5 ms·

The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'. People just want to know why it's x and not something

The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'. People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.

GodelNumbering 2y ago
thank Descartes
- ckolkey 2y ago
  I thank, therefore I am...
raverbashing 2y ago
> nobody is really teaching the concept of a symbol in a math class. This was what? 5th grade? What kind of crap teachers never taught that
- mschuster91 2y ago
  > What kind of crap teachers never taught that It's rarely the fault of the teachers. The problem is, in many MANY MANY schools, teachers are more like social workers that have to compensate for utter horrifics outside of school. You got a ton of children so poor they didn't have breakfast which means their first (and all too often: only) meal will be the school-provided lunch (Covid showed that - a bunch of schools were open at least for lunches). You got children that are literally homeless and living with their parents in some car on a Walmart parking lot. You got children whose parents are in and out of jail. You got children living with their siblings in way too small, pest and mold ridden "apartments". You got children whose parents don't have money to pay for basic school supplies. You got children who are dealing with mental, physical and sexual abuse. You got children where the parents are constantly on drugs or seeking for drugs. You got children with a drug dependency on their own - if they're lucky it's just tobacco or weed, if not it's opioids. You got children with parents or siblings with serious mental or physical health issues. Or you got children with their own mental and physical health issues, or if you want it worse, children with these issues but without access to any kind of treatment. You got children that are being weaponized in nasty divorces. You got children that are being weaponized by street gangs. You got children committing crimes from petty theft to dealing drugs just to survive. You got children that have to literally work (and states like FL pushing to have more working children). You got children having their own children already (either from sexual abuse, from under-education about their own bodies, or intentionally because they fell for some stupid challenge/dare). You got children dealing with bullying, you got some who actually are bullies because they have no other way of dealing with their emotions or getting lunch money. You got children with parents with about zero interest in them. You got children who worry that they'll come home and find out their parents got snatched and disappeared by ICE. You got children who worry that ICE will storm their classroom and deport them. You got children who worry they might not survive the school day because someone will shoot at them. You got children who are constantly on the move because their parents' employment/deployment requires absolute mobility. You got children who are LGBT and have to deal with ever increasing hate against them (and LGBT youth already had significantly higher suicide rates than before the GQP made it a culture war issue). The US doesn't have any kind of system to help these children but schools and libraries, both are horribly underfunded (there's some school districts where teachers gotta take up second jobs because the government can only afford paying them for 4 days a week), and all too often teachers have to pay with their own money for students' school supplies. And on top of dealing with these kind of nightmares, they actually have to try and teach these children something - even if the children in question aren't anywhere near a headspace where they can actually learn.
  - Viliam1234 2y ago
    I taught at a nice middle-class school, so most of the problems you mention were not relevant there. And yet, it seemed like half of the kids' families were either recently divorced or in the process of divorce. I couldn't really blame those kids for not paying attention to school. And this seemed like the best case, so probably at most places it gets much worse. Education has a problem with scaling, especially at the elementary level. Sometimes people figure out a nice solution, but when you tell them "great, and now do this in every village" the problem becomes obvious. But there are kids in that village, too, and you want them to know reading and math and hopefully also something more.
    - mschuster91 2y ago
      > Education has a problem with scaling, especially at the elementary level. Not if you actually provide the money. Europe gets this down decently well - although I'll admit, in rural areas in Germany we got some serious consolidation issues thanks to urban flight. But at least our teachers are well paid government jobs and the job is decently attractive.
      - vacuity 2y ago
        There's plenty of money thrown at schools in the US, but the issue is that the students that live in poor socioeconomic conditions tend to not do well. The "simple answer" that addresses the root cause would make individuals not subject to poverty and whatnot. But throwing money at institutions is already on the ropes in the US, let alone throwing money at the "undeserving". (Yes, this is a political opinion. No, do not blame me for that. Politics does not come wrapped up neatly with a bow tie in a box. If you want to debate the veracity of my claim, go do that instead.)
        mschuster91 2y ago
        > If you want to debate the veracity of my claim, go do that instead. I'd do no such thing because you are completely correct - the only thing I'd add is that poverty, while being very dominant, isn't the only issue that desperately needs to be fixed.
somenameforme 2y ago
