Each topic area contains courses (e.g., Number Theory Logic). Since my topic this year is discrete math, let’s consider Brilliant’s number theory course.īrilliant divides its content into top-level topic areas (Math Science Computer Science).
Instead, they have a small section of text and images, followed by a short multiple-choice problem, followed by a more detailed explanation once the students submits an answer. But unlike the text and images found in textbooks, the ones on Brilliant don’t have large sections of prose and math interspersed with examples. To explain math concepts, Brilliant relies on text and images rather than videos. Brilliant tries to address this using a different approach to problems. Besides being inaccurate, this is problematic for a couple of reasons: It’s difficult to remember procedures, and procedures probably won’t help when you’re trying to solve more conceptual problems, like proofs. Problems solidify the concepts in your mind and verify that you understand the main ideas and edge cases.īut despite the benefits of this approach, it has one major drawback: by focusing on learning a process and matching it with a problem type, students risk learning math as just a collection of procedures. As much as you might think you understand properties of exponents (for example), you don’t know for sure how well you know them until you have solved a lot of problems. To practice it, you need problems and solutions.
The best way to learn math is by practicing it. There is much to be said for the traditional approach as interpreted by Khan Academy. But Khan Academy offered two innovations: rather than a live instructor, give students recorded videos they can watch at home as many times as they need to and rather than a fixed problem set that’s the same for every student, keep giving students problems of the same type until they demonstrate mastery of a concept. The Khan Academy system mirrors the traditional American primary and secondary school approach to math instruction: teach students a process for each problem type, then have them practice using that process to solve problems. A similar online offering is Brilliant, which like Khan Academy has online math problems, but which uses a different philosophy of learning.
I wrote earlier this year about the benefits of practicing on Khan Academy, even if you’re not in its target audience. Back in the day, textbooks and classes were the way to learn math.
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