#8, Part 2 – Failure Modes in Teaching

#8, Part 2 – Failure Modes in Teaching

What we covered: – In elementary school, there's often an intense focus on conceptual understanding, but not enough time spent building real fluency with core skills. And this has left many kids without automaticity on basic things like multiplication facts. Math is extremely hierarchical, and when students don't have the basic facts at their fingertips, they quickly run into bottlenecks as the material gets more complex. – Sure, drills can be made more fun, but the bottom line is that they have to get done. In high school and college, most of the class time is spent copying notes from the board -- and these notes are often copied by the instructor from a textbook or from other source material. This game of telephone through transcribing is just a performative activity. It's theater. It's passive and it does next to nothing for learning and retention. – In upper level college math courses especially, students may only receive short weekly problem sets, which really aren't enough to build mastery, even if the problems are really hard, because students just spend most of their time flailing around. – The bottom line is that students need reps: lots of them, building up scaffolding to the highest, hardest levels that they're expected to reach. High school assignments tend to be better in that regard, but students frequently don't receive timely feedback, and often their work isn't even graded for accuracy. That feedback loop is so critical: without it, students won't know what they're doing wrong or how to improve. – So rather than just pattern matching to how math has traditionally been taught, what actually makes training effective? There's a few core principles: 1) Maximize the amount of time spent actively learning, interleaving minimum effective doses of explicit guided instruction active practice. 2) Make sure students are consistently working at the edge of their abilities: not bored, but not overwhelmed. 3) Provide frequent, timely feedback so students can adjust and improve. These principles should be applied to math education and training environments everywhere. Outline: 0:00 - Introduction 3:13 - Professors often wing pedagogy 5:37 - Too much class time is spent transcribing notes 7:41 - College problem sets are too short 12:53 - A lot of homework isn’t even graded for accuracy 18:22 - Copying notes in class is performative productivity 22:29 - Alex taught math courses at University College London 25:35 - Teaching is often an annoying obligation for research professors 30:03 - The bar for teaching is on the floor 32:34 - Even football practices often waste players’ time 34:20 - Most training is inefficient because people pattern match to the status quo 34:57 - First principles for effective training 37:13 - Too many models can paralyze and become a crutch for kids 39:24 - Kids can get stuck using training wheels in math forever 42:05 - Non-standard methods are often distracting and inefficient 46:18 - Designing 6th-8th grade courses to align with school curricula 52:30 - Conceptual understanding without ability is useless 55:17 - Skills practice can and should be gamified 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

#8, Part 1 – Role of Teachers in the Math Academy Classroom

What we covered: – A lot of schools have recently begun using Math Academy in their classrooms. And one of the biggest benefits of using Math Academy is that it automates all the mechanical parts of teaching, like writing questions, keeping track of what students know and what they don't know, monitoring student progress, assigning extra practice when needed, grading, all that grindy stuff. – None of these tasks is enjoyable. They suck. Just ask any teacher. I mean, we grinded through all that back when we were teaching ourselves, and it takes so much effort just to get even a halfway decent approximation of doing it right. And there's just a limit to how well that you can do it if you're doing it manually. It's the whole reason why we built the system. – And what that system does, what Math Academy we does is it frees up teacher bandwidth to focus on the human elements of teaching: building relationships, connecting what students are working on to their own unique interests. Those kind of things that enhance the learning experience, but that really can't replace skills practice. – I mean, in-class projects can be great, but only if students have the prerequisite knowledge to be successful with them. If they don't, then projects are frustrating, and the students who understand the material will end up doing all the work and carrying everybody else, who will learn next to nothing. It's inefficient and frustrating all around unless students have their skills in place. – Ultimately, if students don't master the math in each class, they'll be unprepared for the next one. And in a subject as hierarchical as math, these gaps compound quickly. True empowerment isn't simply telling students they have potential. It's making sure they actually have the real skills to move forward and realize that potential. Outline: 00:00 - Introduction 02:56 - What is the teacher’s role alongside Math Academy? 05:37 - Math Academy frees up teachers to do the human parts of teaching 07:03 - Projects are great if students have the prerequisite skills 07:42 - Drills without context are boring 08:43 - Games without skills are inefficient 11:14 - Build fun activities on top of a solid foundation of skills 12:15 - Teachers can tailor the class to the students’ preferences 13:28 - Implementing mastery learning is too much work for a single teacher 15:27 - Doing projects without prerequisites is frustrating 16:57 - True empowerment is giving kids the skills they need to succeed 19:30 - Missing skills compound in hierarchical skill trees 24:06: Lack of automaticity in lower level skills slows down higher level tasks 27:14 - The MA team builds and improves courses through experience 29:21 - The MA team targets tasks with low pass rates for additional scaffolding 31:03 - Alex built knowledge graph intuition through years of experience 37:40 - Social media enforces hyper-accountability 39:19 - Differential equations courses are often a hodgepodge of disjointed techniques 43:20 - Math Academy university courses are a superset of elite university content 45:18 - Differential equations is a highly branching subject 49:21 - The breadth of Differential Equations makes it often poorly taught *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

