5 ms·

The sad thing is that the cool stuff isn't even always complex. It's little things, like going through how the quadratic formula is derived instead of just tel

by Ntrails 11y ago

The sad thing is that the cool stuff isn't even always complex. It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules. But at the same time - I know I'd have/did enjoy that stuff but maybe 60% of my classes would have played up if a whole lesson was spent deriving and exploring concepts without rote learning. Being a maths teacher has to be pretty rough, especially given the number of students who are openly hostile to it as a subject. As an aside, I often think about my Religious Studies teacher who'd disparage topics like Maths as being irrelevant after school. We'd never use them she said. RS was vital to life success, Maths a pointless exercise. It still winds me up to remember.

deleted 11y ago
[deleted]
jacobolus 11y ago
To anyone else confused, apparently “played up” is a British colloquialism for “misbehaved”. :-)
fluxquanta 11y ago
>It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules. Once you get in the mindset of deriving equations, rote memorization becomes insanely difficult, at least in my opinion. During my last year as an undergrad majoring in physics I got a 4.0 in quantum mechanics, but very nearly failed introductory chemistry (which I was taking to fill a science distribution requirement at a liberal arts college), despite many of the chemistry concepts just being edge cases of applied quantum mechanics. There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. I understood the solution to the problem itself, but when the professor started giving me hints I had to admit in front of the whole class that my issue wasn't with the number theory proof -- it was with the multiplication table we learn as children.
- dingo_bat 11y ago
  >what 9 times 7 was Is there a reason you didn't whip out a calculator and do it there? Although I must say that I remember everything till 20x20 :P
  - fluxquanta 11y ago
    I was standing at the blackboard in front of the class. I've always been flaky on multiplication tables for some reason, and doing arithmetic in my head isn't my strongest suit. That said I excelled in math throughout high school and college. It just goes to show that elementary math really has no bearing on the type of mindset one may have for "more complex", logic based math and computation. Trust me -- since that experience of being humiliated in front of the best students in the math department at my college, I haven't forgotten what 9 times 7 is.
    - j2kun 11y ago
      Once in a graduate abstract algebra class (without being prompted) I interrupted the professor's lecture to remark that he had skipped the prime "15" in a list of primes he wrote on the board.
- JadeNB 11y ago
  > There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. If it's any consolation, the great mathematician Alexander Grothendieck (https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck), when asked to supply a prime number (at some point in a lecture)—and being puzzled by the idea of actually naming a specific prime number—famously thought for a while before suggesting 57. (https://en.wikipedia.org/wiki/57_%28number%29#In_mathematics https://en.wikipedia.org/wiki/57_%28number%29#In_mathematics)
- jimbokun 11y ago
  10 - 1 = 9 9 * 7 = (10 - 1) * 7 = 70 - 7 = 63 I often do little calculations like this when I forget multiplication table entries.
norswap 11y ago
Consider all the people who had the opposite experience though (I'm certainly not one of them however).
poshenloh 11y ago
I think that one main issue is that many people unfortunately equate math with routine calculations or rote memorization. I think it's valuable to communicate that actually math is the art of creative thinking. To do this, it helps to share some "gems", or examples with powerful "Aha" factors. Along these lines, I have a very fresh one: last week, I just had a very shocking (mathematical) realization while thinking about football: There is a way to instantly see the optimal running angle when evading an equal-speed defender in football: eyeball the line which runs through the midpoint between you and the defender, and see where it hits the edge of the field - run straight there. I was immediately floored by this observation, because it is so easy in retrospect that it should be common knowledge. Yet literally everybody I've told this to has said that it was new to them - mathematicians & people from the general public. I quickly threw together a video to share it across the community: https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1tML4A33u https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1... I think that by thinking of and packaging cool nuggets of "math" like this to share, we can help rebrand the image of math. :)
- wallflower 11y ago
  Very nice video. I like how you actually made it out to a football stadium to start the video. One suggestion if you want to make this more 'shareable': start with the 2d graphics and then transition to video shot using a drone. This will let you get overhead video illustrating the defender/attacker scenarios. If your stand-in extras can't run fast, just have them run in slow-mo and then speed it up in post. Please keep up the good work!

by Ntrails 11y ago

deleted 11y ago

[deleted]

jacobolus 11y ago

To anyone else confused, apparently “played up” is a British colloquialism for “misbehaved”. :-)

fluxquanta 11y ago

>It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules. Once you get in the mindset of deriving equations, rote memorization becomes insanely difficult, at least in my opinion. During my last year as an undergrad majoring in physics I got a 4.0 in quantum mechanics, but very nearly failed introductory chemistry (which I was taking to fill a science distribution requirement at a liberal arts college), despite many of the chemistry concepts just being edge cases of applied quantum mechanics. There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. I understood the solution to the problem itself, but when the professor started giving me hints I had to admit in front of the whole class that my issue wasn't with the number theory proof -- it was with the multiplication table we learn as children.

dingo_bat 11y ago
>what 9 times 7 was Is there a reason you didn't whip out a calculator and do it there? Although I must say that I remember everything till 20x20 :P
- fluxquanta 11y ago
  I was standing at the blackboard in front of the class. I've always been flaky on multiplication tables for some reason, and doing arithmetic in my head isn't my strongest suit. That said I excelled in math throughout high school and college. It just goes to show that elementary math really has no bearing on the type of mindset one may have for "more complex", logic based math and computation. Trust me -- since that experience of being humiliated in front of the best students in the math department at my college, I haven't forgotten what 9 times 7 is.
  - j2kun 11y ago
    Once in a graduate abstract algebra class (without being prompted) I interrupted the professor's lecture to remark that he had skipped the prime "15" in a list of primes he wrote on the board.
JadeNB 11y ago
> There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. If it's any consolation, the great mathematician Alexander Grothendieck (https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck), when asked to supply a prime number (at some point in a lecture)—and being puzzled by the idea of actually naming a specific prime number—famously thought for a while before suggesting 57. (https://en.wikipedia.org/wiki/57_%28number%29#In_mathematics https://en.wikipedia.org/wiki/57_%28number%29#In_mathematics)
jimbokun 11y ago
10 - 1 = 9 9 * 7 = (10 - 1) * 7 = 70 - 7 = 63 I often do little calculations like this when I forget multiplication table entries.

norswap 11y ago

Consider all the people who had the opposite experience though (I'm certainly not one of them however).

poshenloh 11y ago

I think that one main issue is that many people unfortunately equate math with routine calculations or rote memorization. I think it's valuable to communicate that actually math is the art of creative thinking. To do this, it helps to share some "gems", or examples with powerful "Aha" factors. Along these lines, I have a very fresh one: last week, I just had a very shocking (mathematical) realization while thinking about football: There is a way to instantly see the optimal running angle when evading an equal-speed defender in football: eyeball the line which runs through the midpoint between you and the defender, and see where it hits the edge of the field - run straight there. I was immediately floored by this observation, because it is so easy in retrospect that it should be common knowledge. Yet literally everybody I've told this to has said that it was new to them - mathematicians & people from the general public. I quickly threw together a video to share it across the community: https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1tML4A33u https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1... I think that by thinking of and packaging cool nuggets of "math" like this to share, we can help rebrand the image of math. :)

wallflower 11y ago
Very nice video. I like how you actually made it out to a football stadium to start the video. One suggestion if you want to make this more 'shareable': start with the 2d graphics and then transition to video shot using a drone. This will let you get overhead video illustrating the defender/attacker scenarios. If your stand-in extras can't run fast, just have them run in slow-mo and then speed it up in post. Please keep up the good work!