This becomes even more true in higher level maths where programming language style functions would make everything vastly more clear, and easily typeable, than the traditional Greek symbols. sum(x+3, 1, 4) is just so much more clear (and consistent when generalized across other operations) and practically as concise as the mathematical way of expressing that which I cannot even type. Multiple variables would be a bit dirtier, but still much cleaner than the formal expression. Interestingly mathematical symbols in the past also regularly evolved. Then at some point we just stopped doing that and get stuck in a time which is arguably no longer especially appropriate. So we're left with rather inconsistent symbols, oft reused in different contexts, and optimized for written communication.
- serbuvlad 2y ago
  My first thought when I read sum(x+3, 1, 4) was x+3+1+4. Also it should be sum(x+3, x, 1, 4) since you need to encode what the iterator variable is as well.
  - Izkata 2y ago
    I thought that was it too, but you're saying it's not..? I've been thinking about it for a few minutes now and I still can't figure out what other meaning it could have. Edit: Oh wait, someone else mentions map/filter, did they mean this as a combination of range->map->sum and the latter two numbers are the range portion, like sum(map(x+3, 1..4)) ? Edit2: And now I'm remembering sigma. I think it would have been more obvious to me if the order was flipped and your issue handled the way it is in that notation: sum(x=1, 4, x+3), though I'd still prefer the range notation: sum(x=1..4, x+3)
    - serbuvlad 2y ago
      Yep. I agree and now we've basically reinvented sigma. Take the x=1 and put it below, take the 4 and put it above take the x+3 and put it to the right. Granted I always found sigma a bit quirky for separating the range ends like that. Either x below and 1..4 above, or x=1..4 below/above would have been more intuitive. But it's just a notation you learn once and then you know it.
maccard 2y ago
I don’t recall the exact age, but when I was doing math in primary school (somewhere around age 9/10) we were absolutely using symbols - “Paul has two apples, and the basket can hold 10 apples. How many more apples can Paul put in the basket” is the same as 2 + x = 10 We did these sorts of problems for a long time, with addition/multiplication/fractions, and even when we started doing actual algebra the problems were introduced the same way “let’s look at a problem we’ve solved already, and write it in a different way”.
HdS84 2y ago
I will die on the hill that most of math would benefit from better naming, less short names and longer format. Yes, the crack math guys have no problems with terse symbols. But most people do. Good example is Greek letters for geometry. They are not really taught in school so an easy formula gets 'weird squiggly thing times another squiggly thing....' and that does not help understanding at all
- ndriscoll 2y ago
  For any given problem, you usually know what it is your studying, so writing out names doesn't have much benefit. On the other hand, a more visual language (which is what mathematical writing is) lets you easily look at specific portions of the picture and read off how it behaves, which is very useful. Basically, getting hung up on names means you're reading it wrong.
- globular-toast 2y ago
  This is like trying to change English or arguing that we should all speak Esperanto. Mathematical notation isn't the way it is to save ink or make it look difficult. It's that way because it works. Notation isn't set by committee, it's just a way of communication that works. If you read cutting edge research you'll find notations being invented all over the place. Most of them will never go anywhere, some will become standard in their field (like big-O) and others will become universally used (like dropping the multiplication symbol and using epsilon for a small number).
  - tenacious_tuna 2y ago
    I think this is a very limited take for a hacker forum. We talk about how useful accurate names for variables are all the time, or generally how working to encode more natural/context-related semantics to code helps anyone reading it understand what the goal is better than an extremely terse symbology. Yeah, lots of existing math texts will forever exist with greek alphabet soup, but we don't have to rely on those as our be-all-end-all teaching tools. To operate at a high level in mathematics I would agree that having the skill of easily abstracting complex things into compact symbols is a necessary skill, just as I would agree to the same concept applied to software engineering or really any complex engineering system; by the same token, we don't have to START on hard mode with all of our students. Math is infamously difficult for some, largely (I think) because we make it unnecessarily opaque out of some misguided sense of traditionalism. If we want to have lots of people who are good at math we should embrace whatever pedagogy is effective.
amluto 2y ago
One answer: sometimes you need a name, especially because there’s more than one of them. Suppose you’re looking for one digit numbers like this: 10•_ + _ = 73 Now try saying the answer: “7 and 3”. This gets vague quite quickly —- which blank is 7 and which is 3?
carabiner 2y ago
Reminds me of how the Σ symbol in math is just a for-loop.
florbnit 2y ago
> People just want to know why it's x and not something else or how a letter can have value. The way I was taught it and the way that worked now for my now 3 year old is just to say pirates buried a number under the X, and that we need to guess what they buried. If the concept of a number being hidden is a barrier to understanding for anyone they have seriously bad teachers.

