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> We aren't taught about what it is our (sic) how it works My biggest frustration learning math when I was younger was not knowing -why- I was doing something

> We aren't taught about what it is our (sic) how it works My biggest frustration learning math when I was younger was not knowing -why- I was doing something a certain way or how it worked. It was incredibly discouraging because it didn’t just “click” like it seemed to with my peers.

westoncb 8y ago
I was the same way. I think the way we typically teach math (in the U.S. at least) to young people is particularly hard for those who insist on understanding rather than memorizing things. I was the same as how you describe yourself, and I always just assumed the kids who were best in the class were doing what I was trying to do also, but were much better at it. And then you see later how fragile/limited one's understanding is when taking the memorization approach—but as a kid you don't have many options.
joshvm 8y ago
There is a certain danger in trying to learn maths with this mindset though. A lot of topics seem intuitively easy, but the proofs only come somewhere near the end of a degree level course. It's a very healthy mindset to have, but it's a blessing and a curse. Some people are just very good at just abstracting away the details and getting on with things; what seems like "clicking" is not always the same as intuition. Probably it's good to operate in both modes. It's a really really useful skill to know when you need to care about the internals and when you can safely ignore them.
- finaliteration 8y ago
  I’ve definitely learned that now after 10 years of development experience. But as a curious kid who didn’t just want to memorize and regurgitate it was quite a challenge. I’ve debated restarting mathematics all the way from basic algebra and geometry to see if I’d do any better these days.
  - ficklepickle 8y ago
    I noticed my high school math(s) teachers were very bad at explaining why and what we were doing. Arbitrary example: One teacher kept saying "f(x)" but couldn't explain what a function is. He just said "it's anything", then "don't worry about it". If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would have helped us grok. I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was.
    - diffeomorphism 8y ago
      > If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would have helped us grok. Helpful but not quite right and one of the common misconceptions students seem to carry over from high school. A function is something that takes inputs out of a set (its domain, e.g. people in this class) and gives you exactly one output with a prescribed data type (e.g. a date. The function than for instance being person -> birthdate). Neither numbers nor a formula are needed. > I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was. I think he probably could, but the syllabus said explicitly not discuss this ("too abstract") and there is time pressure. High school maths mostly is somewhat handwavy and stringing "definitions" together by examples. So you would mostly see lots of examples of functions and the "definition" of 'function' is then simply "things like that".
diffeomorphism 8y ago
https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament Schools tend to not teach mathematics but memorization, unmotivated formulas and computation. Mathematics as its own discipline is basically only "why and how", i.e. proofs.

westoncb 8y ago

I was the same way. I think the way we typically teach math (in the U.S. at least) to young people is particularly hard for those who insist on understanding rather than memorizing things. I was the same as how you describe yourself, and I always just assumed the kids who were best in the class were doing what I was trying to do also, but were much better at it. And then you see later how fragile/limited one's understanding is when taking the memorization approach—but as a kid you don't have many options.

joshvm 8y ago

There is a certain danger in trying to learn maths with this mindset though. A lot of topics seem intuitively easy, but the proofs only come somewhere near the end of a degree level course. It's a very healthy mindset to have, but it's a blessing and a curse. Some people are just very good at just abstracting away the details and getting on with things; what seems like "clicking" is not always the same as intuition. Probably it's good to operate in both modes. It's a really really useful skill to know when you need to care about the internals and when you can safely ignore them.

finaliteration 8y ago
I’ve definitely learned that now after 10 years of development experience. But as a curious kid who didn’t just want to memorize and regurgitate it was quite a challenge. I’ve debated restarting mathematics all the way from basic algebra and geometry to see if I’d do any better these days.
- ficklepickle 8y ago
  I noticed my high school math(s) teachers were very bad at explaining why and what we were doing. Arbitrary example: One teacher kept saying "f(x)" but couldn't explain what a function is. He just said "it's anything", then "don't worry about it". If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would have helped us grok. I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was.
  - diffeomorphism 8y ago
    > If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would have helped us grok. Helpful but not quite right and one of the common misconceptions students seem to carry over from high school. A function is something that takes inputs out of a set (its domain, e.g. people in this class) and gives you exactly one output with a prescribed data type (e.g. a date. The function than for instance being person -> birthdate). Neither numbers nor a formula are needed. > I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was. I think he probably could, but the syllabus said explicitly not discuss this ("too abstract") and there is time pressure. High school maths mostly is somewhat handwavy and stringing "definitions" together by examples. So you would mostly see lots of examples of functions and the "definition" of 'function' is then simply "things like that".

diffeomorphism 8y ago

https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament Schools tend to not teach mathematics but memorization, unmotivated formulas and computation. Mathematics as its own discipline is basically only "why and how", i.e. proofs.