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but "it's unfamiliar if you don't use FP" is a terrible one I get the sense that there is a large contingent of programmers who feel disdain for mathematics an

but "it's unfamiliar if you don't use FP" is a terrible one I get the sense that there is a large contingent of programmers who feel disdain for mathematics and FP gets caught in the crossfire. It’s unfair toward both mathematics and functional programming. I would love it if North American culture could adopt a better attitude toward mathematics in general. I think far too many people decide they’re bad at mathematics at some point in high school and never look back. This attitude is far less prevalent in many Asian cultures, where the emphasis is put on hard work instead of talent.

greggman2 7y ago
I know no good math teachers. Most math teachers pre-college don't know the material themselves. I still don't know why something is "efficient with" (a coefficient). And every time I try to get into any math there's 79 unspecified prerequisites I supposedly need to understand all the jargon. 3blue1brown is preaching to the choir AFAIK. I get lost trying to watch his videos as they also expect you already know the material.
- ColinWright 7y ago
  > I still don't know why something is "efficient with" (a coefficient). I can't parse this - would you care to expand on it? > 3blue1brown is preaching to the choir AFAIK. I get lost trying to watch his videos as they also expect you already know the material. If you care, you can always track back to earlier material and build your knowledge. Most people I know in a similar situation to yours don't actually care, and won't actually put in any effort. And that's a reasonable choice. There are places where math is hard, needs work, and most people have come to a point where they feel that the effort won't be worth it, that the ROI isn't there. But if that's your decision, then own it. If that's not your decision, and you actually want to know more, there are things you can do about it. FWIW, I know a lot of really good math teachers, but I agree that there are also some really poor teachers. If yours were bad then I feel bad about that, although there's nothing I can do about your experience in the education sector. What you do about it now, if anything, is up to you.
  - zelos 7y ago
    > There are places where math is hard... This is the realisation I had (20 years late). Especially beyond high school, maths is hard. You have to put the effort in, and you have to do the example problems. I think its expressiveness and conciseness makes it more dispiriting to study: one page of a maths textbook can contain so much information, and it feels like you're just stupid when it takes an hour to understand that page fully.
    - bonoboTP 7y ago
      > I think its expressiveness and conciseness makes it more dispiriting to study: one page of a maths textbook can contain so much information, and it feels like you're just stupid when it takes an hour to understand that page fully. This is very important. Apparently some people get frustrated by this because they are used to studying lower-information-density textbooks. Maybe there would be value in teaching these meta-skills, like how to approach learning each subject. People may apply techniques, like rote learning or brute-force cramming, reading the same page for hours on end, expecting to magically grok it, where these are ineffective of even counterproductive. Not sure how well this is teachable though.
      - K0SM0S 7y ago
        My personal experience says two things: - illustration — whether drawings, gestures, animations, using objects, whatever works, but have a visual equivalent to 'translate' notation; the typical example would be fractions which are as simple as it gets with drawings and hard as hell using only numbers, for most people discovering them. The same is true for most common functions and transformations (which, when you reduce it to the maximum, are the entire body of applied math). - real-world application (typically the best candidates are simple physics or statistics in high school). The point here is to give a point of reference, a "feeling" of the mechanism or logic or paradigm. The deeper problem is that this application must feel 'interesting', like a puzzle, and not everyone is interested by the same things. That's where, imho, narrow AI could help craft customized courses with ad hoc examples that fit people's "world view" and "approach" to problems, and show animations for every variable, equation, let people play with those and see the results. Both probably fit in the "faster feedback" approach, i.e. have the teacher/teaching material give feedback as fast and as often as possible, to guide the learning mind on the right path. This is an extremely important discovery of UX in the last 50 years and I believe education has much to learn from these very applied insights into human cognition.
- bonoboTP 7y ago
