External Links
These are external resources I've found to be very helpful on my personal MetaCog9 journey. I hope you will, too!
Click on the images to go to each resource's webpage.
3Blue1Brown
Upon graduating from Stanford, Grant Sanderson started the 3B1B project using a Python-based visualization program of his own design to illustrate mathematical concepts in some of the most beautiful ways I have ever seen. Very little emphasis is placed on the gritty parts of math (e.g., working through dozens of practice problems), but rather his approach is to help you see – easily, obviously—the logic of mathematical reasoning. While a lot of the content deals with very high-level mathematics, he has excellent content on geometry, calculus, and probability that is very suited for middle- and high-schoolers.
Better Explained
Kalid Azad’s most recent project is a pedagogic inspiration and an academic delight. His tagline is “Learn right, not rote,” and emphasizes a highly intuition-based understanding of mathematical concepts that works from the feel of the math to the language of mathematical notation. His signature ADEPT method (Analogy, Diagram, Example, Plain English, Technical Language) teaching structure should be taught to every practicing or aspiring teacher, and for thorny and intractable concepts, his content is simply peerless.
Organic Chemistry Tutor
Nothing fancy here, which is part of the reason I like it so much. This channel features simple, easy-to-follow worked examples (lots of them), on virtually every topic of math the average person will ever encounter. For the nuts-and-bolts how-to of working problems, this channel is indispensable.
.jpg)
Brilliant
A freemium-model app and website, Brilliant is an excellent addition to any math-learning toolbox. In general, I view this as a supplementary resource, not a primary instructional device. The gamified, self-quizzing, puzzle-based approach almost strikes me as an extension (or retention) tool – once you’ve got the mechanics of a subject, this app helps you connect dots, go deeper, and see application in terms of science and engineering.
Khan Academy
A classic, I don’t always find Khan’s videos to be the most helpful in terms of illustrating concepts or performing exercise (pretty annoying, especially with the more constructive questions, as it requires manually clicking your way through tedious online equation-builders). Still, two absolutely essential components of learning are made available through this project: 1) tons of practice, including requirements of certain scores or sequences of correct answers to proceed (ensuring no one is skipping through with a foggy understanding), and 2) immediate feedback. I’ve discussed the importance of immediate feedback previously, but K.A. automatically informs you when you’ve missed a question, and helps to reinforce flow when you get one right. Learn more at my post, “An Open Letter to Khan Academy.”
.png)
LessWrong
An online, decentralized community dedicated to rationality, logic, learning, economics, computer science, statistics, and other tools for getting things wrong a bit less frequently…
Duolingo
Duolingo: The meteoric rise and ongoing monopolization of the language-learning industry is justly conferred. Duolingo is the essence of effective education: bite-sized bits, daily goals, progress data-monitoring, tailored skill levels determined by placement testing, immediate feedback, streak challenges, other incentives, spaced repetition – Duo has it all. If only we had a Duo-numero…
Jazon Jiao
Jazon Jiao uses 3Blue1Brown-style animations to explain concepts in linear algebra and regression.
.jpg)
Automate the Boring Stuff
Al Sweigart offers his step-by-step guides to help you learn to automate using Python -- all for free!
.jpg)