Resources

NEW! Hard Problems DVD
A documentary about the 2006 US IMO team. Features many current and past AoPS members!
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Learning Through Teaching
by Richard Rusczyk

Most people are familiar with learning through books or in classes or from teachers and peers, but many overlook perhaps the most thorough learning experience – teaching. The best test of whether or not you really understand a concept is trying to teach it to someone else. Teaching calls for complete understanding of the concept. You can’t just 'kind of get it' or know it just well enough to get by on a test; teaching calls for complete understanding of the concept.

  • How do you know that?
  • When would you use that?
  • How could you come up with that in the first place?

If you can’t answer these questions for something you ‘know’, then you can’t teach it. You can’t teach it because you don’t really ‘know’ it after all. When learning, we can fool ourselves into believing we have a complete grasp of an idea before we really understand it. If we can do a couple problems, we think we’re set; however, we might have only seen such easy problems that we didn’t hit the boundary of our understanding. Teaching removes this possibility of self-deceit. More accurately, your would-be students will remove it. They’ll ask the questions above, along with all sorts of ‘What ifs’ you won’t be able to handle without mastery of what you’re teaching. It’s being forced to grapple with these challenging questions, and figuring the answers out for yourself so you can explain them to others, that make teaching such a powerful tool for cementing your understanding of a subject.

Teaching also forces you to communicate your thoughts clearly and precisely. As our society becomes ever more interlocked and interdependent, cooperation becomes more and more important. This cooperation requires communication; however, being heard is not enough. You must also be understood. Your ideas will never be more effective than your ability to make others comprehend them. Teaching helps you develop the extremely important skill of describing your ideas well enough for others to use them.

Teach. It’s not just good for those you help; it’s good for you, too.

Try your hand at teaching others on our Forum.
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