  > I still don't know why something is "efficient with" (a coefficient). That's just a name. You don't need to know the etymology to understand the topic at hand. But if you want to know, you can think of co-efficient as "together-effector". In 3x, 3 is a coefficient of x, as it's something that "acts together" with x. There isn't really much more to it. You don't understand concepts by studying their names in much detail. Another thing to get used to is that the same word may be used for different concepts in different contexts (or different words for the same thing). Often there is very little connection between them. You have to accept this as a fact of history. You can of course try to look for connections, but don't get frustrated because of not finding any. And some concepts are just badly named. Naming things is hard. Don't try to deduce things based on the names of things. Learning to understand names as just labels is an important step in acquiring good abstraction skills necessary for math. I think this may be an issue for certain people that they approach math from just the wrong angle. The jargon and terminology is of course important for understanding of the content, but the prerequisites are not really lingo-understanding, but concept-understanding. Unlike in other fields, you don't learn math by pouring over the text and reading page after page. You read something and try to understand it. You play with it, you stand up, take a walk and try to work out why something is the way it is, think of examples, try to clear up what you don't quite get. You cannot use the same learning tactics that you'd use for, say, accounting or humanities. The pages read per hour is pretty low in math.
  - ColinWright 7y ago
    > you don't learn math by pouring over the text and reading page after page. You read something and try to understand it. You play with it, you stand up, take a walk and try to work out why something is the way it is, think of examples, try to clear up what you don't quite get. Absolutely this. Math is a not a spectator sport, you can't acquire the skill and knowledge by reading. You must engage with it, fence with it, wrestle with it, make it your friend and spend time with it. I remember not so long ago playing with some equations and accidentally proving Pythagoras' Theorem. It wasn't new, it wasn't deep, but it was satisfying, in much the same way as getting code to perform as you want, accomplishing some task in an elegant way. But if you don't spend the time, you'll never get the insight(s).
- chongli 7y ago
  I know no good math teachers. Most math teachers pre-college don't know the material themselves I’m hoping to change this, not for all high school students, but for those I meet. I’m majoring in pure mathematics with a teaching option right now. My current plan is to teach high school algebra and calculus, as well as physics. The other comments are right about terminology. I have no idea where the word coefficient comes from, yet I use them every day and understand them pretty well. At the moment, I’m studying ring theory, ideals, quotient rings, and ring homomorphisms and isomorphisms. Trying to figure out where these abstract terms come from may be interesting but it doesn’t help me in my proofs at all. If you want to understand anything in math, the best approach is to read the definition, read some basic theorems, look at a few examples, and then start playing around with these things to get a feel for them. Try to prove some of the basic properties of the object you’re working with in terms of the axioms. Keep going, proving larger and more complicated theorems, and try some exercises that apply this knowledge to solve counting problems or measurement problems. If you’re learning about isomorphisms then look at some examples and try to understand how classes of object relate to one another, for example by having the same structure in their operations. If you’re not able to understand 3blue1brown’s videos then you might benefit from using Khan academy to build up your understanding of the fundamentals. It has material stretching from grade 1 to college. Solving problems feels like playing a game, so it can be fun to sit there for hours just doing the problem sets. Math is a deep, deep subject but it doesn’t require memorization. It just requires lots of effort and struggle in order to develop mastery.
  - 0x445442 7y ago
    You've probably seen this lecture but I'll pass it along anyway as I found it to be very insightful on the topic of teaching math and physics by using computation. As someone with a mechanical engineering degree with minors in math and physics I would have loved to have been exposed to this while I was learning the stuff. https://www.youtube.com/watch?v=Rk76BurH384 https://www.youtube.com/watch?v=Rk76BurH384
Ma8ee 7y ago
I've never connected FP with math than any other paradigm. FP is easier to grok than OO, it's just that OO was the popular paradigm when most working programmers today started out.
- yoz-y 7y ago
  > FP is easier to grok than OO For you. But I think this is far from being a given. At some point programming is a complicated thing and both OOP and FP get weird in their own ways. I wonder, are there toy FP languages for kids, like there is a ton of imperative ones? If not, maybe there is an opening ?
rusticpenn 7y ago
I am working with 10 Phds ( mostly in mathematics) who have no interest in learning FP.

