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Most people can tell when their practice is too easy, but what about when your tasks are too hard? That’s often less obvious.
Jul 23, 2024
Accumulating mathematical knowledge gaps can lead students to reach a tipping point where further learning becomes overwhelming, ultimately causing them to abandon math entirely.
Jul 22, 2024
When you’re knowledgeable/skilled enough to grapple with problems in a more directly applicable field, math gives you the superpower of being able to compress those problem representations into an abstract space where they’re easier to solve.
Jul 20, 2024
You haven’t learned unless you’re able to consistently reproduce the information you consumed and use it to solve problems.
Jul 16, 2024
The only way to argue against the existence of learning loss and grade inflation is to argue against the very idea of measuring learning objectively (i.e., radical constructivism).
Jul 16, 2024
A silly bug turned genius hack.
Jul 16, 2024
The hard truth is that if you want to build a serious educational product, you can’t be afraid to charge money for it. You can’t back yourself into a corner where you depend on a massive userbase. Why? Because most people are not serious about learning, and if you depend on a massive base of unserious learners, then you have to employ ineffective learning strategies that do not repel unserious students. Which makes your product suck.
Jul 15, 2024
834 XP = 834 minutes = 14 hours of work in a single day. You’re probably wondering, what kind of person does that much math in a day? Time for a little story.
Jul 14, 2024
When students are not given the opportunity to learn math seriously, and are instead presented with watered-down courses and told that they’re doing a great job, they’re being set up for failure later in life when it matters most.
Jul 14, 2024
The underlying principle that it all boils down to is deliberate practice.
Jul 14, 2024
Jul 14, 2024
First, you need extensive and solid content knowledge. Then, you need to work through tons of practice exams for the specific exam you’re taking. This might sound simple, but every year, countless people manage to screw it up.
Jul 13, 2024
Research mathematicians are like professional athletes.
Jul 13, 2024
Math gets hard for different students at different levels. If you don’t have worked examples to help carry you through once math becomes hard for you, then every problem basically blows up into a “research project” for you. Sometimes people advocate for unguided struggle as a way to improve general problem-solving ability, but this idea lacks empirical support. Worked examples won’t prevent you from developing deep understanding (actually, it’s the opposite: worked examples can help you quickly layer on more skills, which forces a structural integrity in the lower levels of your knowledge). Even if you decide against using worked examples for now, continually re-evaluate to make sure you’re getting enough productive training volume.
Jul 13, 2024
“…[D]eliberate practice requires effort and is not inherently enjoyable. Individuals are motivated to practice because practice improves performance.”
Jul 12, 2024
Long-term learning is represented by the creation of strategic electrical wiring between neurons.
Jul 11, 2024
Research indicates the best way to improve your problem-solving ability in any domain is simply by acquiring more foundational skills in that domain. The way you increase your ability to make mental leaps is not actually by jumping farther, but rather, by building bridges that reduce the distance you need to jump. Yet, higher math textbooks & courses seem to focus on trying to train jumping distance instead of bridge-building.
Jul 8, 2024
Many educators think that the makeup of every year in a student’s education should be balanced the same way across Bloom’s taxonomy, whereas Bloom’s 3-stage talent development process suggests that the time allocation should change drastically as a student progresses through their education.
Jul 8, 2024
Learning math with little computation is like learning basketball with little practice on dribbling & ball handling techniques.
Jul 8, 2024
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.
Jul 7, 2024
There are many, many studies that measure variation in WMC vs variation in other metrics.
Jul 6, 2024
Challenge problems are not a good use of time until you’ve developed the foundational skills that are necessary to grapple with these problems in a productive and timely fashion.
Jul 5, 2024
If you start to flail (or, more subtly, doubt yourself and lose interest) after jumping into ML without a baseline level of foundational knowledge, then you need to put your ego aside and re-allocate your time into shoring up your foundations.
Jul 5, 2024
If you understand the interplay between working memory and long-term memory, then then you can actually derive – from first principles – the methods of effective teaching.
