuck in limbo at his current skill level. And if you really wanna use math throughout the rest of your life, like really have a good time with it, work on mathematically interesting problems, well guess what? Algebra skills, arithmetic skills, not enough. You gotta keep climbing higher. That’s how you unlock more of this thing that you love But kids, you know, they don’t always see the long game. Anybody who’s worked with kids knows how kind of just in the moment short-sighted they can be But ultimately, as an adult, it’s kinda your responsibility to help kids see that long game and at least take actions that are progressing them along in that long game. So that kid Once his parents and I pushed him to learn calculus, He was a little resistant at first, but he ended up loving it! And now he’s doing some serious math and engineering using ideas from this area that he originally resisted. You know, sometimes a push is what opens the door.

Nothing succeeds like success

The best kind of practice is challenging, but it still lets you succeed. It’s like an exercise, right? If you, if you can’t do a pushup, Then don’t just keep trying harder and failing to push your body off the ground, getting frustrated, demotivated. Just, just accept the situation, Put your knees down, make it a little easier Do some reps of that to build up some strength, and then, and then reattempt a full pushup after a few days of that. And learning anything should work the same way. You’re learning to solve a new equation? Well, start out with the simplest case So that you get comfortable with the process and then gradually ramp up the difficulty. Master the full skill at an easier level. You know, the, the full range of motion, whether it be physical or cognitive. Do the real skill, but on a simpler case, and then build up to more advanced cases, more advanced settings.

Full ass everything

Feeling drained doesn’t automatically mean that you’re doing too much. It can also happen if you’re not really doing anything fully. You work while thinking about resting You rest while you’re feeling guilty about not working You’re always just halfway somewhere else. And halfway is exhausting. Now, that’s the problem Then the solution is really simple: it’s just when it’s time to work, work. Immerse yourself and give it everything. And then when it’s time to rest, actually rest. Like recover When you go to bed, actually focus on sleeping. Don’t turn your rest into a half-conscious state of worry or guilt or whatever. Don’t half-ass your rest Cause if you’re not full-assing your rest, then you’re not full-assing everything.

Much practice, little progress

A lot of people say that they practice a lot But then they end up making very little progress towards the things that they’re trying to do. And often the reason why is that they’re not actually practicing anything. They’re just spending time near the skill. They’re doing the cognitive equivalent of watching sports on TV and thinking that it’s turning them into a better player. That’s what it’s like when you’re just watching a bunch of math videos and not working out problems, just looking at pretty images generated by somebody else who actually did the work. See, good practice makes progress visible. And The work has to be hard enough to force improvement. You gotta be breaking a sweat, whether that means physically, literally, or, or cognitively. Cause if you just keep doing things you already know how to do and can do reliably, consistently, You can practice for hours, days, months, years without actually getting any better. And ultimately, that inefficient practice kills your motivation Cause you don’t see yourself getting any better! Whereas efficient practice that actually builds skill It creates visible progress and it really makes you want to keep going.

Still counting on your fingers?

What happens when you don’t memorize your addition facts? Well, for one, you become painfully slow at subtraction. And trust me, you will encounter this in your daily life. It’s unavoidable. Let’s say you’re setting the table for nine people. Four plates are already out, and how many more do you need to grab? I mean, if you don’t instantly know that nine minus four is five, You gonna pull out your phone calculator in front of all your guests? Seriously?! Or stand there counting backwards on your fingers: 9, 8, 7, 6… no, that’s, it, it’s ridiculous. You should not need technology or a five-step finger counting exercise to set a table. Just, just memorize your addition facts. You’re gonna need them.

