American Enterprise Institute’s “The Report Card” Podcast: Math Academy
2025 Dec, ~1.25h • You know the kind of trainer an actor gets to prep them for the superhero role in a Marvel film? We're that, for math. If you want to understand what we’re doing but don’t have time to skim our 400+ page book, this episode sums it up in about an hour.
Here's a summary of what we covered:
[1:34] The big problem in math education is a lack of individualized instruction. In a classroom with one teacher teaching the same thing to all the students, it's way too easy for the top half of the class and way too hard for the bottom class. What we do is pinpoint the exact problem that each student should be working on right at this moment to make maximum progress in their math learning.
[4:46] So much difficulty in math learning can be traced back to missing prerequisite knowledge. That's why it's important to start each student off with a diagnostic that combs through many years of prerequisite knowledge that they need to know to succeed in their chosen course. If we find any knowledge gaps, we fill them in before asking the student to learn any more advanced material that depends on it.
[6:50] We get a very high-resolution picture of the student's knowledge profile by overlaying every question/answer event onto a structure called a "knowledge graph". The knowledge graph encodes all the dependency relationships between mathematical topics. We leverage it to squeeze a ton of information out of every single question that we ask the student -- not just figuring out what they know and don't know, but also figuring out exactly what learning tasks they should be working on to maximize their learning efficiency every step of the way.
[8:44] Elsewhere, lots of students struggle with calculus due to gaps in prerequisite knowledge. Good teachers know this, and try to fill those gaps, but there's a limit to how well the teacher can do this because all the students have knowledge gaps in different places and the teacher can only teach one thing at a time to all the students. But we can target these gaps precisely, backfill them, and move on based on what each individual student knows -- fully individualized instruction for all students in parallel, delivering exactly what they need to work on, focusing on those weaknesses and not wasting time on things they already know cold.
[12:05] If you have more talent/aptitude, then you're going to get more bang for your buck out of practice. You're going to require fewer reps before getting solid enough to move on, and you're going to generalize more naturally. However, of the students who get all the way up to calculus before struggle really sets in, the biggest roadblock is typically not talent/aptitude but rather gaps/weaknesses in prerequisite knowledge, an issue that can be resolved with fully individualized instruction.
[14:50] Math Academy origin story: Jason/Sandy coached their son's 4th grade math field day team, which turned into a pull-out class 3 days per week the following year, which -- after the superintendent came by and saw 5th graders doing trigonometry, advanced algebra, even a little bit of calculus -- turned into a pilot for the Math Academy school program in the Pasadena Unified School District, where students learned all of high school math (prealgebra through precalculus) during 6th/7th grade and took the AP Calculus BC exam in 8th.
Students were invited to the program by scoring in the top 7-8% of a middle school math placement that all students in the district took at the end of 5th grade -- and about two-thirds of students in the district were on free or reduced lunch. Also keep in mind that nearly half of Pasadena K-12 students are educated in private schools, compared to the California average of ~10%. Generally speaking, these were not smartest kids in California, and their parents were not Caltech professors.
Jason developed software to automate the process of assigning/grading homework, and together during the pandemic we upgraded it to figure out what each individual student should work on and teach it to them directly without any human intervention. We worked like maniacs to get it ready before school went fully remote the next year, and once we put the school program on it, educational outcomes (including AP Calculus BC scores) skyrocketed. Because of the software, our students experienced a massive learning GAIN, not a loss, during the pandemic. Naturally, it only made sense to keep the school program using the software even after class returned in-person.
[21:55] We have spent thousands and thousands of hours over the years building and fine-tuning our knowledge graph. It's not off-the-shelf, it's not automatically generated. It's the hard work from domain experts, primarily our director of content Alex Smith for the forwards graph (what are all the prerequisites you need to learn in order to unlock a topic) and myself for the backwards graph (when you practice a topic, what component sub-skills are implicitly getting practiced and to what extent).
[25:04] We analyze our knowledge graph by overlaying a big heatmap of where students are doing well or struggling at various parts in the graph. It's almost like traffic intersections in a city -- which ones are where most accidents happen? Let's go make those safer. We've been building and refining the knowledge graph for nearly a decade now with all these analytics.
[27:22] We have a wide variety of user segments. We can help anyone who seriously wants to learn math. Basically, anyone in any sort of educational situation, kids, adults, public school, private school, charter school, homeschool, grade school, high school, college, students who are accelerating, students who are just trying to keep up, "math team" people, people who don't yet think of themselves as "math people", adults changing careers to a math-ier field or pursuing a math-ier subfield within their current career, the list goes on and on.
[29:31] The best predictor of how long someone will use the system and how much math they'll learn is what kind of habit structure they have in place. Students who are consistent, as opposed to sporadic, go much further. It's that simple.
[34:13] The only math learner persona we can't help is the crammer -- the student who has an exam in a week, is nowhere near prepared, and wants a "quick fix". We are like a gym, and there's always people who walk in the gym and think they're going to work out really hard for a week and look like Thor by the weekend. There is no way to make that happen in a week, no matter how hard you work out. If you show up consistently, like 3-6 times per week for a 30-90 minute session, and then you keep that up for months, then you're going to come out looking like the mathematical equivalent of a Greek god. But if you are looking for some kind of easy, "how can I change my lief in one week," then I'm sorry, I don't know what to tell you.
[37:16] We alternate between minimum effective doses of text-based guided instruction followed by active problem-solving. It's the mathematical equivalent of a tennis instructor showing a quick demonstration of how to hit a ball, just for a minute, and then students practice hitting the ball with that technique until they're solid enough to move onto the next technique.
[40:16] Real-time reactions and hot takes: Jason on collaborating with school districts, my thoughts on the edtech industry, Jason founding a company with his wife, my experience interacting/growing on X, Jason's impression of Waymo, my impression of math textbooks, Jason's thoughts on the "move fast and break things" ethos, Justin's thoughts on people's screen time concerns.
[52:10] People say, "just give me the intuition." But intuition comes through repetition. That's how you get the automaticity, the natural feel, and that's what intuition is.
At the same time, it's important to be efficient. Don't work 100 problems of the same type in one day. Maybe do 10 to start, then 5 the next day, another 5 a week later, and so on, while you're filling the empty space with practice on a ton of other skills. You have to get your reps, but you also have to distribute them out over time. That's how you learn efficiently and build long-term retention.
When people want their math learning to be less skill-heavy and more concept-oriented, what they're often really saying is that they want a fast overview of a subject without going into the details, without really getting your reps on everything. A video that explains all of calculus in an hour, or how neural networks work in 20 minutes.
But what we're focused on is building up a true level of mastery. Not surface-level, not shallow. The optimization problem we're solving is NOT "how fast can we imbue you with a shallow level of understanding, enough that you can tell your friend something cool or that you think you have opinions about it." What we're focused on is how quickly we can get you to operating mathematically almost like a professional musician plays their instrument, or a professional athlete plays their sport.
[55:51] As a rule of thumb, if it wouldn't work in sports, it's not going to work in math.
[57:31] Students on our system typically learn about 3-4x as fast as a normal class. That's why, in our school program, the students could go from pre-algebra through AP Calculus BC in 3 years, from 6th-8th grade. When that first happened, and the Washington Post wrote articles about it, lots of people couldn't believe it. Which is why we had them take the AP Calculus BC exam so we actually have results.
[58:49] We hear all the time about students who are behind in their school class, and then use our system to catch up, and then start crushing their class, and then go well beyond their school class -- as well as the resulting change in the student's level of confidence. In just one year or less, just months, a student can go from thinking "I'm not a math person, I'll never be good at it" to "I'm crushing my school class, it's so easy." That change in the student's experience does wonders for their confidence.
[1:01:28] Is there an upper limit to how much math you can do per day and have it carry over into real learning results? Think about it like going to the gym. If you work out for 45 minutes, 5-6 days per week, you'll get in incredible shape. You can do more if you want, but there is a point where you hit diminishing returns. Whether it's Math Academy or the gym, it really comes down to how long you can sustain a productive full-intensity effort. It's hard to keep that up for multiple hours, though you might be able to get better mileage by splitting up a multi-hour session into a shorter morning session and evening session. But every person is kind of different in their breaking point, how much they can stay focused and work intensely on the system. In general, one hour per weekday is what we've found to be the upper end of a sustainable approach for most students.
[1:03:38] We make students do review problems indefinitely into the future, but with expanding intervals -- spaced repetition. It's the optimal way to keep your knowledge base fresh enough to keep building on it without constantly having to go back and re-learn things. But we make this review process as efficient as possible by tracking all the subskills that are implicitly reviewed when you do a review problem, and we're always trying to select tasks that kill many birds with one stone by exercising many subskills in need of review.
[1:08:41] Lots of people mistakenly think that students need a million different explanations of the same thing, and that one of those explanations is going to stick, and it's different for each student. But really, all you need is one really good explanation that's been battle-tested across a large number of students, and the students need to come into that explanation with all their prerequisite knowledge in place.
If you do that then you can get students learning the skills really well -- students pass our lessons over 95% of the time on the first attempt, and over 99% of the time within two attempts, without any additional remediation (because enough knowledge has consolidated into their brain from the first attempt that it makes it cognitively easier for them to get over the hump the second time around).
That's often surprising to people who think that every student needs a different explanation, but typically what they're seeing is a symptom of the student lacking prerequisite knowledge, and you're trying to come up with some explanation that allows them to grasp "enough" of the topic (not the whole thing) while at the same time not requiring too much in the way of prerequisite knowledge they're missing.
[1:11:08] What makes math hard is the same thing that makes climbing a mountain hard: the steepness of the gradient. What we do is break every steep section of math into smaller steps. If you break things into small enough steps, anyone can learn. And that's what we do with our analytics: where are the congestion points? Where are students struggling? It's always where we're trying to do too much at one time, so we break it up into more steps.
[1:12:25] It's so important to have a reliable source of truth about what a student really knows, and grades are no longer a good source of truth. You remove test scores from the admissions process, the last objective metric and the last Jenga block, and you get bad situations like at UCSD where 8% of students were not proficient in middle school math. So many issues in education stem from a student having a piece of paper that says they've learned something when they actually haven't.