Jul 4, 2024
Hard-coding explanations feels tedious, takes a lot of work, and isn’t “sexy” like an AI that generates responses from scratch – but at least it’s not a pipe dream. It’s a practical solution that lets you move on to other components of the AI that are just as important.
Jun 28, 2024
Systems want to grow and grow, but without pruning, they collapse. Slowly, then spectacularly.
Jun 28, 2024
… and they should be treated as such.
Jun 27, 2024
Our AI expert system is one of those things that sounds intuitive enough at a high level, but if you start trying to implement it yourself, you quickly run into a mountain of complexity, numerous edge cases, lots of counterintuitive low-level phenomena that take a while to fully wrap your head around.
Jun 26, 2024
Jun 25, 2024
An idea for a paper that I don’t currently have the bandwidth to write.
Jun 15, 2024
If all the knowledge you show up with is high school math and AP Calculus, and you’re not a genius, then there’s a substantial likelihood you’re going to get your ass handed to you.
Jun 9, 2024
Download NeoServer: SSH Client|Terminal by Space-Time Transformation Technology Co., Ltd. on the App Store. See screenshots, ratings and reviews, user tips, and…
Jun 4, 2024
When you’re developing skills at peak efficiency, you are maximizing the difficulty of your training tasks subject to the constraint that you end up successfully overcoming those difficulties in a timely manner.
Jun 3, 2024
Students eat meals of information at similar bite rates when each spoonful fed to them is sized appropriately relative to the size of their mouth. (Note that equal bite rates does not imply equal rates of food volume intake.)
Jun 1, 2024
It’s the act of successfully retrieving fuzzy memory, not clear memory, that extends the memory duration.
May 23, 2024
To transfer information into long-term memory, you need to practice retrieving it without assistance.
May 22, 2024
There’s a cognitive principle behind this: associative interference, the phenomenon that conceptually related pieces of knowledge can interfere with each other’s recall.
May 21, 2024
It’s actually the opposite – to get students actively retrieving information from memory, while minimizing their cognitive load.
May 19, 2024
Learning is the incremental gain in your ability to perform a tangible, reproducible skill.
May 19, 2024
Perform the desired transformation on identity matrix to get a left-multiplier, and maybe transpose the output.
May 14, 2024
There are numerous cognitive learning strategies that 1) can be used to massively improve learning, 2) have been reproduced so many times they might as well be laws of physics, and 3) connect all the way down to the mechanics of what’s going on in the brain.
May 11, 2024
To love someone is to give them the freedom to become themselves, because they know you will be there if they fall.
May 9, 2024
Solving equations feels smooth when basic arithmetic is automatic – it’s like moving puzzle pieces around, and you just need to identify how they fit together. But without automaticity on basic arithmetic, each puzzle piece is a heavy weight. You struggle to move them at all, much less figure out where they’re supposed to go.
May 1, 2024
First, fun and exciting playtime. Then, intense and strenuous skill development. Finally, developing one’s individual style while pushing the boundaries of the field.
Apr 30, 2024
It highlights the aversion that people have to doing hard things. People will do unbelievable mental gymnastics to convince themselves that doing an easy, enjoyable thing that is unrelated to their supposed goal somehow moves the needle more than doing a hard, unpleasant thing that is directly related to said goal.
Apr 17, 2024
In general, when you feel yourself running up against a ceiling in life, the solution is typically to pivot and into a direction where the ceiling is higher.
Mar 22, 2024
Loosely inspired by the German tank problem: several witnesses reported seeing a UFO during the given time intervals, and you want to quantify your certainty regarding when the UFO arrived and when it left.
Mar 15, 2024
But in talent development, the optimization problem is clear: an individual’s performance is to be maximized, so the methods used during practice are those that most efficiently convert effort into performance improvements.
Mar 4, 2024
No matter what skill is being trained, improving performance is always an effortful process.
Mar 3, 2024
By periodically revisiting content, a spiral curriculum periodically restores forgotten knowledge and leverages the spacing effect to slow the decay of that knowledge. Spaced repetition takes this line of thought to its fullest extent by fully optimizing the review process.
Mar 2, 2024