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A startup spent months building a sophisticated lecture tool and raising over half a million dollars in investments – but after observing students in the lecture hall, they completely abandoned the product and called up their investors to return the money.
Feb 9, 2024
True active learning requires every individual student to be actively engaged on every piece of the material to be learned.
Feb 8, 2024
Six weeks of pure review and six official practice exams.
Feb 7, 2024
It’s easier to run into roadblocks, but also easier to maintain what you’ve learned.
Feb 6, 2024
Passive consumption. Lack of depth. Lack of rigorous assessments. Failing upwards. Lack of skill development.
Feb 5, 2024
Initial parameter range, data sampling range, severity of regularization.
Feb 4, 2024
It’s like going to the gym without a solid workout plan in place.
Feb 3, 2024
If you know your single-variable calculus, then it’s about 70 hours on Math Academy.
Feb 2, 2024
… is to present a problem where known simpler techniques fail.
Feb 1, 2024
My training has been scattered and fuzzy until recently. Here’s the whole story.
Jan 30, 2024
I’d start off with some introductory course that covers the very basics of coding in some language that is used by many professional programmers but where the syntax reads almost like plain English and lower-level details like memory management are abstracted away. Then, I’d jump right into building board games and strategic game-playing agents (so a human can play against the computer), starting with simple games (e.g. tic-tac-toe) and working upwards from there (maybe connect 4 next, then checkers, and so on).
Jan 28, 2024
Solving problems, building on top of what you’ve learned, reviewing what you’ve learned, and quality, quantity, and spacing of practice.
Jan 25, 2024
An oval () fits inside a rectangle [ ] with the same width and height.
Jan 21, 2024
If you do poorly in a math class, it doesn’t necessarily mean that you are incapable of learning that level of math. There are a number of reasons that could be the root cause of your struggle.
Jan 14, 2024
Not everybody can learn every level of math, but most people can learn the basics. In practice, however, few people actually reach their full mathematical potential because they get knocked off course early on by factors such as missing foundations, ineffective practice habits, inability or unwillingness to engage in additional practice, or lack of motivation.
Jan 14, 2024
Learning math early guards you against numerous academic risks, opens all kinds of doors to career opportunities, and allows you to enter those doors earlier in life (which in turn allows you to accomplish more over the course of your career).
Jan 13, 2024
Acceleration does not lead to adverse psychological consequences in capable students; rather, whether a student is ready for advanced mathematics depends solely on whether they have mastered the prerequisites. Acceleration does not imply shallowness of learning; rather, students undergoing acceleration generally learn – in a shorter time – as much as they would otherwise in a non-accelerated environment over a proportionally longer period of time. Accelerated students do not run out of courses to take and are often able to place out of college math courses even beyond what is tested on placement exams. Lastly, for students who have the potential to capitalize on it, acceleration is the greatest educational life hack: the resulting skills and opportunities can rocket students into some of the most interesting, meaningful, and lucrative careers, and the early start can lead to greater career success.
Jan 12, 2024
Effortful processes like testing, repetition, and computation are essential parts of effective learning, and competition is often helpful.
Jan 11, 2024
The most effective learning techniques require substantial cognitive effort from students and typically do not emulate what experts do in the professional workplace. Direct instruction is necessary to maximize student learning, whereas unguided instruction and group projects are typically very inefficient.
Jan 10, 2024
Different people generally have different working memory capacities and learn at different rates, but people do not actually learn better in their preferred “learning style.” Instead, different people need the same form of practice but in different amounts.
Jan 9, 2024
Students and teachers are often not aligned with the goal of maximizing learning, which means that in the absence of accountability and incentives, classrooms are pulled towards a state of mediocrity. Accountability and incentives are typically absent in education, which leads to a “tragedy of the commons” situation where students pass courses (often with high grades) despite severely lacking knowledge of the content.
Jan 8, 2024
In terms of improving educational outcomes, science is not where the bottleneck is. The bottleneck is in practice. The science of learning has advanced significantly over the past century, yet the practice of education has barely changed.
Jan 7, 2024
Cognition involves the flow of information through sensory, working, and long-term memory banks in the brain. Sensory memory temporarily holds raw data, working memory manipulates and organizes information, and long-term memory stores it indefinitely by creating strategic electrical wiring between neurons. Learning amounts to increasing the quantity, depth, retrievability, and generalizability of concepts and skills in a student’s long-term memory. Limited working memory capacity creates a bottleneck in the transfer of information into long-term memory, but cognitive learning strategies can be used to mitigate the effects of this bottleneck.
Jan 5, 2024
Talent development is not only different from schooling, but in many cases completely orthogonal to schooling.
Jan 3, 2024
Many students who pattern-match will tend to prefer solutions requiring fewer and simpler operations, especially if those solutions yield ballpark-reasonable results.
Jan 2, 2024
The average tutored student performed better than 98% of students in the traditional class.
Jan 2, 2024
Only optimists can create a great future. One day, I decided to become an optimist and life became much more fun.
Dec 30, 2023
The problem with most "cure procrastination" content on the Internet is that it falls into two useless, even dangerous, paths: 1. Why one procrastinates. Then content dives into circle jerk of shadow…
This is what AI chat will look like in 1yr. The days of text-in, text-out are over. AI apps will handle on-the-fly generation of custom UIs - microapps - that are best suited to help you with your t…
1) The reported learning rates are not actually as quantitatively similar as is suggested by the language used to describe them. 2) The learning rates are measured in a way that rests on a critical assumption that students learn nothing from the initial instruction preceding the practice problems – i.e., you can have one student who learns a lot more from the initial instruction and requires far fewer practice problems, and when you calculate their learning rate, it can come out the same as for a student who learns a lot less from the initial instruction and requires far more practice problems.
Nov 27, 2023
Is there a standard “order of operations” for parallel vs nested absolute value expressions, in the absence of clarifying notation?
Nov 10, 2023
Q: Draw a 10 x 10 square grid. How many squares are there in total? Not just 1 x 1 squares, but also 2 x 2 squares, 3 x 3 squares, and so on. A: The total number of square shapes is the total sum of square numbers 1 + 4 + 9 + 16 + … + 100.
Nov 9, 2023
As a child, you touched something hot, and it burned you. That pain gave you a piece of information: be careful touching hot things. Some knowledge can only ...
Nov 9, 2023
First, you want to form a habit. Second, you want to operate at peak productivity during your session. Third, you want to minimize the amount you forget between sessions.
Nov 1, 2023
Answer: It’s not very useful (not in practice, not in theory).
Oct 31, 2023
Quality software is like quality food from the farmer’s market. A jar of handmade organic jam is not the same as mass-produced corn syrup-laden jam from the ...
Oct 27, 2023
For many (but not all) students, the answer is yes. And for many of those students, automation can unlock life-changing educational outcomes.
Oct 26, 2023
As of 2023-10-15, tags still have a few remaining advantages. It has to do with quickly and simply pulling up results—and this is more pronounced with nested tags. So before the details, the advantages are: clickable s…
Oct 22, 2023
As you climb the levels of math, sources of educational friction conspire against you and eventually throw you off the train. And one of the first warning signs is when you stop understanding things at the core, and instead try to memorize special cases cookbook-style.
Oct 19, 2023
In general, you can manipulate total derivatives like fractions, but you can’t do the same with partial derivatives.
Oct 11, 2023
Why it’s common for students to pass courses despite severely lacking knowledge of the content.
Oct 10, 2023
Spaced repetition is complicated in hierarchical bodies of knowledge, like mathematics, because repetitions on advanced topics should “trickle down” to update the repetition schedules of simpler topics that are implicitly practiced (while being discounted appropriately since these repetitions are often too early to count for full credit towards the next repetition). However, I developed a model of Fractional Implicit Repetition (FIRe) that not only accounts for implicit “trickle-down” repetitions but also minimizes the number of reviews by choosing reviews whose implicit repetitions “knock out” other due reviews (like dominos), and calibrates the speed of the spaced repetition process to each individual student on each individual topic (student ability and topic difficulty are competing factors).
Oct 5, 2023
Won first place in a state-level competition by finding and exploiting a loophole in the points scoring logic.
Oct 1, 2023
Whenever I buy things I try to prioritize cost per use. Sometimes I consider other priorities such as cost per smile, cost per thrill, cost per externality, ...
Sep 30, 2023
Drawing –> Latex commands –> ChatGPT summary –> Google more info
Sep 28, 2023
Having a style collapses hundreds of future decisions into one, and gives you focus.
Sep 3, 2023
If you look at the kinds of math that most quantitative professionals use on a daily basis, competition math tricks don’t show up anywhere. But what does show up everywhere is university-level math subjects.
Sep 2, 2023
While some may view Feynman-style pedagogy as supporting inclusive learning for all students across varying levels of ability, Feynman himself acknowledged that his methods only worked for the top 10% of his students.
Sep 1, 2023
If you want to progress faster, write concise explanations. Explain ideas in simple terms, strongly and clearly, so that they can be rebutted, remixed, rewor...
Aug 20, 2023
There is a parasite, I see it everywhere. It consumes your health and wealth. It preys on ignorance and is easy to catch. It’s so common you may not even not...
Aug 13, 2023