The Metagame Podcast #39: Math Academy and The Science of Learning
2025 Apr, ~2h • The most comprehensive 2h overview of my thoughts on serious upskilling, to date. Not just how to train efficiently, but also how to find your mission. Not just the microstructure, but also the metagame. We covered tons of bases ranging from the micro level (science of learning & training efficiently) to the macro level (broader journey of finding, developing, and exploiting your personal talents).
[~0:30] What is Bloom's two-sigma problem, how did Bloom attempt to solve it, why does it remain unsolved, and what is Math Academy's approach to solving it?
[~9:00] Efficient learning feels like exercise. The point is to overcome a challenge that strains you. It is by definition unpleasant.
[~13:30] Knowledge graphs are vital when constructing efficient learning experiences. They allow you to systematically organize a learner's performance data to identify their edge of mastery (the boundary between what they know and don't know), what previously learned topics below the edge are in need of review, and what new topics on the edge will maximize the amount of review that's knocked out implicitly.
[~18:00] None of this efficiency stuff matters if you don't show up consistently. Progress equals volume times efficiency. If either of those factors are low then you don't make much progress.
[~21:30] Getting excited about the idea of getting good provides an initial activation energy, but seeing yourself improve is what fuels you to keep playing the long game, and efficiency is vital for that.
[~26:30] Your training doesn't have to be super efficient at the beginning. You can gradually nudge yourself into higher efficiency training even if you don't have a whole lot of intrinsic motivation to begin with. However, there's often a skill barrier you need to break through to really get to the fun part, and it's advisable to do that in a timely manner so you don't stall out. But at the same time, don't rush it and fall off the rails.
[~34:30] A common failure mode: being unwilling to identify, accept, and start at the level you're at.
[~41:30] Center your identity on a mission that speaks to you, that you can contribute to, and do whatever else is needed to further it, regardless of whether you perceive these other things to be "you" or not. You'll be surprised what capabilities you develop, that you hadn't previously perceived to be a part of your identity.
[~48:30] How to find your mission: sample wide to figure out what activities speak to you, then filter down and pick one (or a couple) that you're willing to seriously invest your time and effort climbing up the skill tree and going on "quests". You may not understand this early on, but skill trees branch out, and quests beget follow-up quests, and the act of climbing to these branch-points will imbue you with perspective that you can leverage to keep filtering down. If you iterate this process enough, it gradually converges into a single area that you can describe coherently and uniquely. That's your mission.
[~55:30] Every stage in the journey to your mission is hard work, and the earlier you get to putting in that work, the better off you're going to be. It's never too late, but the longer you wait, the rougher it gets. At the same time, don't make a rash decision, don't tear the house down and build up a new house that you don't even like. But don't underestimate how fast you can progress when your internal motivation is aligned with your external incentives.
[~1:12:00] Focus on what matters. That's obvious, but it's so easy to mess up lose focus and not realize it until after you've wasted a bunch of time.
[~1:15:30] How to get back on the horse after you've fallen off. How to avoid feeling bad when something outside of your control temporarily knocks you off your horse. A good social environment can push you to get back on your horse.
[~1:26:30] If you're a beginner, don't feel like you have to be advanced to join a community of learners. You can do this right away. And don't shy away from posting your progress -- it's not about where you are, it's about where you're going and how fast. It's only people who are insecure who will make fun of you. Most people, especially advanced people, will be supportive.
[~1:31:30] There are numerous cognitive learning strategies that 1) can be used to massively improve learning, 2) have been reproduced so many times they might as well be laws of physics, and 3) connect all the way down to the mechanics of what's going on in the brain. The biggest levers: active learning (as opposed to passive consumption), direct/explicit instruction (as opposed to discovery learning), the spacing effect, mixed practice (a.k.a. interleaving), retrieval practice (a.k.a. the testing effect).

Chalk and Talk Podcast #42: Math Academy: Optimizing Student Learning
2024 Dec, ~1.25h • The best podcast about Math Academy to date. If you want to understand what we're doing but don't have time to skim our 400+ page book, this episode sums it up in just an hour.
[~5:00] What is Bloom's two-sigma problem, how did Bloom attempt to solve it, why does it remain unsolved, and what is Math Academy's approach to solving it?
[~10:00] What is mastery learning? Why is full individualization important? What is our knowledge graph and how do we use it to implement mastery learning? How do we use data to improve our curriculum?
[~21:00] Why is it so important to be proficient on prerequisite skills? How does this relate to cognitive load? You see this same phenomenon everywhere outside of math education. Jason has a "learning staircase" analogy that elegantly encapsulates the core idea.
[~26:30] Why are worked examples so important? How do we leverage them?
[~29:30] Our perspective on memorization. Yes, students need to memorize times tables (among other things). No, they should not be expected to do this before they know what multiplication means (and how to calculate it using repeated addition).
[~33:30] Our perspective on the concrete-pictorial-abstract approach -- what it's useful for, and how it often gets misapplied.
[~41:00] What is spaced repetition? How does that work in a hierarchical body of knowledge like math? What are "encompassings" and why are they so important? How do we choose tasks that maximize learning efficiency? How do we calibrate the spaced repetition system to student performance and intrinsic difficulty in topics?
[~48:00] What is the testing effect (retrieval practice effect) and how do we leverage it? How do we gradually wean students off of reference material? How do quizzes play into this?
[~52:00] What does a student need to do to be successful on Math Academy? What does an adult need to do to facilitate their kid's success, and what are our plans to build more of this directly into the system?
[~55:30] We have a streamlined learning path specifically designed for adults, to get them up from foundational middle-school material up to university-level math in the most efficient way possible. What the learning experience often feels like for adults: it can be an emotional experience when you successfully learn math that you used to be intimidated by, and realize that the reason you struggled in the past wasn't because you're dumb but rather because you were missing prerequisites.
[~1:02:00] How did Math Academy get 8th graders getting 5's on the AP Calculus BC exam? What's our origin story? Can any student be successful on Math Academy? The students in our original Pasadena program -- what was their background, what did they learn in our program, and what are they doing now?
[~1:10:00] What's next for Math Academy? We want to become the ultimate math learning platform and empower the next generation of students with the ability to learn as much as they can.

Scraping Bits Podcast #137 (Round 4): Learning Math is Hard, Proof Writing, Which Order to Learn Math
2025 Feb, ~2.75h • [0:00] How to get stuff to stick in your head. The importance of retrieval practice: comfortable fluency in consuming information is not the same as learning. Making connections to existing knowledge and/or emotions, exploring edge-cases in your own understanding. How to get stuff to actually enter your head in the first place: the importance of prerequisite knowledge.
[~19:00] Math Academy's upcoming Machine Learning and programming courses. Closing the loop on the pipeline from learning math to producing seriously cool ML/CS projects. How to get learners to persist through that pipeline at scale by breaking it up into incrementally simple steps.
[~40:00] Why it's worth learning proof-writing if you want to do any kind of mathy things in the future (including any sort of applied math). When to make the jump into proof-writing. What learners typically find challenging about proof-writing.
[~53:00] The advantages and challenges of modeling the world with differential equations. The importance of physics-y intuition about how the world works, what features actually matter enough to be incorporated into your model, and how much approximation you can get away with.
[~1:14:00] The experience of diving down the deep trench of mathematics (and also coming back to concrete everyday life).
[~1:22:00] The advantages and challenges of modeling the world with probability and game theory. The importance of understanding human nature and deviations from probabilistic / game-theoretic rationality.
[~1:33:00] The importance of getting through the grindy stage of things, especially at the beginning when you have no data points to look back at to see the transformation underway. You often need to stick with it for several months, not just several days or even several weeks, before you really see the transformation get underway.
[~1:54:00] Even after reaching a baseline level of initial mastery, it takes repeated exposures over time for knowledge to become fully ingrained. The importance of spaced review and continually layering / building new knowledge on top of old knowledge. Gaining procedural fluency opens up brainspace to think more deeply about components of the procedure.
[~2:25:00] People who hate on vs support others who are on an upskilling journey. Supporters tend to be more skilled themselves.
[~2:37:00] Progress update on the upcoming ML course. The mountain of positive sentiment online surrounding Math Academy. Our learners being incredibly supportive to each other. How calculus, linear algebra, and probability work together as prerequisites for machine learning.

CS Primer Show #23: MathAcademy and the efficient pursuit of mastery
2025 Jan, ~1h • Math Academy was originally built to support a school program. How come it also works so well for adults? What makes someone a student a good fit for Math Academy -- what's required to succeed? The idea of calibrating to student interest/motivation profiles in the future, just like we currently calibrate to student knowledge profiles.

Golden Nuggets Podcast #40 (Round 4): How Justin learns, new ML course, the magic of Twitter
2024 Nov, ~1h • Developing coding projects for the upcoming ML course. How would I go about learning a new subject where there's not an adaptive learning system available? The power of instructional guidance and a good curriculum Why I want to learn biology, why I haven't done so yet, how I wish that "Math Academy for biology" existed, and how I'm going to try to get myself over the hump by instructing an LLM how to tutor me at least more efficiently than a standard textbook. Strategies I use to improve my output, especially writing output. Viewing Twitter as a mode of production instead of a mode of consumption.

Scraping Bits Podcast #116 (Round 3): Essential Math for Machine Learning, Math Intuition/Creativity, Proof Vs Computation
2024 Nov, ~3h • Why go through lots of concrete computational examples first before jumping into abstract proofs. The importance of having a zoo of concrete examples. The evolution of Math Academy's content. How to identify the right "chunks" of information and the right prerequisites for the knowledge graph. How to continue learning math as efficiently as possible after you finish all the courses on Math Academy. Frustrations with the lack of existing ML learning resources. How to know whether you're ready for ML projects or you need to learn more math. The blessing and curse of intellectual body dysmorphia. Harnessing reality distortion as a helpful tool. Journaling and documenting one's life.

Golden Nuggets Podcast #39 (Round 3): MA’s upcoming machine learning course
2024 Oct, ~2h • Rationale, vision, and progress on Math Academy's upcoming Machine Learning I course (and after that, Machine Learning II, and possibly a Machine Learning III). Design principles behind good math explanations (it all comes down to concrete numerical examples). Unproductive learning behaviors (and all the different categories: kids vs adults, good-faith vs bad-faith). How to get the most out of your learning tasks. Why I recommend NOT to take notes on Math Academy. What to try first before making a flashcard (which should be a last resort), and how we're planning to incorporate flashcard-style practice on math facts (not just times tables but also trig identities, derivative rules, etc). Using X/Twitter like a Twitch stream.

Golden Nuggets Podcast #37 (Round 2): Balancing learning with creative output
2024 Sep, ~1.75h • Balancing learning math with doing projects that will get you hired. The role of mentorship. Designing social environments for learning. Why it's important to let conversations flow out of scope. Misconceptions about "slow and deep" learning. How to create career luck. The sequence of steps that led me to get involved in Math Academy (lots of people ask me about this so here's the precise timestamp: 1:13:45 - 1:24:45). Strategies to maximize your output. The "magical transition" in the spaced repetition process.