greggman2 7y ago

I know no good math teachers. Most math teachers pre-college don't know the material themselves. I still don't know why something is "efficient with" (a coefficient). And every time I try to get into any math there's 79 unspecified prerequisites I supposedly need to understand all the jargon. 3blue1brown is preaching to the choir AFAIK. I get lost trying to watch his videos as they also expect you already know the material.

ColinWright 7y ago
> I still don't know why something is "efficient with" (a coefficient). I can't parse this - would you care to expand on it? > 3blue1brown is preaching to the choir AFAIK. I get lost trying to watch his videos as they also expect you already know the material. If you care, you can always track back to earlier material and build your knowledge. Most people I know in a similar situation to yours don't actually care, and won't actually put in any effort. And that's a reasonable choice. There are places where math is hard, needs work, and most people have come to a point where they feel that the effort won't be worth it, that the ROI isn't there. But if that's your decision, then own it. If that's not your decision, and you actually want to know more, there are things you can do about it. FWIW, I know a lot of really good math teachers, but I agree that there are also some really poor teachers. If yours were bad then I feel bad about that, although there's nothing I can do about your experience in the education sector. What you do about it now, if anything, is up to you.
- zelos 7y ago
  > There are places where math is hard... This is the realisation I had (20 years late). Especially beyond high school, maths is hard. You have to put the effort in, and you have to do the example problems. I think its expressiveness and conciseness makes it more dispiriting to study: one page of a maths textbook can contain so much information, and it feels like you're just stupid when it takes an hour to understand that page fully.
  - bonoboTP 7y ago
    > I think its expressiveness and conciseness makes it more dispiriting to study: one page of a maths textbook can contain so much information, and it feels like you're just stupid when it takes an hour to understand that page fully. This is very important. Apparently some people get frustrated by this because they are used to studying lower-information-density textbooks. Maybe there would be value in teaching these meta-skills, like how to approach learning each subject. People may apply techniques, like rote learning or brute-force cramming, reading the same page for hours on end, expecting to magically grok it, where these are ineffective of even counterproductive. Not sure how well this is teachable though.
    - K0SM0S 7y ago
      My personal experience says two things: - illustration — whether drawings, gestures, animations, using objects, whatever works, but have a visual equivalent to 'translate' notation; the typical example would be fractions which are as simple as it gets with drawings and hard as hell using only numbers, for most people discovering them. The same is true for most common functions and transformations (which, when you reduce it to the maximum, are the entire body of applied math). - real-world application (typically the best candidates are simple physics or statistics in high school). The point here is to give a point of reference, a "feeling" of the mechanism or logic or paradigm. The deeper problem is that this application must feel 'interesting', like a puzzle, and not everyone is interested by the same things. That's where, imho, narrow AI could help craft customized courses with ad hoc examples that fit people's "world view" and "approach" to problems, and show animations for every variable, equation, let people play with those and see the results. Both probably fit in the "faster feedback" approach, i.e. have the teacher/teaching material give feedback as fast and as often as possible, to guide the learning mind on the right path. This is an extremely important discovery of UX in the last 50 years and I believe education has much to learn from these very applied insights into human cognition.
bonoboTP 7y ago
> I still don't know why something is "efficient with" (a coefficient). That's just a name. You don't need to know the etymology to understand the topic at hand. But if you want to know, you can think of co-efficient as "together-effector". In 3x, 3 is a coefficient of x, as it's something that "acts together" with x. There isn't really much more to it. You don't understand concepts by studying their names in much detail. Another thing to get used to is that the same word may be used for different concepts in different contexts (or different words for the same thing). Often there is very little connection between them. You have to accept this as a fact of history. You can of course try to look for connections, but don't get frustrated because of not finding any. And some concepts are just badly named. Naming things is hard. Don't try to deduce things based on the names of things. Learning to understand names as just labels is an important step in acquiring good abstraction skills necessary for math. I think this may be an issue for certain people that they approach math from just the wrong angle. The jargon and terminology is of course important for understanding of the content, but the prerequisites are not really lingo-understanding, but concept-understanding. Unlike in other fields, you don't learn math by pouring over the text and reading page after page. You read something and try to understand it. You play with it, you stand up, take a walk and try to work out why something is the way it is, think of examples, try to clear up what you don't quite get. You cannot use the same learning tactics that you'd use for, say, accounting or humanities. The pages read per hour is pretty low in math.
- ColinWright 7y ago
  > you don't learn math by pouring over the text and reading page after page. You read something and try to understand it. You play with it, you stand up, take a walk and try to work out why something is the way it is, think of examples, try to clear up what you don't quite get. Absolutely this. Math is a not a spectator sport, you can't acquire the skill and knowledge by reading. You must engage with it, fence with it, wrestle with it, make it your friend and spend time with it. I remember not so long ago playing with some equations and accidentally proving Pythagoras' Theorem. It wasn't new, it wasn't deep, but it was satisfying, in much the same way as getting code to perform as you want, accomplishing some task in an elegant way. But if you don't spend the time, you'll never get the insight(s).
chongli 7y ago
I know no good math teachers. Most math teachers pre-college don't know the material themselves I’m hoping to change this, not for all high school students, but for those I meet. I’m majoring in pure mathematics with a teaching option right now. My current plan is to teach high school algebra and calculus, as well as physics. The other comments are right about terminology. I have no idea where the word coefficient comes from, yet I use them every day and understand them pretty well. At the moment, I’m studying ring theory, ideals, quotient rings, and ring homomorphisms and isomorphisms. Trying to figure out where these abstract terms come from may be interesting but it doesn’t help me in my proofs at all. If you want to understand anything in math, the best approach is to read the definition, read some basic theorems, look at a few examples, and then start playing around with these things to get a feel for them. Try to prove some of the basic properties of the object you’re working with in terms of the axioms. Keep going, proving larger and more complicated theorems, and try some exercises that apply this knowledge to solve counting problems or measurement problems. If you’re learning about isomorphisms then look at some examples and try to understand how classes of object relate to one another, for example by having the same structure in their operations. If you’re not able to understand 3blue1brown’s videos then you might benefit from using Khan academy to build up your understanding of the fundamentals. It has material stretching from grade 1 to college. Solving problems feels like playing a game, so it can be fun to sit there for hours just doing the problem sets. Math is a deep, deep subject but it doesn’t require memorization. It just requires lots of effort and struggle in order to develop mastery.
- 0x445442 7y ago
  You've probably seen this lecture but I'll pass it along anyway as I found it to be very insightful on the topic of teaching math and physics by using computation. As someone with a mechanical engineering degree with minors in math and physics I would have loved to have been exposed to this while I was learning the stuff. https://www.youtube.com/watch?v=Rk76BurH384 https://www.youtube.com/watch?v=Rk76BurH384

Ma8ee 7y ago

I've never connected FP with math than any other paradigm. FP is easier to grok than OO, it's just that OO was the popular paradigm when most working programmers today started out.

yoz-y 7y ago
> FP is easier to grok than OO For you. But I think this is far from being a given. At some point programming is a complicated thing and both OOP and FP get weird in their own ways. I wonder, are there toy FP languages for kids, like there is a ton of imperative ones? If not, maybe there is an opening ?

rusticpenn 7y ago

I am working with 10 Phds ( mostly in mathematics) who have no interest in learning FP.