Justin Skycak

I guess these workbooks usually come in two different "shapes" - one, a guided workbook with a high-level goal that combines several concepts, and another would be a practice worksheet where we do a bunch of exercise of the same algorithm (say, long division, calculating summations, or matrix multiplication) over and over. For the "workbook" pattern, we first discuss with the LLM the final goal (e.g. a scratch program that can calculate a rocket's position using the rocket equation). Then we flesh out the steps towards the goal - is it reasonable to add the math for air resistance? air resistance that decreases with altitude? gravity turn? how do we integrate the velocity and position for each frame? How can we relate the integration by step size to the underlying integral, by showing that the result gets more precise (but slower to calculate) the smaller your delta-t is? Then, produce a Scratch code sample that implements the velocity and position calculation. Of course, there are things subtly wrong with the code sample (usually, if the math formulas are well-known, they're correct), which requires debugging - just another type of problem-solving.

The second shape, worksheets, is a lot more straightforward. Just define the type of problem you want to practice and have chatgpt make a bunch of problems. Then switch to one of the newer reasoning models and have it work the problems, and refine to get rid of any bogey problems (for example, for polynomial exercise, you could…

Once your child grows a bit older (or is particularly precocious), I recommend Math Academy.

If you search for "Math Academy" on Twitter, you'll find all sorts of great stories about it. The creators have studied the science of pedagogy pretty well to optimize the learning process at scale to every user. Justin Skycak in particular on Twitter discusses what goes into creating the content, the scaffolding, interleaving methods they use, buildup of automaticity through memory, and how working memory affects rates of learning. Justin has even shared a textbook on his Twitter page that details a high overview of the various teaching methods that go into the curriculum (although from what I understand it's still a work in progress).

You can even try it yourself. A few mathematicians use it to brush up on old concepts they haven't used in a while or to add a little that they didn't know previously.

They're also constantly expanding the courses.

There was a great Reddit thread where the creators answered some questions about the program and why they made certain decisions (posts from thread below).

Highly recommend since it'll answer a lot of doubts you may have about it. I really do believe it's probably the most effective way to learn math today.

" '[Question 2] It's hard to believe that 5 hours a week for a year starting from basic multiplication tables (found on your homepage) will have me completely prepared for higher-level university courses. I'd prefer an explanation…

Inspired by MathAcademy, I'm developing:

1) a note-taking workflow in Obsidian (you take bite-sized notes about a topic, then connect "prerequisite" notes in Obsidian's canvas editor)

2) a tool that uploads each note and graph data to a database

3) a webapp that presents those notes algorithmically using spaced repetition. This enables you to allow others to "traverse" your note graph in a guided and self-paced manner.

You can add "challenge presets" to each note so that your mastery of each piece of knowledge can be tested with simple flashcards, multiple choice, free response, or some visual/actionable task to force active recall. An algorithm uses your success rate and spaced repetition data to introduce & drill more advanced notes into your long term memory.

Here's some more reading I was inspired by:

https://www.mathacademy.com/pedagogy

https://www.justinmath.com/individualized-spaced-repetition-in-hierarchical-knowledge-structures/

Even if there are a lot of imperfections and flaws about this project (like the sheer difficulty of curating a good knowledge graph to begin with), I'm hoping to make my note-taking in Obsidian more structured and thorough, replace my Anki routine, and make any of my notes into an automated + algorithmic course. If someone has another similar project (combining note-taking with hierarchal, topological knowledge graphs with spaced repetition and testing all in one platform) I would love to hear more about your approaches. Quick…

I'm doing the same kind of thing for my college classes no matter the subject. But mine is a little different. Instead I do:

1. Feed lecture slides, labs, homework into ChatGPT and have it generate flashcards.

2. Write these flashcards into Anki and study them using Anki.

3. Run through some practice problems

I had originally intended for this system to be used long-term, but I get irresponsible and study the day of the exam. It really depends on the material, but for the most part, it takes around 5–7 hours of studying and preparation to feel completely confident about the exam. Often times, I wake up super early on the exam day to give me some time. This is not ideal of course and is just a product of my bad habits.

It's definitely doable to ace exams with only 2–3 of studying, but usually I need to pad it with another 2–3 hours of preparation like creating high quality flash cards and stuff. I believe most people can adopt this system and perform very well, but at the same time it's a very radical departure from traditional study practices and even then I'm not even using this system in the way it's actually intended (not the day of cramming-style method).

This system is not something I made up, but rather backed from a collective community effort that has produced amazing techniques, guides, research, etc.:

https://isaak.net/mandarinmethods/ - in depth guide detailing best practices with Anki regarding language learning (THE…

> less of the ... repetitive manual arithmetic exercises

I think this post (from a math academy employee) has a good argument for why these sorts of exercises are important. It's about basic arithmetic, but I think it applies to tedious things like performing gaussian elimination on small matrices as well.

https://www.justinmath.com/if-you-want-to-learn-algebra-you-need-to-have-automaticity-on-basic-arithmetic/

I like to come at it from both angles - higher level with useful applications, and then lower level "I could maybe implement this if I had to" exercises. The latter are tedious, and hard to motivate effort for without the former. Ultimately, as the post argues, I agree that if you don't understand the lower level (tedious) operations, you will only get so far in your ability to apply LA.

I am halfway through an online degree in ICT. We had a Instructional Design course that went over the differences. There is a textbook that has a chapter on it called Trends in Instructional Design but it is pricey. My position is adult learning works better online to reorganize cognitive schemas but children benefit from social learning theory. It is something like 1-5% complete MOOCs, they really need some kind of personal feedback. But generative AI may change this too. Look at Math Academy for example (Skycak has a book about it) (and they don't use gen AI for the tutoring either). https://www.justinmath.com/books/