Educational malpractice

One of my friends tutored Calculus 1 students at WashU last year, And during one of their review sessions, They realized that instead of doing the regularly scheduled calculus work, they had to do a remedial math session. Not just like you’re a college student, you need some review on your high school math. These knowledge gaps traced back to not only middle school math, but elementary school math. Calculus students unable to add fractions Much less work with exponent rules or solve equations with trig or square roots. How do you expect students to take derivatives of these functions when they can’t even work with them algebraically, when they can’t even add fractions?! And so many of these students, they think that they have a calculus problem. They don’t. They don’t have a calculus problem. They have a years of missing prerequisites problem. Years of knowledge gaps, of holes in their foundations. But instead of actually filling these holes, Much of the education system has decided just to keep on shoving them into more advanced classes and calling it rigor. It isn’t rigor. It’s educational malpractice.

Calculus students who can't subtract negative numbers

One of my friends tutored Calculus 1 students at WashU last year, and there’s so many crazy stories of educational dysfunction. Like one day, they were helping a student who was stuck on subtracting negative numbers. Yeah, a calculus student stuck on subtracting negatives. They were doing a problem that asked them to calculate a derivative, And the student couldn’t do -27 minus 14. I mean, no wonder they had no idea what was going on in the class or how to choose what derivative rule to apply to each function or how to work with functions. Like, for crying out loud, they don’t know how to do arithmetic! And just because you graduated doesn’t mean you get to leave all that math you’re supposed to learn behind cause everything builds on each other. Algebra builds on arithmetic. Calculus builds on algebra. You’re never done with anything. It always comes back, And you gotta keep building on top of it. If you wanna solve calculus problems, it’s not just the new stuff in calculus that you need to know. It’s also all the foundational material from algebra and arithmetic, trigonometry, everything that is gonna come back and get exercised. And if you can’t do it, you’re gonna struggle until you refresh that knowledge. So when we’re putting students into calculus who don’t know middle school math, It’s no surprise that they’re completely underwater.

What can you learn after calculus?

What can you learn after calculus? Well, let me tell you, there’s this whole world of math afterwards where you learn how to construct proofs And then you might take real analysis, where you attack calculus with those proofs rather than computations. You kind of go up another level of abstraction. And then there’s number theory Again, more proofs, and you focus on the behavior and properties of numbers. There’s discrete math, where you study objects like graphs and networks. See, calculus is not the end of math. It’s really just the point where you start getting to choose your own adventure.

How to see the big picture in math

You ask a 10th grader to factor something… nothing crazy, just like x squared plus 11x plus 28 And before they even get to the algebra, they’re stuck on the multiplication! What’s 7 times 4? Seven times what? What is that? Let me recompute it. You do four plus four plus… oh, wait, I should just add seven. Seven plus seven plus seven… geez! Y’all already got one job, which is to do the algebra And now you’re spinning out on computing basic facts? And even if you’re using some kind of strategy like seven times five, then minus a seven, or seven times two, you know, double it and double it again, I mean, Your whole brain is thinking about this. It’s pulling away your attention from the algebra that you really need to be focused on If you’re gonna see the forest for the trees and really understand and get intuition about what you’re doing. You need to be able to look up Like a basketball player who’s dribbling the ball and is able to look around them, see what’s happening you can’t get good at basketball if you’re constantly having to like look at the ground and you’re dribbling the ball. Like, it doesn’t work that way. Anybody who plays sports knows the importance of getting automatic on your basic skills so that you can build on top of them and they don’t continually hijack your mental bandwidth. And it’s the same way with math.

Cognitive ankle weights

If you’re having to do algebra and think about basic arithmetic, If every problem makes you recompute multiplication from scratch, Doing strategies or repeated multiplication or God forbid, finger counting You’re just carrying these cognitive ankle weights around that nobody can see but they stay with you, they get heavier over time, they drag you down. And you’re going as fast as you can, putting as much effort as you can and it’s all getting wasted on lower level stuff that you haven’t automated yet. And everybody else who has automated those skills, they’re just passing you up. You’re huffing and puffing, going slow, and they’re just joking around and having a good time and passing you up.

