All Annotations of How to Develop a Mindset for Math | BetterExplained[Preview]

saved by11 people, first byJoel Liu on 2007-11-27, last byBlake M on 2008-07-30

• Elegant, “a ha!” insights should be our focus, but we leave that for
  students to randomly stumble upon themselves. I hit an “a ha” moment after
  a hellish cram session in college; since then, I’ve wanted to find and share
  those epiphanies to spare others the same pain.
• • Factual knowledge is not understanding. Knowing “hammers drive nails” is not the same as the insight that any hard object (a rock, a wrench) can drive a nail.
  • Keep an open mind. Develop your intuition by allowing yourself to be a beginner again.

  A university professor went to visit a famous Zen master. While the master quietly served tea, the professor talked about Zen. The master poured the visitor’s cup to the brim, and then kept pouring. The professor watched the overflowing cup until he could no longer restrain himself. “It’s overfull! No more will go in!” the professor blurted. “You are like this cup,” the master replied, “How can I show you Zen unless you first empty your cup.”

  • Be creative. Look for strange relationships. Use diagrams. Use humor. Use analogies. Use mnemonics. Use anything that makes the ideas more vivid. Analogies aren’t perfect but help when struggling with the general idea.
  • Realize you can learn. We expect kids to learn algebra, trigonometry and calculus that would astound the ancient Greeks. And we should: we’re capable of learning so much, if explained correctly. Don’t give up until it makes sense or that mathematical gap will haunt you. Mental toughness is critical — we often give up
• Factual knowledge is not understanding.
• Math provides models; understand their relationships and apply them to real-world objects.