Goal • Deep Dive into Math Academy and Talent Development Research • Math Academy Origin Story • Upskilling in General • Upcoming ML and Programming Courses • Miscellaneous

If we're doing a podcast together, I'm aware that it takes quite a bit of time and effort to compile background information about an interviewee to have a thoughtful conversation.

So, I've compiled some resources that hopefully make your life easier! Don't feel obligated to read all this, but some might be worth a skim if the description catches your eye.

If I had to briefly distill down what I spend the majority of my time thinking about, what my goal in life is, it's this.

Nerd Level 1: Why Not Just Learn From a Textbook, MIT OpenCourseWare, Khan Academy, etc.? -- I learned from those kinds of resources myself, and while I came a long way, for the amount of effort I put into learning, I could have gone a lot further if my time were used more efficiently. That's the problem that Math Academy solves.

Nerd Level 2: Overview of our pedagogy, how our AI system works (it's an "expert system," throwback to old-school AI) and a deep dive into our spaced repetition system.

Nerd Level 3: The Math Academy Way, our 400+ page working draft book that compiles and synthesizes evidence from hundreds of scientific papers to answer the following questions: What techniques exist to maximize student learning and talent development, particularly in the context of math? Why are these techniques so impactful, and if they are indeed so impactful, then why are they so often absent from traditional classrooms? How does Math Academy leverage these techniques?

The table of contents of The Math Academy Way is very extensive and functions as a summary of the book. Each chapter also has a one-paragraph summary. Here is a not-too-out-of-date collection of all that summary info.

Kris Abdelmessih went down the rabbit hole reading The Math Academy Way and many of my blog articles, took extensive notes, and compiled them into an incredibly interesting and thoughtful synthesis called The Principles of Learning Fast.

Math Academy's original school program is a highly accelerated 6-12th grade math program in Pasadena where 6th graders start in Prealgebra, and then learn the entirety of high school math (Algebra 1, Geometry, Algebra 2, Precalculus) by 8th grade, and then in 8th grade they learn AP Calculus BC and take the AP exam, and then in high school they study a full undergraduate math curriculum.

It's the most accelerated math program in the USA, there have been plenty of other news articles written about it, and there's plenty of other information straight from the horse's mouth including a summary of events 2014-20 (from Sandy and Jason's perspective), a summary of events 2019-23 (from my perspective, with a focus on teaching in the school program and getting the algorithms in place to turn it into a fully automated system), and another summary of events 2014-20 that I gave on Anna Stokke's Chalk and Talk Podcast #42 (I'll paste the relevant snippet below):

• "So back to this eighth graders taking AP Calc BC story. We originally started as a nonprofit school program founded by Jason and Sandy Roberts. One of their kids, Colby, was on the fourth-grade math field day team, and his parents were coaching that team. Their kid and his friends were all really excited about learning math, so they did the standard fourth-grade field day stuff. But the kids were so excited that they didn’t want to just stop at fourth grade. Something they would often ask Jason and Sandy was, “What’s the highest level of math?”
  
  Jason and Sandy would have to say, “Well, it goes really, really high, but for your purposes, let’s just say it’s calculus, because that’s what seniors in high school take if they are on the honors track.” And the next question was, of course, “When do we get to learn it? Can we learn it now? Can we learn calculus tomorrow?” They were just so excited about it.
  
  Jason and Sandy were teaching a bunch of these kids advanced math, even through fifth grade. They got up through a bunch of high school math and to the point where they could start learning calculus. One thing led to another, and this turned into an official school program that was not just a pullout class but became a daily Math Academy class. There were other cohorts that came in following years.
  
  What this turned into was that we would get students in sixth grade who were solid on their arithmetic. They might know what a variable is, but they didn’t really know how to solve equations or anything. They were kind of at an early pre-algebra level. We would scaffold them up, teach them all of high school math within the next two years—sixth and seventh grade. Pre-algebra, algebra one, geometry, algebra two, and pre-calculus. In eighth grade, they’d be ready to take calculus.
  
  Then, they would take the AP Calculus BC exam. We got to the point where most of the students who took the AP Calc BC exam in eighth grade passed, and most who passed got a perfect five out of five on the exam.
  
  A couple of things I should say, these are not national talent search students.
  