How math can level up your career

A lot of people realize later who go into software engineering maybe at first they don’t really care about math in school But eventually they build up their foundations of coding, and then they realize that if they just had taken it seriously and learned all their math, They could be doing so much more! Just imagine a kid graduating high school Not only do they know precalculus with coding applications But also calculus, linear algebra, multi-variable calc, differential equations, basically all your core engineering math, right? And they come to college And they’re just blowing the socks off of anybody who gives them an opportunity to do some research, an internship They already got the basics of everything, and they’re actually ready to make a serious impact Do you know how rare that is? How rare that is to see in an undergraduate researcher or an intern? Usually you can’t count on them, so you just throw them a toy problem for them to play around with. But if you can actually make a serious impact at a young age Cause you have the skills to do so, You can just compound that into a massive compression of time.

Universities are having to teach middle school math

One in 12 students entering UCSD in 2025, they don’t know middle school math. We’re talking below Algebra 1: Fractions, order of operations, what’s an exponent? I mean, it’s so ridiculous. You know, UCSD, they had a remedial math course for students coming in who are missing their high school foundations. And that remedial course was too advanced for a lot of these students coming in So they had to make a remedial remedial course. Remediation for the remedial course for the calculus course. I mean that’s crazy!

Standardized tests are a better signal of knowledge than grades

You know, UCSD, they had a remedial math course for students coming in who are missing their high school foundations. And that remedial course was too advanced for a lot of these students coming in So they had to make a remedial remedial course. And that’s not even the craziest part though. The craziest part is that you don’t actually get a good signal of who’s gonna be in remedial, remedial math based on their high school grades. Cause the grades are fake Instead, the best predictor is really the SAT and ACT scores. And it’s been that way for decades, and that’s what the UCSD math department found: that you can’t trust high school grades. You have to look at the standardized tests if you really wanna know what math skills the students have. And guess what’s happened in recent years? Well, all the UCs, all the University of Californias, They didn’t require those standardized test scores to be sent. They’re just YOLOing the admissions on the basis of fraudulent high school grades. So now you’re flying blind in admissions, you’re admitting tons of people who don’t have their foundational skills I mean, the, the math department has been pleading about this for years Like please bring back the standardized tests, but You know, not everybody is interested in ascertaining the truth of the situation. So now we have this kind of shit show that’s happening.

Project-based learning can be taken way too far

The whole project-based learning can be taken way too far. See, projects are built on a foundation of skills. You can’t do projects without the skills. And if you’re trying to fill in all these skills on the fly at the same time as trying to do the project, it’s just it’s not efficient at all. It makes the project take forever, You don’t really learn the underlying skills that well. You just learn it just enough to get over the hump ahead of you. You don’t really master it. The teacher kind of carries you Or the smartest kid in your group. And you don’t really learn the things that the project was supposed to be a milestone certifying that you’ve learned.

Stop making kids reinvent math

The idea that students should discover everything for themselves is one of the biggest wastes of human potential that I’ve ever seen. Thing is, we have thousands of years of accumulated knowledge Entire civilizations of thought compressed into things that can be taught and learned efficiently, quickly I mean, that’s the whole point of instruction, right? is to get you to inherit all sorts of insights and knowledge and discoveries that took other people lifetimes to figure out. And not just like other random people. I mean like literal geniuses The brightest minds of each century grinding away for lifetimes Through thousands of years, Handing the baton and extending human knowledge. Just take the baton and run with it! You don’t have to rediscover all of that on your own from scratch. It’s gonna take you forever, and you’re gonna be spinning out doing years of research on things that are already known. So just suck it up, learn your foundations, and then build new discoveries on top of them where it’s actually novel, Where your inventions are actually pressing forward human knowledge.

