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The strongest people lift weights heavy enough to make them feel weak.
Mar 1, 2024
There’s only so much fun you can have trying to follow another person’s footsteps to arrive at a known solution. There’s only so much confidence you can build from fighting against a problem that someone else has intentionally set up to be well-posed and elegantly solvable if you think about it the right way.
Feb 27, 2024
Humans are not the last level of life’s fractal pattern. The Earth itself is becoming a sentient organism, a new stage of life, a species that exists on a sc...
Feb 26, 2024
The network becomes book-smart in a particular area but not street-smart in general. The training procedure is like a series of exams on material within a tiny subject area (your data subspace). The network refines its knowledge in the subject area to maximize its performance on those exams, but it doesn’t refine its knowledge outside that subject area. And that leaves it gullible to adversarial examples using inputs outside the subject area.
Feb 25, 2024
While there is plenty of room for teachers to make better use of cognitive learning strategies in the classroom, teachers are victims of circumstance in a profession lacking effective accountability and incentive structures, and the end result is that students continue to receive mediocre educational experiences. Given a sufficient degree of accountability and incentives, there is no law of physics preventing a teacher from putting forth the work needed to deliver an optimal learning experience to a single student. However, in the absence of technology, it is impossible for a single human teacher to deliver an optimal learning experience to a classroom of many students with heterogeneous knowledge profiles, each of whom needs to work on different types of problems and receive immediate feedback on each of their attempts. This is why technology is necessary.
Feb 23, 2024
Gamification, integrating game-like elements into learning environments, proves effective in increasing student learning, engagement, and enjoyment.
Feb 22, 2024
The testing effect (or the retrieval practice effect) emphasizes that recalling information from memory, rather than repeated reading, enhances learning. It can be combined with spaced repetition to produce an even more potent learning technique known as spaced retrieval practice.
Feb 21, 2024
Interleaving (or mixed practice) involves spreading minimal effective doses of practice across various skills, in contrast to blocked practice, which involves extensive consecutive repetition of a single skill. Blocked practice can give a false sense of mastery and fluency because it allows students to settle into a robotic rhythm of mindlessly applying one type of solution to one type of problem. Interleaving, on the other hand, creates a “desirable difficulty” that promotes vastly superior retention and generalization, making it a more effective review strategy. But despite its proven efficacy, interleaving faces resistance in classrooms due to a preference for practice that feels easier and appears to produce immediate performance gains, even if those performance gains quickly vanish afterwards and do not carry over to test performance.
Feb 20, 2024
Imitating without analyzing produces a robot / ape who can’t think critically; analyzing without imitating produces a critic who can’t act on their own advice.
Feb 20, 2024
When reviews are spaced out or distributed over multiple sessions (as opposed to being crammed or massed into a single session), memory is not only restored, but also further consolidated into long-term storage, which slows its decay. This is known as the spacing effect. A profound consequence of the spacing effect is that the more reviews are completed (with appropriate spacing), the longer the memory will be retained, and the longer one can wait until the next review is needed. This observation gives rise to a systematic method for reviewing previously-learned material called spaced repetition (or distributed practice). A repetition is a successful review at the appropriate time.
Feb 18, 2024
Layering is the act of continually building on top of existing knowledge – that is, continually acquiring new knowledge that exercises prerequisite or component knowledge. This causes existing knowledge to become more ingrained, organized, and deeply understood, thereby increasing the structural integrity of a student’s knowledge base and making it easier to assimilate new knowledge.
Feb 17, 2024
Associative interference occurs when related knowledge interferes with recall. It is more likely to occur when highly related pieces of knowledge are learned simultaneously or in close succession. However, the effects of interference can be mitigated by teaching dissimilar concepts simultaneously and spacing out related pieces of knowledge over time.
Feb 16, 2024
Automaticity is the ability to perform low-level skills without conscious effort. Analogous to a basketball player effortlessly dribbling while strategizing, automaticity allows individuals to avoid spending limited cognitive resources on low-level tasks and instead devote those cognitive resources to higher-order reasoning. In this way, automaticity is the gateway to expertise, creativity, and general academic success. However, insufficient automaticity, particularly in basic skills, inflates the cognitive load of tasks, making it exceedingly difficult for students to learn and perform.
Feb 15, 2024
Different students have different working memory capacities. When the cognitive load of a learning task exceeds a student’s working memory capacity, the student experiences cognitive overload and is not able to complete the task.
Feb 14, 2024
Mastery learning is a strategy in which students demonstrate proficiency on prerequisites before advancing. While even loose approximations of mastery learning have been shown to produce massive gains in student learning, mastery learning faces limited adoption due to clashing with traditional teaching methods and placing increased demands on educators. True mastery learning at a fully granular level requires fully individualized instruction and is only attainable through one-on-one tutoring.
Feb 13, 2024
Deliberate practice is the most effective form of active learning. It consists of individualized training activities specially chosen to improve specific aspects of a student’s performance through repetition and successive refinement. It is mindful repetition at the edge of one’s ability, the opposite of mindless repetition within one’s repertoire. The amount of deliberate practice has been shown to be one of the most prominent underlying factors responsible for individual differences in performance across numerous fields, even among highly talented elite performers. Deliberate practice demands effort and intensity, and may be discomforting, but its long-term commitment compounds incremental improvements, leading to expertise.
Feb 12, 2024
Active learning leads to more neural activation than passive learning. Automaticity involves developing strategic neural connections that reduce the amount of effort that the brain has to expend to activate patterns of neurons.
Feb 11, 2024
During practice, the elite skaters were over 6 times more active than passive, while non-competitive skaters were nearly as passive as they were active.
Feb 10, 2024
If you want to build principled software, avoid becoming VCware. Stay user-supported. It is now possible for tiny teams to build principled software that mil...
Feb 10, 2024
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
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