  How the kids were selected was that they scored at or above the 90th percentile on a middle school math placement exam, which is typically taken by all fifth graders in the district around February or March. They were then invited to join the program. It's a seventh-grade math skills test, so it provides a somewhat high skill level, but it's not designed to identify math aptitude.
  
  This is also in the Pasadena Unified School District, where about two-thirds of the student population qualifies for the federal free and reduced lunch program, and about 44 percent of all K-12 students are educated in private schools, compared to the California average of 11%.
  
  This is not a particularly talented group of students. It's not a biased group of the top students in the nation. Just think of a standard school and kids in the standard honors class. They can be accelerated way, way, way higher than they currently are.
  
  When Jason and Sandy were teaching, they were doing this all manually and achieving very good results. But these results got even better once students started working on the Math Academy system. Jason got tired of the kids saying, “I forgot to do my homework,” or “Oh, I forgot a pencil,” or all these excuses for not doing work. So, he just built a system where he could pick problems for them to do, and then all they had to do was log in at home and do the problems online.
  
  It would automatically grade the problems and keep track of all the kids’ stats, keep track of the class accuracy, and various topics. Over time, this evolved into a system that did more and more of the teaching work.
  
  In the summer of 2019, that’s when Jason pulled me in to make this system a fully automated platform that would actually select learning tasks for students. So, we built this automated task selection algorithm and continued refining it. By the time the pandemic hit in 2020, the big question was how to maintain this level of efficiency from manual instruction.
  
  The answer was, “Well, we have this halfway baked task selection algorithm. Let’s just get it all in place over the summer and put the whole school program on it.” And that’s what we did. That’s how our AP Calc BC scores skyrocketed, from putting them on the system."

We really leaned into the automated system -- it allowed us to leverage these learning-enhancing practice techniques to the fullest extent, selecting individualized learning tasks tailored to each student's own knowledge profile, so that every student would always be working on the exact tasks that would move the needle most on their learning. From my summary of events 2019-23:

• I got involved at the core of Math Academy's software during the summer of 2019. At that time, the software had existed for several years as a tool that Math Academy instructors used to create and grade assignments -- they would manually select problems from the database (which contained a mountain of content written by Math Academy's team of PhD mathematicians), students would complete the problems online for homework, and the software would automatically grade the assignments and keep track of each student's grades. But it was very time-consuming to manually choose a mix of problems that covered the multiple topics taught during class each day and also provided spaced review on previously-learned topics.
  
  It was clear that while students were learning an incredible amount of math, giving the same assignment to each student in a class still left a lot of learning efficiency unrealized: even within a single class, different students had different strengths and weaknesses, had different sets of topics that they were ready to learn, and needed different amounts of practice on different topics to reach a sufficient level of mastery. Giving each student the same assignment virtually guaranteed that every student wasted lots of time being bored or lost -- either way, not actually learning. To solve this problem, different students would need to learn different topics at different times, and get different amounts of practice (including review) on those topics, and each student's learning plan would need to continually adapt to their individual performance.
  
  The need for fully individualized learning, as well as other needs (e.g., financial sustainability and the constant effort to maintain accountability & standards across multiple classes / teachers / schools) led Jason and Sandy to the realization that the only way forward was for the system to become a fully-automated standalone online learning platform, commercially available to the general public. Aware of my background, Jason asked me to develop an algorithm that would automatically assign personalized learning tasks (personalized to each student's individual knowledge profile) while leveraging effective learning techniques like mastery learning, spaced repetition, and interleaving.
  
  By the end of summer the we had an implementation that -- despite being very rough, brittle, and in many ways incomplete -- was good enough to test out with a real student. During the 2019-20 school year, we started out with a single independent learner, a student who was previously in Math Academy and had moved to another state. She learned AP Calculus BC using only the system (i.e. no external help, no human intervention) and got a 5 on the AP exam. This proved the concept that we could upgrade the software from a manual assignment creation tool to a fully-automated adaptive learning system supporting independent learners without any human intervention.
  
  A major transition point happened in Spring 2020, with the onset of the COVID-19 pandemic. I moved in with Jason and his family to quarantine, which led to a makeshift startup incubator experience run out of his living room. We worked every waking hour, well into the night, every day including weekends, so that by the end of summer we were ready to run entire school classes on the automated system. During the 2020-21 school year and COVID-19 pandemic, the automated system proved to be significantly more effective than traditional remote instruction, and by spring 2021 nearly all of Math Academy's school classes were running on it (a couple of which I personally managed as a makeshift usability lab until 2023).
  