Scraping Bits Podcast #107: Proof Writing, Discovering Math, Expert Systems, Learning Math Like a Language
2024 Sep, ~1.75h • Why aspiring math majors need to come into university with proof-writing skills. My own journey into learning math. Math as a gigantic tree of knowledge with a trunk that is tall relative to other subjects, but short relative to the length of its branches. The experience of reaching the edge of a subfield (the end of a branch): as the branch gets thinner, the learning resources get sh*tter, and making further progress feels like trudging through tar (so you have to find an area where you just love the tar). How to fall in love with a subject. How to get started with a hard subject that you don't love: starting with small, easy things and continually compound the volume of work until you're making serious progress. How to maintain focus and avoid distractions. The characteristics of a math prodigy that I've tutored/mentored for 6 years and the extent to which these characteristics can be replicated. How Math Academy's AI expert system works at a high level, the story behind how/why we created it, and the stages in its evolution into what it is now. How Math Academy's AI is different from today's conventional AI approach: expert systems, not machine learning. How to "train" an expert system by observing and rectifying its shortcomings. How to think about spaced repetition in hierarchical bodies of knowledge where partial repetition credit trickles down through the hierarchy and different topics move through the spaced repetition process at different speeds based on student performance and topic difficulty. Areas for improvement in how Math Academy can help learners get back on the workout wagon after falling off. Why you need to be fully automatic on your times tables, but you don't need to know how to do three-digit by three-digit multiplication in your head. Analogy between building fluency in math and languages. #1 piece of advice for aspiring math majors.

Golden Nuggets Podcast #35: Optimizing learning efficiency at Math Academy
2024 Sep, ~2.5h • Why are people quitting their jobs to study math? How to study math like an Olympic athlete. Spaced repetition is like "wait"-lifting. Desirable difficulties. Why achieving automaticity in low-level skills is a necessary for creativity. Why it's still necessary to learn math in a world with AI. Abstraction ceilings as a result of cognitive differences between individuals and practical constraints in life. How much faster and more efficiently we can learn math (as evidenced by Math Academy's original school program in Pasadena). Math Academy's vision and roadmap.

Scraping Bits Podcast #102: Learning Mathematics Like an Athlete
2024 Sep, ~1h • My background. Why learn advanced math early. Thinking mathematically. A "mathematical" / "first principles" approach to getting in shape with minimalist strength training. Benefits of building up knowledge from scratch & how to motivate yourself to do that. Goal-setting & gamification in math & fitness. Maintaining motivation by looking back at long-term progress (what used to be hard is now easy). Traits of successful math learners. How does greatness arise & what are some multipliers on one's chance of achieving it. How to build habits, solidify them into your identity, and have fun with it.

Road to Reading Podcast #23: Discussing Cognitive Science
2024 Sep, ~1.5h • [0:00] What is the science of learning?
[~7:00] Students learn better when they're actively solving problems and explicitly being told how to solve them.
[~13:00] Students retain information longer when they space out their review with expanding intervals.
[~19:00] Spaced repetition is so similar to weightlifting that you might as well call it "wait"-lifting. The wait creates the weight.
[~22:00] Desirable difficulties: making the task harder in a way that overcoming the difficulty produces more learning -- but not all difficulties are desirable, and no difficulty is desirable if the student is unable to overcome it in a timely manner. Other desirable difficulties include interleaving (mixed practice) and the testing effect (retrieval practice).
[~32:00] The testing effect (retrieval practice effect): students retain information longer when they're made to practice retrieving it from memory. Again, it's just like weightlifting. The way to build long-term memory is to use long-term memory. You're picking up a weight off of the ground of long-term memory and lifting it up into working memory.
[~36:00] The power of automaticity, the ability to execute low-level actions without them exhausting your mental bandwidth. It's important to develop automaticity because we all have limited working memory capacity. Automaticity helps us overcome that limit.
[~44:00] Automaticity is a critical component of creativity. It frees up space for creative thinking.
[~48:00] The expertise reversal effect: the difficulty of the task needs to be calibrated to the ability of the learner. If expert-level tasks are given to non-experts (or vice versa), little learning will occur.
[~55:00] Why it's important to transition from massed/blocked practice (repeating the same exercise consecutively) to interleaving (mixing/varying up the exercises).
[~1:02:00] Effective learning strategies can feel counterintuitive / unnatural because the point is to increase effort, not to reduce effort. It's completely different from typical work or chores that you might do in batch. It's completely different from reading a fluent story from start to finish. It's about interrupting the flow of thought and coming back to it later.
[~1:09:00] Deliberate practice: a high-level description of the most effective form of practice identified by the academic field of talent development.
[~1:15:00] To what extent does the accumulated volume of deliberate practice predict whether someone is going to become an expert? Deliberate practice is the primary factor, but genetics is an important secondary factor.
[~1:17:00] NON-examples of deliberate practice. Common pitfalls when people try and fail to do deliberate practice, and how to avoid them.
[~1:23:00] How to learn more about the science of learning.
[~1:29:00] The #1 takeaway: use interleaved spaced retrieval practice. You can use this in the classroom.

On The Rails and Out Of Scope - Math Academy Podcast #6, Part 2
2026 Jan, ~1.25h • What we covered:
– The benefits of short problems. Math Academy problems typically take only a minute or two. This way, students can stay on the rails with lots of reps, successfully building up complexity instead of getting crushed by it from the start.
– What goes wrong in college math classes: they tend not to scaffold content very well, forcing students to build their own bridges across knowledge & skill gaps. Weekly problem sets often consist of a handful of hour-long problems that instructors hope students will “self-scaffold” up to. In reality, what happens more often is that students fall off the rails.
– Founders of growing start-ups cannot be hands-off. “Things falling off the rails” is the most realistic and most dangerous failure mode, not micromanaging. Founders of small, scaling companies need to be in “founder mode,” not the “manager mode” that CEOs of huge, well-established companies are in.
– Within teams, it’s important to let conversations flow out of scope. Every innovation, every solved problem, requires relevant background context, and you often don't know what the full context is beforehand. It's easy to let conversations flow out of scope when you like who you're working with and what you're working on.