#7, Part 2 – Earning the Right to Scale

What we covered: – As Math Academy has grown over the past year, we're getting a better sense of general do's and don'ts when scaling a startup. We've learned hard lessons about overloading the database, the task processor, and our team, requiring numerous infrastructure and process updates. – Schools have been using the system and we've built plenty of additional features to, among other things, accommodate unique billing schemes and make it easy for teachers to manage classes on the system. – We've intentionally grown organically and were self-funded, which forced us to do things manually at the beginning. Years ago, we taught math classes in person and Jason onboarded our first online users on hundreds of hour-long individuals and calls. These were crucial experiences to learn who our customers are, what they want from the product, and common failure modes. – In our experience, doing things manually at the beginning ensures that you 1) build a product that customers actually get value from, and 2) you don't clutter your product with unnecessary bells and whistles that don't add value. In other words, you have to do the manual work to earn the right to scale. Outline: 0:00 - Introduction 2:18 - Building infrastructure to handle increasing load 3:41 - Bringing on AWS expertise to robustify the backend 4:22 - An overloaded database enters a new realm of physics 5:50 - Prioritizing execution over perfection in start-ups 6:33 - Paying the bill for accumulated infrastructure debt 7:53 - Improving job prioritization of the task processor 9:52 - Benefits of scaling organically 11:42 - Wisdom is the result of failures 12:18 - There is no substitute for experience 13:17 - Focusing on solving problems, not advertising 14:48 - Upgrading with surgical precision 15:35 - The pain-point compass 17:04 - Managing finite time and resources 18:27 - Development of the gravity feature 20:42 - Gravity is a suggestion, not a hard override 22:25 - Limiting gravity to avoid cognitive overload 28:29 - Balancing customization and customer confusion 31:28 - The feature sandbox 33:58 - Increasing volume of customer support emails 35:22 - Additional infrastructure requirements for schools 36:18 - Learning about the customer through direct interaction 38:14 - Step 1: Manually added schools using spreadsheets 40:22 - Step 2: Developed tools to handle specialized school requests 41:23 - Step 3: Goal is 100% self-service sign-ups for schools 42:32 - Solve the problem manually first, then automate it 43:44 - Why focus on schools? 46:15 - Math Academy goes to college 49:37 - You can’t anticipate every edge case 52:14 - Letting user behavior build the product roadmap 58:54 - Becoming successful means working harder 1:00:24 - The customer support hurdle 1:03:27 - How Justin’s expanding roles drove growth (both personal & company) 1:09:03 - Teaching as market research for Math Academy 1:10:52 - The value of having been inside the trade Follow on X: Math Academy - https://x.com/_MathAcademy_ Justin Skycak - https://x.com/justinskycak Jason Roberts - https://x.com/exojason

#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

#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