6 ms·

This is wonderful. I love when memes breed philosophy. We're teaching math wrong. It's as plain as day to me. Or rather we teach the wrong maths to the wrong st

This is wonderful. I love when memes breed philosophy. We're teaching math wrong. It's as plain as day to me. Or rather we teach the wrong maths to the wrong students. If Marcie can't find a useful application on day one of the "theory" she learns in school, what is the point? It's a 19th century curriculum for a 21st century world. Basic accounting and personal finance would probably serve most students better. As to the epistemological quandary, I always return to Geometry or Visual Mathematics. Consider the infinite ways of calculating the digits of PI. In "Playing Pool with PI", Galperin demonstrated an analog computer that could calculate the digits of PI using only the perfectly elastic collisions of two billiard balls on a pool table. It works for all integral base number systems, and can even be extended to irrational numbers. And recently Google Brain's Adam Brown made an equally stunning observation: Galperin's bouncing billiard balls look identical to the Grover Quantum Search algorithm! Playing Pool with |ψ⟩: from Bouncing Billiards to Quantum Search https://arxiv.org/abs/1912.02207 https://arxiv.org/abs/1912.02207

yeellow 6y ago
> If Marcie can't find a useful application on day one of the "theory" she learns in school, what is the point? It's a 19th century curriculum for a 21st century world. Basic accounting and personal finance would probably serve most students better. Sorry, but following this logic we will end up with a conclusion that almost no school knowledge is "useful". How useful is playing volleyball? Reading poetry? Painting? Studying history? Biology would be reduced to first aid and basic medicine. I have those discussions with my daughters who learn how to do long multiplication. How is it useful if even I who know how to do it would rather use a calculator on my mobile instead? We would reduce math to basic operations on a calculators, probably nothing more would be considered useful by the majority of the population. The same apply to all other subjects.
- unjurios 6y ago
  I think "application" is the wrong focus. The real thing to help students understand is this exact question: what is math? That remains a mystery to most students. It gets conflated with the problem of application, but I think the real problem is most educations don't make clear the idea of abstraction, symbol systems, and logic. When you don't understand something, especially why it might be useful or at least intrinsically interesting, it's hard to get motivated about it.
  - yeellow 6y ago
    But this exact question has no answer or has many different, contradictory answers as this discussion shows. I doubt that such discussion would be interesting for someone who struggles with algebra. Moreover the same questions could be asked about all subjects. The point of the school is to show kids different things even if they cannot see their usefulness right away. One person will enjoy math, other poetry or history. But all will have a chance to try different things and to choose what to study deeper. Of course it's nice to give some motivation and her teachers failed if she cannot see applications of basic algebra.
    - unjurious 6y ago
      I responded to the comment above with some examples of the kind of thing I'm hoping for. I don't think a deep philosophical discussion about math is necessary. Just reinforce the idea that math is a symbol system for dealing with questions of shape, quantity, and logic, and give multiple examples of applications of the same concept. Also convert between symbols and diagrams/drawings frequently (for example, I'm willing to bet an absurd number of Americans can't understand how a virus spreads exponentially; if you draw a pyramid of infected people, I bet they'd get it immediately; but instead we use curves and lines that don't connect with people).
unjurios 6y ago
Personal anecdote: I never understood what math "was," and this totally demotivated me to study it. I got A's all the way through high school mathematics because I was a systematic and logical thinker who had no problem following rules or algorithms, but I never once saw the point. When I reached college, I had already tested out of Calculus and never took a formal math course again. Fast-forward ten years. I am a self-taught programmer and now find mathematics absolutely fascinating and beautiful, and I see its applications. So I'm taking math classes on Udemy, buying hundreds of dollars of textbooks, and trying to teach myself. I can't help feeling like I got a little robbed. I understand that teaching is hard, and some kids just don't care to learn certain things and it's best for them and society to force some absolute fundamentals down their throats. But at a certain point around middle or high school, I think there needs to be a hard pivot to focusing on motivating students. If you do that well, they will have the ability to teach themselves and learn for the rest of their lives. If you don't they either end up like me, playing catch up a decade too late, or they just leave entire fields of knowledge untapped forever. With some subjects that's inevitable and probably ok, but math doesn't seem like it should be one of those subjects.
- abhishekjha 6y ago
  Which courses/books are you buying? I am on a similar path and would like to know more.
- yeellow 6y ago
  What do you think would convince you in the high school that math was important and worth studying?
  - unjurious 6y ago
    I think three things would have done it: 1. A clear explanation of a symbol system and how math is a symbol system to deal with issues of quantity, shape, structure, and logic. 2. Frequently converting between diagrams/drawings and symbols (show "x x x" at times and "3" at other times). I actually have a concept for a game I want to program that does this. 3. Showing multiple concrete applications of different ideas, and lots of word problems. In retrospect I think this was always reversed in the American system. We would learn the symbolic and algorithmic aspects of a math concept, then use it to solve some word problems. Once I went back and started teaching myself some of this stuff, I read that the Russian system is quite the opposite: lots of word problems, multi-faceted problems. I suspect I would have learned from that style a lot better. EDIT: One more point I should make. I scored in the 85th percentile on my SAT math. It is probably not a great sign for our system of education that I could do so well with nothing but the most rudimentary understanding of what I was doing.