0:00 - Introduction
1:32 - Why Math Academy problems are short by design
9:48 - Long problems dilute reps on the skill that actually matters
11:00 - Isolate the new skill first, then recombine into full problems
14:10 - Typical undergrad math classes: too few problems, too complex from the start
18:07 - The proof skills gap: often assumed and not taught
29:32 - Alignment decay: teams naturally drift out of sync unless continually aligned
35:04 - Small misalignments compound fast
38:28 - Founder mode: stay in the weeds to stay in sync
49:07 - Early, frequent parent communication avoids end-of-term blowups
50:48 - High-trust collaboration requires relentless communication
57:42 - Out-of-scope conversation enables context sharing
59:14 - Over-scoping kills context sharing
1:00:51 - Enjoyment & trust fuel context sharing
1:06:13 - Missing context produces confidently wrong outcomes
1:10:01 - LLMs fail when context is missing
1:11:38 - Humans fail when context is missing
1:14:19 - Online discourse fails when context is missing

Why Can’t College Students Do Middle School Math? - Math Academy Podcast #6, Part 1
2026 Jan, ~1h • What we covered:
– A recent report from the University of California San Diego revealed that 1 in 12 incoming freshmen were not proficient in middle school math – basically, anything above arithmetic with fractions. Their existing remedial math course was too advanced for these students, so they had to design even lower remedial remedial math courses. Even crazier, over a quarter of these students had a perfect 4.0 GPA in their high school math courses.
– It’s not just UCSD. This is everywhere. A similar thing happened at Harvard, too, having to add remedial support to their entry-level calculus courses. It’s like that movie Olympus Has Fallen, except this time it’s Harvard. It’s a catastrophe.
– How did things get this bad? Teachers and administrators face relentless pressure to inflate grades, and during the pandemic many universities went test-optional, removing the only signal that reliably correlated with actual math readiness. That decision simultaneously elevated high school grades to the sole gatekeeping metric, intensifying incentives to inflate them.
– This has all coincided with the advent of LLMs, which make it increasingly easy for students to cheat. The result was predictable: grades became untethered from real competence, and multiple cohorts of students entered college without ever having to demonstrate foundational math skills.
– Teachers have to play both good cop and bad cop, and there is no avoiding the latter. If you refuse to play bad cop at all, you eventually end up playing it constantly. The best teachers are strict from the start and ease up later, once students understand that hard, honest work is non-negotiable.

Timestamps:
0:00 - Introduction
2:11 - Freshmen math collapse: 1 in 12 UCSD freshmen don't know middle school math
6:45 - Remedial remedial math: UCSD created remediation for remedial math
8:40 - Inflated grades: 25% of remedial-remedial students had perfect GPA in HS math
10:06 - Test-optional admissions removed the last objective metric
12:13 - Pandemic inflation: GPAs skyrocketed
14:37 - Removing tests pressures teachers to inflate grades
16:52 - Grade-grubbing: endless negotiating, complaining, accusations
19:01 - Then vs. now: parents, tests, accountability
27:38 - Crisis opportunism: "Never let an emergency go to waste"
29:33 - No tests = no knowledge requirements
33:28 - Elite collapse: Harvard has the same problem
36:31 - No enforcement means no standards
37:40 - LLM cheating is trivially easy
38:25 - Catching a cheater and turning him around
48:46 - Cheating is like taking mob money. Now you’re in, you’re never out.
50:41 - Assessments must be done in person
55:06 - LLM cheating is often obvious yet hard to prove
57:17 - How to prevent cheating on long papers
58:28 - Start hardcore, then lighten up gradually
1:01:37 - Good teachers play bad cop when needed

Getting Kids To Do Hard Things - Math Academy Podcast #5, Part 2
2025 Dec, ~1.75h • What we covered:
– Most kids are not intrinsically motivated to do the hard things: practice their soccer drills, do their math homework, eat their broccoli. Getting them to do the hard things often requires gamification and/or incentives.
– A little gamification goes a long way. Jason gamified drills for his kids’ soccer team to get the most out of each practice (e.g., “zombie attack”), and it was unreasonably effective. The XP leaderboards on Math Academy are also unreasonably effective.
– A good incentive can change kids' behavior overnight. The incentive doesn’t need to be big; it just needs to be something the kid really cares about. Find the thing the kid would rather be doing, and use it to motivate them to do what they’re supposed to be doing. They won’t need the incentive forever; as the kid gets used to the feeling of a new behavior, it gradually turns into a habit that they can maintain on their own.
– Even when you’re doing what you love, there will be grindy phases. But kids typically don’t understand this. They might get interested in a talent domain and want to become good enough to build a life around it, while simultaneously resisting doing the hard work to make that happen (i.e., stage 2 in Bloom’s talent development process). It’s often up to parents, who can see the long game, to push their kids through the difficult parts in paths that they find rewarding.
– For instance, the most mathematically gifted student I ever worked with, who was drawn into math by his own intrinsic interest, still needed to be pushed to learn calculus. Now he’s having the time of his life working on physics-y, calculus-heavy research-level math problems in high school. Even after finding something he loves and is good at, he still needed to be pushed to do the hard work to unlock more of it.