  During the 2021-22 school year, even after school was back in person, we reached the point that the system was 4x as efficient as traditional in-person classes covering the same material. Seemingly impossible things started happening like some highly motivated 6th graders (who started midway through Prealgebra) completing all of what is typically high school math (Algebra I, Geometry, Algebra II, Precalculus) and starting AP Calculus BC within a single school year. Math Academy's AP Calculus BC exam scores rose, with most students passing the exam and most students who passed receiving the maximum score possible (5 out of 5). Four other students took AP Calculus BC on our system, unaffiliated with our Pasadena school program, completely independent of a classroom, and all but one of them scored a perfect 5 on the AP exam (the other one received a 4).
  
  Finally, during the 2022-23 school year, we opened up mathacademy.com commercially to the world at large, became accredited, grew to hundreds of commercial users, and hit operating break-even. Even more commercial students aced the AP Calculus BC exam, including an elementary schooler.

There's plenty more to this story -- we also ran a quantitative CS course sequence within the original school program from 2020-23, where we scaffolded our high schoolers up from having little to no coding experience to doing masters/PhD-level coursework (reproducing academic research papers in artificial intelligence, building everything from scratch in Python). We called this the "Eurisko" program.

It’s still pretty early on, and as of spring 2025 the very first cohort is still in undergrad (it’s currently their junior year). However, there have already been some amazing student outcomes in terms of college admissions, accelerated graduate degrees, research publications, and science fairs.

Just to name some impressive stats on 4 of the 16 students in the Eurisko program:

• Anton attends MIT
• Justin is attending Caltech
• Colby started taking grad courses his 2nd year of college and is considering an early master's degree
• Matteo published a math-heavy research paper, solo author, in high school, and won 1st place in the Regeneron Science Talent Search (his poster and presentation are available here). He'll be attending Stanford in 2026.

We haven't been systematically tracking this info or sending out alumni surveys or anything, so there's probably even more interesting stuff going on that we haven't heard about yet. As I summarized on Anna Stokke's Chalk and Talk Podcast #42:

• "In 9th through 12th grade, what they do is learn a bunch of undergraduate math. We have PhD-level math instructors who teach the 9th through 12th graders, and they learn linear algebra, multivariable calculus, probability statistics, real analysis, abstract algebra, and algebra.
  
  They go through all this content, and they are also often working on some independent math projects. In terms of full outcomes for the students, it's still pretty early, so the first cohort is still in their junior year of college, and they haven't really hit their careers yet.
  
  We’ve been hearing a lot of really cool things from them. One kid is doing an accelerated master's degree in undergrad. Some other kids got into MIT and Caltech. Another kid is currently a senior in high school, and he did an internship at Caltech the summer of his sophomore year, then worked there on a research project for his junior year. He actually let me know a couple of weeks ago that he got a paper published as a high schooler, a solo-authored paper in a legit journal. It's interesting to see his author affiliations: Pasadena High School and California Institute of Technology."

Since summer 2024 I've written a ton of scattered pieces on upskilling. I recently cleaned them up and pulled them all together into a booklet called Advice on Upskilling.

Old table of contents (not bad, but has been continually refined) for our upcoming ML course, along with context around it

Our pedagogical approach to the ML course

We're also going to have plenty of cool coding projects, and those projects will stretch all the way up to implementing research papers from scratch.

Some info about our upcoming Intro Programming courses: here and here.

Podcast transcript where I talked a lot about the upcoming ML course at the beginning.

Previous podcasts I've been on, with summaries and transcripts, lots of stuff about Math Academy in general.

Story about a time we thought the model was broken because a 6th grader was getting Calculus tasks the same year that they placed into Prealgebra, but it turned out to be legit -- the kid completed all of what is typically high school math (Algebra I, Geometry, Algebra II, Precalculus) within a single school year.

Previous podcasts I've been on, with summaries and transcripts, lots of stuff about Math Academy in general.

Math Academy, Jason, Justin, and Alex on X/Twitter

All posts with "Math Academy" tag: