Math Academy

Math Academy
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Stories, challenges, and discoveries from the front lines of building the ultimate math learning system.

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  1. ١٠ فبراير

    #7, Part 1 – 2025 in Review: Content Production

    0:00 - Introduction 3:57 - Added 115 “Missing Middle” topics to SAT Prep 6:06 - Integrating the SAT Missing Middle topics into other courses 9:42 - Added tens of thousands of free response questions 10:34 - Free response questions are useful because they don’t prime you 13:33 - When to use free response vs. multiple choice questions 14:54 - Too many free response questions taxes learners 16:39 - Limiting the length of free response answers 18:08 - Building infrastructure for free response questions was a beast 20:42 - SAT test prep course 22:22 - Machine Learning has been the hardest course to develop so far. 23:12 - People who know machine learning, math, and how to teach them are rare 25:06 - The Eurisko book was the best resource for developing the Machine Learning course 28:51 - Balancing repetition and computational load in Machine Learning problems 29:43 - Designing minimum viable problems for Machine Learning 33:53 - Building the infrastructure for dynamic select questions was a nightmare 36:12 - Dynamic select questions are good for proofs and university-level math 38:03 - The Differential Equations course is almost finished 40:23 - Iterating on course development to make better courses 42:00 - 2026 is the year of scaling up course production 43:03 - How to scale up the team without sacrificing course quality 44:39 - Learning the hard way about hiring too quickly 46:20 - Challenges of managing a fully remote, geographically dispersed team 48:54 - Building tools to measure company output 50:06 - Optimizing content writer performance is like optimizing student learning 52:31 - Incentivizing content creation to improve output 56:36 - Courses planned for the longer term 58:01 - You need to learn concrete computations before abstract proofs 59:32 - Why we separate university-level courses into computational vs proof-based 1:01:07 - The best textbooks for beginners are NOT the most complex 1:02:37 - Teaching proofs and computations at the same time overloads most students 1:04:16 - Intuition through repetition 1:04:49 - Wisdom is the abstract compression of lived experiences 1:07:39 - Mastering details before abstracting Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason Alex Smith - https://x.com/ninja_maths

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  2. ٢٨ يناير

    #6, Part 3 – Learning Debt and Skill Insolvency

    What we covered: The dangers of accumulating learning debt: the gap between what you can do and what you need to be able to do.If you miss building up your foundational skills in school or sports, you can get by for a while. You develop some compensatory strategies, like favoring your forehand over your backhand, or using ChatGPT to write all your school essays.But learning debt is like any other kind of debt: it accrues interest and eventually comes due. Over time, the workarounds become more complex. The cognitive load increases. You start avoiding situations that expose the gap, and this is where you hit your ceiling. You can’t pursue an engineering degree if you can’t do algebra. You can’t be competitive in tennis if you can’t hit with your backhand.Learning debt often begins because of a lack of oversight by adults. Parents, teachers, and even coaches sometimes think they’re being nice not telling you that you need to work on your weaker side, or you need to stop using a calculator on your math problems. It feels like nagging, and it can create conflict between adults and learners. So they let it slide.But this failure to hold the line early on inhibits students’ future potential. And when it occurs across many students across many schools, it degrades the whole educational system – leading to the current situation in which many students are totally unprepared for the rigors of college. Outline: 0:00 - Introduction 2:04 - Course phases: instruction, final review, final exam, remediation if needed 5:25 - Generating full-length SAT exams for our prep course 6:53 - Loosening up the gravity throttle for high-performing students 14:59 - Aptitude is measured by accuracy rate 18:07 - Accuracy correlates first with aptitude, second with conscientiousness 21:35 - Assessment vs. non-assessment accuracies 23:43 - Propagating accuracy through the knowledge graph 24:27 - Hidden skill gaps force bad compensations 25:27 - Sports make skill deficits and bad compensations obvious 33:38 - The Math Academy system holds you accountable for every skill 34:18 - Completing the square: a common skill deficit with temporary workarounds 36:15 - Reliance on Desmos undermines students’ ability to graph functions 37:38 - You need to know your multiplication facts for factoring 38:13 - Foundational deficits are usually caused by lack of adult oversight 38:52 - Shoring up foundations is effortful but has huge ROI 40:40 - Filling in missing foundations makes kids so much more confident 41:12 - Missing foundations stall learning and drive cheating 42:12 - Faking competence backfires downstream 45:33 - The truth hurts but is the kindest thing in the long run 46:26 - Learning debt eventually comes due, with students paying the biggest price 47:12 - Kicking the can down the road in education 49:46 - The cost of a broken education system Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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  3. ١٤ يناير

