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.

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.

Demonstration of Setting Encompassing Weights
2024 Nov, ~25m • Encompassing weights control how much spaced repetition credit is propagated backwards from a more advanced topic to a simpler prerequisite topic when a student does a spaced repetition on the more advanced topic. Setting them is tedious, and it sucks, but it's completely necessary. That's sometimes what you’ve got to do when you want to build a solution that actually solves a problem. You have to put in the hard work.

Golden Nuggets Podcast #40 (Round 4): How Justin learns, new ML course, the magic of Twitter
2024 Nov, ~1h • 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.

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.

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 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.