Timestamps:
00:00:00 - Most kids are not intrinsically motivated to do hard things – homework, drills, practice. They usually need incentives to get through.
00:08:16 - A little gamification goes a long way. Jason gamified drills for his kids’ soccer team to get the most out of each practice (e.g., “zombie attack”).
00:14:05 - A good incentive can change behavior overnight. It doesn’t need to be big, just something the kid really cares about, and they won’t need it forever. It’s about building a habit until they can maintain it on their own.
00:54:16 - The most mathematically gifted student Justin ever worked with needed to be pushed to learn calculus, and now he's having the time of his life working on calculus-heavy research-level math problems.
01:11:54 - Even when you’re doing what you love, there will be grindy phases. It’s important for parents to help kids push through those grindy phases so that they can unlock more of what they love.

Building Without Bloat - Math Academy Podcast #5, Part 1
2025 Dec, ~1.25h • What we covered:
– Any successful endeavor requires a great team: capable people, who like and trust each other, and have complementary skillsets and ways of thinking. Some modes of thinking cannot be performed at the same time within a single brain.
– Accountability requires control. You can’t hold someone responsible for outcomes unless you also give them control over the system that produces those outcomes (though you can set reasonable operational boundaries).
– Solve today’s problems today. Smart people can invent endless hypotheticals and build giant solutions to fake problems. Not only does this waste time, but it also burdens the system with complexity that becomes a future straitjacket. Everything you build must be carried forward, so focus on what’s present in front of you, not on imagined futures five steps away.
– In a scaling system, the sheer volume of interactions will expose a long tail of bizarre scenarios, almost like rare diseases you’d never anticipate. Users will often try to repurpose software beyond its design, like hauling a trailer with a motorcycle.

Timestamps:
00:00 - Introduction
03:48 - The importance of finding your complements
24:07 - The origin story of Math Academy's content team
43:36 - No meta-work; just solve the problems in front of you
54:26 - Jason time vs real time (real time is longer)
59:00 - The long tail of rare edge cases and unexpected user behavior

Knowledge Graph Engineering: Mental Models & War Stories - Math Academy Podcast #4, Part 2
2025 Dec, ~1.25h • What we covered:
– Building a knowledge graph is like city planning & road construction. Too many prerequisites leading into a single topic creates a cognitive traffic jam.
– Elegantly rewiring a live knowledge graph: the evolution of our tooling and automatic validations. How to avoid staging servers & migrations and NOT have it blow up in your face.
– UI work takes time and adds complexity, so we spend it on the customer. Internal tools are almost entirely command-line; clickable buttons are for customers.
– Justin's transition from research coding to real-time systems. He started with mathy, notebook-driven quant code and had to learn production engineering the hard way. Once he did, it was a massive level-up.
– Alex's plan for dealing with "content papercuts" - small issues that pile up. Inspired by Amazon’s "papercuts team."
– Our upcoming differential equations course, the last course in the core undergrad engineering math sequence.

Timestamps:
00:00:00 - Building a production-grade knowledge graph is like city planning and road construction
00:07:26 - Elegantly rewiring a live knowledge graph: the evolution of our tooling and automatic validations
00:24:47 - Justin's transition from research coding to real-time systems
00:44:51 - Alex's plan for dealing with "content papercuts" - small issues that pile up
00:58:02 - Our upcoming differential equations course

The Unreasonable Effectiveness of the Knowledge Graph - Math Academy Podcast #4, Part 1
2025 Nov, ~1.25h • What we covered:
– Why "problem solving" is often just a vague label people use when they haven't explicitly enumerated the underlying skills, and how those skills can in fact be exhaustively mapped in a knowledge graph.
– How to approach research problems: Alex's PhD journey, top-down familiarity vs bottom-up mastery.
– If you have natural talent, use it, but not as a crutch, otherwise you'll stunt your long-term development. Don't turn your blessing into a curse.
– The story behind building our SAT prep curriculum: realizing that the standard school curriculum leaves a massive "missing middle" unaddressed; identifying 115+ missing topics to bridge the gap between textbook math and the hardest SAT questions.
– Watching the manifold hypothesis play out in test prep: the SAT may appear to allow an astronomical space of possible problem types, but in reality the actual problems live on a compact, highly structured manifold that can be fully enumerated and scaffolded in a knowledge graph

Timestamps:
00:00:00 - Intro: "problem solving" is what you call it when you don't really know what it is (i.e. you haven't explicitly enumerated the skills)
00:04:11 - How to approach research problems: Alex's PhD journey, top-down familiarity vs bottom-up mastery
00:20:28 - If you have natural talent, don't use it as a crutch. Don't turn your blessing into a curse.
00:29:06 - SAT prep, iteration 1: Realizing that the standard school curriculum leaves a massive "missing middle" unaddressed
00:33:45 - SAT prep, iteration 2: Covering the "missing middle" problems
00:53:38 - SAT prep, iteration 3: Building the "missing middle" knowledge graph
01:08:11 - Watching the manifold hypothesis play out in SAT prep
01:16:42 - The unreasonable effectiveness of the knowledge graph

Waging War on Mediocrity: Tales From the Trenches - Math Academy Podcast #3
2025 Nov, ~2.5h • What we covered:
-- How bureaucracies instinctively reject new ideas like an immune system attacking a foreign organ, and what it takes to keep your project from being "spit out." Concrete example: how Jason & Sandy muscled past institutional resistance to get 8th graders passing AP Calc BC.
-- Every system inevitably decays into mediocrity unless someone fights to keep the standards high. The way you keep people, systems, and projects moving is by "horsing" them forward. Concrete example: how Justin kept 8th graders passing AP Calc BC, and what it looks like when a school succumbs to the gravity of mediocrity.
-- Justin's math self-study journey in high school: grinding math like a video game, running a secret self-study op inside traditional classes, taking talent development seriously while simultaneously hitting his head on every ledge and making every rookie mistake. Ups and downs, lessons learned, with tons of concrete examples.