    #6, Part 2 – On The Rails and Out Of Scope

    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. Outline: 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 Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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  4. ٣ يناير

    #6, Part 1 – Why Can’t College Students Do Middle School Math?

    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. Outline: 00:00:00 - Introduction 00:02:11 - Freshmen math collapse: 1 in 12 UCSD freshmen don't know middle school math 00:06:45 - Remedial remedial math: UCSD created remediation for remedial math 00:08:40 - Inflated grades: 25% of remedial-remedial students had perfect GPA in HS math 00:10:06 - Test-optional admissions removed the last objective metric 00:12:13 - Pandemic inflation: GPAs skyrocketed 00:14:37 - Removing tests pressures teachers to inflate grades 00:16:52 - Grade-grubbing: endless negotiating, complaining, accusations 00:19:01 - Then vs. now: parents, tests, accountability 00:27:38 - Crisis opportunism: “Never let an emergency go to waste” 00:29:33 - No tests = no knowledge requirements 00:33:28 - Elite collapse: Harvard has the same problem 00:36:31 - No enforcement means no standards 00:37:40 - LLM cheating is trivially easy 00:38:25 - Catching a cheater and turning him around 00:48:46 - Cheating is like taking mob money. Now you’re in, you’re never out. 00:50:41 - Assessments must be done in person 00:55:06 - LLM cheating is often obvious yet hard to prove 00:57:17 - How to prevent cheating on long papers 00:58:28 - Start hardcore, then lighten up gradually 01:01:37 - Good teachers play bad cop when needed Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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  5. ١٨‏/١٢‏/٢٠٢٥

    #5, Part 2 – Getting Kids To Do Hard Things

    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. XP and 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 Justin 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. 00:41:17 - The stress of high school 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. Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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    #5, Part 1 – Building Without Bloat

    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 Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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    #4, Part 2 – Knowledge Graph Engineering: Mental Models & War Stories

    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 Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason Alexander Smith - https://x.com/ninja_maths

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    #4, Part 1 – The Unreasonable Effectiveness of the Knowledge Graph

    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 - 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) 04:11 - How to approach research problems: Alex's PhD journey, top-down familiarity vs bottom-up mastery 20:28 - If you have natural talent, don't use it as a crutch. Don't turn your blessing into a curse. 29:06 - SAT prep, iteration 1: Realizing that the standard school curriculum leaves a massive “missing middle” unaddressed 33:45 - SAT prep, iteration 2: Covering the "missing middle" problems 53:38 - SAT prep, iteration 3: Building the "missing middle" knowledge graph 1:08:11 - Watching the manifold hypothesis play out in SAT prep 1:16:42 - The unreasonable effectiveness of the knowledge graph Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason Alexander Smith - https://x.com/ninja_maths

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    #3 – Waging War on Mediocrity: Tales From the Trenches

    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 Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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    #2 – Teach Like Your Life Depends On It

    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 Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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    #1 – The Long Game: Building Minds and Machines

    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 Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

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Stories, challenges, and discoveries from the front lines of building the ultimate math learning system.

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  • صناع العمل
    Math Academy
  • سنوات النشاط
    ٢٠٢٥ - ٢٠٢٦
  • الحلقات
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  • حقوق النشر
    © Math Academy
  • موقع البرنامج على الويب
    Math Academy

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