yeellow 6y ago

> If Marcie can't find a useful application on day one of the "theory" she learns in school, what is the point? It's a 19th century curriculum for a 21st century world. Basic accounting and personal finance would probably serve most students better. Sorry, but following this logic we will end up with a conclusion that almost no school knowledge is "useful". How useful is playing volleyball? Reading poetry? Painting? Studying history? Biology would be reduced to first aid and basic medicine. I have those discussions with my daughters who learn how to do long multiplication. How is it useful if even I who know how to do it would rather use a calculator on my mobile instead? We would reduce math to basic operations on a calculators, probably nothing more would be considered useful by the majority of the population. The same apply to all other subjects.

unjurios 6y ago
I think "application" is the wrong focus. The real thing to help students understand is this exact question: what is math? That remains a mystery to most students. It gets conflated with the problem of application, but I think the real problem is most educations don't make clear the idea of abstraction, symbol systems, and logic. When you don't understand something, especially why it might be useful or at least intrinsically interesting, it's hard to get motivated about it.
- yeellow 6y ago
  But this exact question has no answer or has many different, contradictory answers as this discussion shows. I doubt that such discussion would be interesting for someone who struggles with algebra. Moreover the same questions could be asked about all subjects. The point of the school is to show kids different things even if they cannot see their usefulness right away. One person will enjoy math, other poetry or history. But all will have a chance to try different things and to choose what to study deeper. Of course it's nice to give some motivation and her teachers failed if she cannot see applications of basic algebra.
  - unjurious 6y ago
    I responded to the comment above with some examples of the kind of thing I'm hoping for. I don't think a deep philosophical discussion about math is necessary. Just reinforce the idea that math is a symbol system for dealing with questions of shape, quantity, and logic, and give multiple examples of applications of the same concept. Also convert between symbols and diagrams/drawings frequently (for example, I'm willing to bet an absurd number of Americans can't understand how a virus spreads exponentially; if you draw a pyramid of infected people, I bet they'd get it immediately; but instead we use curves and lines that don't connect with people).

unjurios 6y ago

Personal anecdote: I never understood what math "was," and this totally demotivated me to study it. I got A's all the way through high school mathematics because I was a systematic and logical thinker who had no problem following rules or algorithms, but I never once saw the point. When I reached college, I had already tested out of Calculus and never took a formal math course again. Fast-forward ten years. I am a self-taught programmer and now find mathematics absolutely fascinating and beautiful, and I see its applications. So I'm taking math classes on Udemy, buying hundreds of dollars of textbooks, and trying to teach myself. I can't help feeling like I got a little robbed. I understand that teaching is hard, and some kids just don't care to learn certain things and it's best for them and society to force some absolute fundamentals down their throats. But at a certain point around middle or high school, I think there needs to be a hard pivot to focusing on motivating students. If you do that well, they will have the ability to teach themselves and learn for the rest of their lives. If you don't they either end up like me, playing catch up a decade too late, or they just leave entire fields of knowledge untapped forever. With some subjects that's inevitable and probably ok, but math doesn't seem like it should be one of those subjects.

abhishekjha 6y ago
Which courses/books are you buying? I am on a similar path and would like to know more.
yeellow 6y ago
What do you think would convince you in the high school that math was important and worth studying?
- unjurious 6y ago
  I think three things would have done it: 1. A clear explanation of a symbol system and how math is a symbol system to deal with issues of quantity, shape, structure, and logic. 2. Frequently converting between diagrams/drawings and symbols (show "x x x" at times and "3" at other times). I actually have a concept for a game I want to program that does this. 3. Showing multiple concrete applications of different ideas, and lots of word problems. In retrospect I think this was always reversed in the American system. We would learn the symbolic and algorithmic aspects of a math concept, then use it to solve some word problems. Once I went back and started teaching myself some of this stuff, I read that the Russian system is quite the opposite: lots of word problems, multi-faceted problems. I suspect I would have learned from that style a lot better. EDIT: One more point I should make. I scored in the 85th percentile on my SAT math. It is probably not a great sign for our system of education that I could do so well with nothing but the most rudimentary understanding of what I was doing.