Ultralearning, the new book by Scott Young, comes out in August. Last week, I briefly covered some key ideas from the book, including the ultralearning philosophy and the nine principles of ultralearning. But ultralearning is about projects, so this week I’d like to explore how you could use the ideas in the book to optimize a mathematics learning project.
What is the most effective way to learn a skill or topic? Scott Young believes that the way to answer that question is to design a learning project, experiment with multiple techniques, and report on the results. For the past thirteen years, he has been doing that on his blog and in his online classes. Later this year, his book Ultralearning will be released, with advice for those of us who want to succeed at similar projects.
To learn effectively, it’s more important to have good study habits than good study skills. Study skills include activities like taking notes, reading with comprehension, and preparing for exams. Study habits cover topics like time management, focus, and prioritization. Skills and habits are both important. But even with the best skills, it’s hard to overcome poor habits. You can be a champion speed reader with the ability to write every word of a lecture in real-time. But if you start studying an hour before an exam and have YouTube videos blaring in the background, you won’t get great results. In contrast, if you consistently plan what you need to get done in the coming week, follow your schedule diligently, and cultivate the ability to concentrate exclusively on the task at hand, you will succeed even without fancy study techniques.
Good study habits don’t happen on their own, especially given the incentives of the online attention economy. You have to develop them. For a practical habit handbook, it’s hard to do better than James Clear’s Atomic Habits. This week, I’ll cover a summary of key ideas in the book. Next week, I’ll suggest ways to apply these lessons to studying technical subjects.
Learning math is often about learning specific math topics. But it can also be useful to step back and take a higher-level view of math learning. Keith Devlin, professor of mathematics at Stanford University and creator of the popular Introduction to Mathematical Thinking course on Coursera, says modern students of math have to master two types of thinking:
- In K-12, the goal is to develop strong number sense.
- In college, those who continue their studies in STEM need to learn mathematical thinking.
Back in the day, textbooks and classes were the way to learn math. Today, we have abundant online options. I wrote earlier this year about the benefits of practicing on Khan Academy, even if you’re not in its target audience. A similar online offering is Brilliant, which like Khan Academy has online math problems, but which uses a different philosophy of learning.
I’m working this year on a specific area of math, but it can also be helpful to browse around and see what math ideas are out there. Last week, I wrote about the kinds of answers that pop up on Quora’s general math topic. Another math destination is Mathematics Stack Exchange. That site works a bit differently.
If you’re studying a high school or undergraduate college math topic and you have a question, the answer is probably somewhere online. Finding it is just a matter of coming up with the right search terms. Or if searching doesn’t work out, you can always ask on Quora. But another way to use Quora is for an overview of what math concepts are available to study.
Math problems on standardized tests have short, simple answers that fit in a multiple-choice format. But college-level math problems require more detailed explanations. In How to Write a Math Solution, Richard Rusczyk and Mathew Crawford of Art of Problem Solving present a detailed checklist for ensuring that your proofs and solutions communicate your thinking as clearly as possible. Here’s some advice from the article that I found especially useful.