Difficulty vs. Rigor

People confuse difficulty with rigor. If you take undergrads and you give them a graduate level textbook, You skip the concrete examples, And you just make them fight their way through it, Yeah, the course is hard, but hard does not automatically mean well-designed or that they’re learning more. Sometimes hard just means inefficient. It takes you a lot more work to ultimately get to the same place you could have gotten with a lot less work, just concentrated on the areas that are gonna move the needle the most. Sometimes a hard math course is just painful for no reason. And that’s the thing about rigor vs. difficulty. Real rigor is not about making the path as brutal as possible. Real rigor is about getting students to understand and master the material without wasting their energy on avoidable confusion.

Don't hold students hostage to the calendar

The rule should not be, “Hey, you’re in eighth grade, so you’re gonna do eighth grade math.” No. No, no, no. The rule, it should be What have you mastered? What new things do you have your prerequisites in place to learn? If you’ve mastered the prerequisites, then move the student forward. If they haven’t mastered the prerequisites, then fix it. That’s it. It’s that simple. The calendar should not be the thing controlling the learning. The mastery profile across all the skills for each individual student, that is what should be controlling their learning. Cause when students are ready and you make them wait, then you just waste their time. And when students are not ready and you push them forward anyway, then you create these knowledge gaps, these holes that follow them for years, sabotaging their attempts at every new thing that they try to learn and build on top and making them think they’re just inherently not cut out for math.

The most hard-hitting two sentences in all of talent development research

The most hard-hitting two sentences in all of talent development research is this: deliberate practice requires effort and is not inherently enjoyable. Individuals are motivated to practice because practice improves performance. That’s according to K. Anders Ericsson, one of the most influential researchers in the field of human development and expertise. In other words: Maximal learning does not happen naturally as a result of maximizing other things like enjoyment, comfort, convenience, ease of practice. In fact, maximal learning is at odds with a lot of these things.

This one idea would fix a lot in math education

Picture a kid who finishes long division in fifth grade Then sixth grade happens, and seventh and eighth, and somehow the big achievement Is finally starting algebra 1 in ninth grade?! That’s a lot of time. That’s a lot of calendar and not much distance. Just spending all of middle school doing laps around the same math. Nah, you know you know a kid who can handle arithmetic they should be doing algebra. They should be building on top of what they learned. And a kid who can already handle basic equations they should be doing functions. Kid who can handle functions, they should be moving towards trig. Readiness should matter a lot more than the calendar and this one idea would fix a lot.

Most math major math is taught backwards

When you’re a math major in undergrad and you get up to those junior and senior level courses you know, real analysis, Abstract algebra, topology You start to realize that a lot of the stuff is really taught backwards: theorem proof, theorem proof But you don’t even have a concrete grasp of what’s going on. You’re just pushing all these symbols around. Maybe you can follow the rules, but you don’t really understand the subject. That’s because you need the concrete examples first. You gotta work through the computations with actual numbers, see how it plays out, get a feeling for the process, and then you do the abstraction. Skipping that concrete stage With actual numbers and test cases that can help you build some experience and intuition Skipping that doesn’t make the course rigorous. It just makes it inefficient.

Abstract math needs concrete roots

Abstract math is not the problem. Proofs are not the problem. Those are not really the primary reason why math gets hard. The biggest reason why math gets hard is that students are thrown into abstraction before they even understand anything concretely. When that happens, the math just turns into symbol pushing. Definitions, theorems, proofs, More theorems, more proofs, But no intuition, no examples No real grip on the objects There’s nothing to hold onto, nothing to grasp And it’s backwards Build the concrete understanding first, Make the calculations instinctive, And then the abstraction actually means something.

There are countably infinite courses after calculus

People think that calculus is this big finish line, But it’s really just the beginning. Cause even after calculus, You still got linear algebra, vector calc, Differential equations, probability and statistics, And all these other specialized courses that branch out. I mean, there are so many University math courses above calculus that a serious student could not even fit them into a standard four-year academic schedule, even if they overloaded every single year. So getting to calculus early is not about being done early. It’s about having enough runway to actually reach all that math that comes after.

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