Better Explained

Topics: Math; Programming
Explanation Quality: Better
Medium: Text; Pictures
Type of Content: Educational

Better Explained is a blog whose motto is "Learn right, not rote." I stumbled across it one day while trying to get a better understanding of the number e. (If you want to know what e is, check out the article on it). My experience with e in school was that it was a number that showed up a lot with exponents and logarithms. No one really explained where it had come from. The article I found on Better Explained really helped me understand. It took the explanation one step at a time, using graphs to approach the idea that e is the base for continuous exponential growth.

The thing I like best about this blog is that it helps you get a sort of intuition. The writing style is friendly. The author, Kalid, uses words and pictures as well as math to help you get a sense of what he is explaining.

From the BetterExplained article on Bayes Theorem

The blog has about 61 articles talking about math, with the topics ranging in complexity from arithmetic to vector calculus. But all of them are readable, no matter what your level is. There is also a section on programming and web development. I haven't looked at this part much (I do want to learn more about computers, but that's a goal for next summer when I have more time). From what I have seen, the explanations look similar to those in the math section. There are also some articles with tips on doing some computer things like working with Ruby on Rails and debugging.

This blog is worth checking out if you have a specific topic you don't understand, or if you're bored and want to see a new way of looking at something.

ViHart

Topics: Math, Music
Explanation Quality: Good
Medium: Video
Type of Content: Recreational

ViHart is a self-proclaimed "mathemusician". She makes lots of short, fun videos discussing math and sometimes music. While these are in some sense "educational" they are not going to help you review something from math class. In fact, the set-up for many videos is the doodles you can make while bored in class.

This isn't to say they aren't a worthwhile watch. I love hexaflexagons - I have quite a collection floating around. ViHart shows more of the fun side of mathematics, which is something you don't get to see in school unless you're pretty lucky.

Khan Academy

Topics: Math, Science, Economics, Computer Science, Humanities
Explanation Quality: Better
Medium: Video, Practice Problems
Type of Content: Teaching Material

Many of you have probably already heard of Khan Academy. It is a website offering short videos and practice problems in a variety of subjects. It was originally created to help the creator tutor his cousin over the internet. The videos feature someone (in many it is the founder Sal) giving a short (under 20 minute) explanation while writing it out on the video screen.

There are videos in economics, math, history, and the sciences. There are only practice problems in chemistry and math, but the difficulty ranges from telling time to calculus. I find the practice problems very helpful. The videos are good too. He attempts to explain each thing in several ways, and does examples in the videos. I have one minor problem with them: I often watch videos to review something from class or to compile all the bits I have learned from different sources. So parts of the video are new things/things I didn't understand, and parts I already know. I end up not wanting to watch the parts I already understand, but I don't want to skip forward in case he mentions something else new. But as I said, this isn't really a big problem.

If you make an account, watching videos and doing problems earns you points and achievements which is a fun additional motivator. They also show stats of how much you have been working on skills or watching videos. Personally, I love things that chart my progress.

If you are a parent/teacher/helpful older sibling, you can monitor your child/student/younger sibling's progress. I have my little sister's account registered as a child account under mine so I can make sure she is still doing work over the summer. When I see that she hasn't done her tasks for the day (she is supposed to learn one skill of her choosing every day to make sure she is doing something educational with her time) I can then react appropriately. But don't worry, you don't need a coach or mentor to use this site. It is good for anyone who wants to learn something.

Brilliant

Topics: Math, Physics, Computer Science
Explanation Quality: Good
Medium: Problems, Text
Type of Content: Recreational, Practice Problems

Brilliant.org is one of my favorite math websites. It offers a a new set of problems every week in a variety of topics. Before you start doing problems in a certain topic, you do a few problems to determine your level. The site then places  you appropriately and you can get started with this week's problem set. You level up if you consistently do well.

What I like about it is that the problems are interesting. You don't immediately know how to go about solving something. I always end up with a few problems I can't figure out. At the end of the week, you can view solutions to all the problems. You can also offer your own solutions and help out others who didn't get it.

While the main section of the site has olympiad type problems, there is also a practice section where you can choose to work on specific techniques. It is helpful for reviewing topics from school. It also actually explains methods of solving the problems, instead of just throwing you in there. I personally don't use that section as much, because I have more fun with the main problem sets. There are also smaller weekly problem sets in physics and computer science. I expect the sections to expand in the near future but for now the bulk of the site is math.

So head on over and have some fun!