Timestamps:
00:00:00 - Intro: Willing Things Into Existence
00:11:43 - How Jason & Sandy Willed Math Academy Into Existence
00:36:45 - Fighting The Gravity of Mediocrity
01:02:29 - Case Studies in Educational Dysfunction
01:21:53 - The Birth of Justin’s Self-Study Madness
01:50:48 - Self-Studying on the Sly During School
02:02:41 - The Highs & Lows of High School Research
02:22:38 - Outro: Paving the Path with Math Academy

Teach Like Your Life Depends On It - Math Academy Podcast #2
2025 Nov, ~2.75h • 0:00 - What Would a Tutor Do, If Their Life Depended On It? (Part 1)
5:47 - Find Your North Star: Why Justin Quit His Data Science Job to do Math Tutoring Full Time
11:23 - Getting "Inside the Trade"
19:31 - What Would a Tutor Do, If Their Life Depended On It? (Part 2)
27:28 - Efficient Learning Techniques are Obvious if You Think About Athletics
33:45 - Enjoyment is a Second-Order Optimization
39:50 - We Need to Stay Hardcore, But Become Less Harsh
51:14 - Math Academy is Like "Yuri's Gym"
59:06 - Vision for the Future of Math Academy
1:14:23 - Goal Setting/Advising and Communicating Progress
1:24:58 - If All You Show Up With is AP Calculus, You're Probably Outgunned
1:51:08 - The Meta-Skills that Kids Need to Work Effectively on Math Academy
2:08:54 - How to Help Students Maintain Successful Learning Habits While Working Independently
2:32:29 - Overhelping: A Common Failure Mode of Well-Intentioned Parents/Tutors

The Long Game: Building Minds and Machines - Math Academy Podcast #1
2025 Oct, ~2.5h • 0:00 - Introduction
4:00 - Applying the MA Way to X Growth
7:40 - Status of the ML Course and its Kick-Ass Coding Projects (Part 1)
25:50 - Jason's Near-Infinite List of Important Things
34:20 - The ML Course Has Been a Massive Undertaking
42:10 - Breadth-First Development
44:30 - Status of the ML Course and its Kick-Ass Coding Projects (Part 2)
50:15 - Why Math Academy Needs To Do a CS Course
56:45 - The Never-Ending Stream of Confusion
1:00:30 - The Story of Eurisko, the Most Advanced Math/CS Track in the USA
1:24:20 - Intuition Through Repetition: Machine Learning Edition
1:29:40 - The Importance of Spaced Review
1:43:30 - Upcoming Course Roadmap
1:47:40 - Spaced Repetition 2.0: Accounting For and Discouraging Reference Reliance
1:54:45 - Overhelping: A Pathology of the Over-Involved Parent/Tutor
1:59:21 - Yes, You Need to be Automatic on Math Facts (and Yes, Rapid-Fire Training is Coming)
2:04:55 - What Happens When Students Don't Know Their Math Facts
2:05:50 - The Horror of Attempting to Teach a Class When Students Have Multi-Year Deficits in Fundamental Skills
2:11:30 - Integrating Coding Into the Math Curriculum
2:18:00 - Combining Math and Coding is the Closest Thing to a Real-Life Superpower
2:18:55 - Creating a Full Math Degree and Getting Full College Credit
2:22:15 - The Power of Pre-Learning: The Greatest Educational Life Hack

Q&A #4: How I Approach Learning in Other Domains
2025 Sep, ~25m • How I've personally applied the Math Academy learning approach to areas outside of math (specifically biology and music).

Q&A #3: Sophisticated vs trivial problems, when to learn coding, how I learned SQL
2024 Dec, ~20m • What it means for a problem to be sophisticated, not made trivial by foundational knowledge. When is the best time to learn coding, at an early age or after you have some university-level math under your belt? How I learned to write, organize, and debug big-ass SQL queries.

Q&A #2: WMC, chunking subskills in LTM, writing down work, using/applying vs deriving/proving
2024 Nov, ~1.5h • Understanding working memory capacity. Scaffolding new skills by chunking subskills into long-term memory. Why it's beneficial to write down your work. Why solving problems is necessary. Using/applying mathematical tools vs deriving/proving them. What's good vs inefficient in the standard math curriculum.

The Future of Multistep Tasks on Math Academy
2024 Nov, ~35m • The primary key to motivation, goal-setting, understanding how to apply all the mad skills you’ve learned... it seems like it's all coming down to multisteps.

Q&A #1: WM taxation, ML ETA, catching errors, coding tutorials, math vs calisthenics, foundations
2024 Nov, ~50m • When to take breaks. How to catch computational errors when working out math problems. There's a lack of resources for people who want to learn machine learning -- coding tutorials and math textbooks typically suck in their own ways. Generalizing the principles of effective learning & skill acquisition to contexts outside of math learning. What to do when you want to complete a project but your base level of knowledge is low.