3 ms·

Memorizing equations is "religion" not "math". "Understanding" is "math".

freeflight 8y ago
I wish more math teachers would actually understand this. The amount of crap I got for using the "wrong way" to calculate something in math class, was probably one of the major reason I never really got into it. I remember math classes in the beginning actually being fun, I loved figuring out more convenient/to me more logical ways to calculate something, only to be constantly shut down by the teachers for using them, as he/she demanded I use the solution given by the book. I do understand the value of getting to the same solution in different ways, I even did back then, but teachers didn't frame it like that; their insistence on the book solution just felt like an accusation against me of not understanding, telling me my way of calculating is wrong (even tho they usually proof calculated right) when to me it looked like it was them not understanding, by insisting on that one formalized, and often awkward, solution, and only that. So as a somewhat rebellious character, it didn't take long for me to start actually despising math classes. If I could go back I'd probably try to do it differently, I'm in my mid-30's now and consider myself "math illiterate". Sure I can do most basic stuff and even the occasional Pythagorean theorem (which fascinates me to this day, take two knowns to figure out the third unknown!), but I still feel like I missed out on something I could probably really have enjoyed.
- lagadu 8y ago
  Easiest way of visualising the pythagorean theorem is to think about it the way it was initially written: think about areas formed by tree squares. This image[0] from wikipedia shows it all: the area of square a plus the area of square b equals the area of square c. It's just really convenient that we can use that to calculate triangle sides without resorting to trigonometry. [0] https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/260px-Pythagorean.svg.png https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Py...
  - caseymarquis 8y ago
    I find that that's a terrible way of visualising the theorum, as it offers no indication of why the theorem is true. I much prefer the below picture: https://www.mathalino.com/sites/default/files/images/01-pythagora.jpg https://www.mathalino.com/sites/default/files/images/01-pyth... It could be improved by putting -(ab/2) inside the triangles, but I'm on mobile, so making something is out of the question.
- ibeckermayer 8y ago
  I consider this a tragic story. It sounds like you have the type of genuine curiosity and will to understand (not just get the answer) that would make you a really good math student, but your dopey teachers--who probably don't have your natural disposition towards math--beat it out of you.
lloeki 8y ago
I happen to like a little metaphor of mine; Math is like cooking: either you blindly follow a recipe (rote "learning") or you truly learn how ingredients combine together (from discovering, to understanding, to — ultimately — grokking).

I wish more math teachers would actually understand this. The amount of crap I got for using the "wrong way" to calculate something in math class, was probably one of the major reason I never really got into it. I remember math classes in the beginning actually being fun, I loved figuring out more convenient/to me more logical ways to calculate something, only to be constantly shut down by the teachers for using them, as he/she demanded I use the solution given by the book. I do understand the value of getting to the same solution in different ways, I even did back then, but teachers didn't frame it like that; their insistence on the book solution just felt like an accusation against me of not understanding, telling me my way of calculating is wrong (even tho they usually proof calculated right) when to me it looked like it was them not understanding, by insisting on that one formalized, and often awkward, solution, and only that. So as a somewhat rebellious character, it didn't take long for me to start actually despising math classes. If I could go back I'd probably try to do it differently, I'm in my mid-30's now and consider myself "math illiterate". Sure I can do most basic stuff and even the occasional Pythagorean theorem (which fascinates me to this day, take two knowns to figure out the third unknown!), but I still feel like I missed out on something I could probably really have enjoyed.

lagadu 8y ago
Easiest way of visualising the pythagorean theorem is to think about it the way it was initially written: think about areas formed by tree squares. This image[0] from wikipedia shows it all: the area of square a plus the area of square b equals the area of square c. It's just really convenient that we can use that to calculate triangle sides without resorting to trigonometry. [0] https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/260px-Pythagorean.svg.png https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Py...
- caseymarquis 8y ago
  I find that that's a terrible way of visualising the theorum, as it offers no indication of why the theorem is true. I much prefer the below picture: https://www.mathalino.com/sites/default/files/images/01-pythagora.jpg https://www.mathalino.com/sites/default/files/images/01-pyth... It could be improved by putting -(ab/2) inside the triangles, but I'm on mobile, so making something is out of the question.
ibeckermayer 8y ago
I consider this a tragic story. It sounds like you have the type of genuine curiosity and will to understand (not just get the answer) that would make you a really good math student, but your dopey teachers--who probably don't have your natural disposition towards math--beat it out of you.

lloeki 8y ago

I happen to like a little metaphor of mine; Math is like cooking: either you blindly follow a recipe (rote "learning") or you truly learn how ingredients combine together (from discovering, to understanding, to — ultimately — grokking).