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A limit problem conjured up from the depths of hell.
Aug 22, 2024
Hi All. I have been doing daily notes in my own weird format for over six months now, but each time I try and sit down and make a weekly template (or monthly) I always get stuck trying to work out what to aggregate and h…
Aug 21, 2024
If any student, anywhere, is looking for advice on how to prepare for a standardized math test, then this is everything I’d tell them.
Aug 18, 2024
It’s the tragedy of the commons.
Aug 17, 2024
A comment to page 165 of Jo Boaler’s new book Math-ish
Aug 14, 2024
Aug 12, 2024
Aug 10, 2024
1) Foundational math. 2) Classical machine learning. 3) Deep learning. 4) Cutting-edge machine learning.
Aug 8, 2024
You gotta develop automaticity on low-level skills in order to free up mental resources for higher-level thinking!
Aug 7, 2024
… is to not overwhelm them. In my experience, students naturally enjoy math when it doesn’t feel overwhelmingly difficult to learn.
Aug 6, 2024
Curiosity/interest motivates people to engage in deliberate practice, which is what builds ability.
Aug 5, 2024
Bloom studied the training backgrounds of 120 world-class talented individuals across 6 talent domains: piano, sculpting, swimming, tennis, math, & neurology, and what he discovered was that talent development occurs through a similar general process, no matter what talent domain. In other words, there is a “formula” for developing talent – though executing it is a lot harder than simply understanding it.
Aug 5, 2024
It can be helpful to take a top-down approach in planning out your overarching learning goals, but the learning itself has to occur bottom-up.
Aug 5, 2024
Each decomposition produces a system of linear equations where the number of unknowns equals the number of equations.
Aug 5, 2024
Effective explicit instruction is all about clarity, and breaking down information, and minimizing the load on working memory.
Aug 4, 2024
1) The information must have already been written to memory. 2) The information must be retrieved from memory, unassisted.
Aug 2, 2024
Aug 1, 2024
Nobody who knows the science of learning is actually debating this.
Jul 31, 2024
I think optimal motivation requires a balance of both intrinsic and extrinsic factors.
Jul 31, 2024
The amount of practice should be determined on the basis of each student’s individual performance on each individual topic. Some students may end up having to do more work, but this ultimately empowers them to learn and continue learning into the future.
Jul 30, 2024
Jul 30, 2024
Jul 30, 2024
Jul 29, 2024
Jul 29, 2024
I can think of 4 possible sources.
Jul 28, 2024
There is an asymmetric tradeoff between 1) blowing your working memory capacity and leaving yourself unable to make progress, versus 2) wasting a couple extra seconds writing down a bit more work than you need to. When in doubt, write it out.
Jul 28, 2024
Write code that makes complicated decisions, often involving some kind of inference.
Jul 27, 2024
Here’s a trick to feel amazingly capable and confident: periodically look back at stuff you originally found challenging months ago.
Jul 27, 2024
Greatness emerges from a virtuous cycle of hard work and luck compounding on each other.
Jul 26, 2024
Around 50-60 XP/day, that is, 50-60 minutes of serious practice per day. Just like the high-end amount of daily exercise you’d expect from people who keep a consistent exercise routine at the gym.
Jul 26, 2024
With the science of learning, it’s less about “keeping up” with what’s happening, and more about “catching up” with what’s already happened.
Jul 24, 2024
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