User:IssaRice/Mental representations in mathematics: Difference between revisions
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I think people don't talk enough about mental representations of objects in math, and I think it's horrible! | I think people don't talk enough about mental representations of objects in math, and I think it's horrible! | ||
Examples: | Examples: | ||
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* People are elitist or otherwise don't want to share "cheat codes" to make the subject easier for others. | * People are elitist or otherwise don't want to share "cheat codes" to make the subject easier for others. | ||
* I'm wrong about the value of mental representations being important to share. One argument could be like "to really learn math you have to struggle to make your own mental representations". | * I'm wrong about the value of mental representations being important to share. One argument could be like "to really learn math you have to struggle to make your own mental representations". | ||
==Related stuff== | |||
Other horrible things about mathematics culture: | |||
* People don't talk enough about their stream of consciousness when thinking about math. | |||
* Not enough "natural proofs" | |||
* people don't talk about how they actually find ideas | |||
Revision as of 05:48, 2 January 2019
I think people don't talk enough about mental representations of objects in math, and I think it's horrible!
Examples:
- rows of a matrix linearly independent vs rows of a matrix spans domain
- mental arithmetic -- actually, this is one place where i think there has been a lot of discussion...
- inf/sup stuff in analysis. I find this so much easier to think about when I draw a line segment and label points on the segment. But many books don't talk about this!
- sup/inf/liminf/limsup: Tao's piston analogy!
- computability: many things can be thought of "abstractly" as enumerations and indices, or more "concretely" as programs. Compare Boolos/Burgess/Jeffrey vs Sipser. But there isn't a book that bridges these mental representations!
Why don't people talk about this? Some things that could be happening:
- It happens in-person rather than in writing, so I don't have access to it.
- Mental representations are too personal. I don't buy this.
- People have low metacognition.
- People are elitist or otherwise don't want to share "cheat codes" to make the subject easier for others.
- I'm wrong about the value of mental representations being important to share. One argument could be like "to really learn math you have to struggle to make your own mental representations".
Related stuff
Other horrible things about mathematics culture:
- People don't talk enough about their stream of consciousness when thinking about math.
- Not enough "natural proofs"
- people don't talk about how they actually find ideas