GodelNumbering 2y ago

thank Descartes

ckolkey 2y ago
I thank, therefore I am...

raverbashing 2y ago

> nobody is really teaching the concept of a symbol in a math class. This was what? 5th grade? What kind of crap teachers never taught that

mschuster91 2y ago
> What kind of crap teachers never taught that It's rarely the fault of the teachers. The problem is, in many MANY MANY schools, teachers are more like social workers that have to compensate for utter horrifics outside of school. You got a ton of children so poor they didn't have breakfast which means their first (and all too often: only) meal will be the school-provided lunch (Covid showed that - a bunch of schools were open at least for lunches). You got children that are literally homeless and living with their parents in some car on a Walmart parking lot. You got children whose parents are in and out of jail. You got children living with their siblings in way too small, pest and mold ridden "apartments". You got children whose parents don't have money to pay for basic school supplies. You got children who are dealing with mental, physical and sexual abuse. You got children where the parents are constantly on drugs or seeking for drugs. You got children with a drug dependency on their own - if they're lucky it's just tobacco or weed, if not it's opioids. You got children with parents or siblings with serious mental or physical health issues. Or you got children with their own mental and physical health issues, or if you want it worse, children with these issues but without access to any kind of treatment. You got children that are being weaponized in nasty divorces. You got children that are being weaponized by street gangs. You got children committing crimes from petty theft to dealing drugs just to survive. You got children that have to literally work (and states like FL pushing to have more working children). You got children having their own children already (either from sexual abuse, from under-education about their own bodies, or intentionally because they fell for some stupid challenge/dare). You got children dealing with bullying, you got some who actually are bullies because they have no other way of dealing with their emotions or getting lunch money. You got children with parents with about zero interest in them. You got children who worry that they'll come home and find out their parents got snatched and disappeared by ICE. You got children who worry that ICE will storm their classroom and deport them. You got children who worry they might not survive the school day because someone will shoot at them. You got children who are constantly on the move because their parents' employment/deployment requires absolute mobility. You got children who are LGBT and have to deal with ever increasing hate against them (and LGBT youth already had significantly higher suicide rates than before the GQP made it a culture war issue). The US doesn't have any kind of system to help these children but schools and libraries, both are horribly underfunded (there's some school districts where teachers gotta take up second jobs because the government can only afford paying them for 4 days a week), and all too often teachers have to pay with their own money for students' school supplies. And on top of dealing with these kind of nightmares, they actually have to try and teach these children something - even if the children in question aren't anywhere near a headspace where they can actually learn.
- Viliam1234 2y ago
  I taught at a nice middle-class school, so most of the problems you mention were not relevant there. And yet, it seemed like half of the kids' families were either recently divorced or in the process of divorce. I couldn't really blame those kids for not paying attention to school. And this seemed like the best case, so probably at most places it gets much worse. Education has a problem with scaling, especially at the elementary level. Sometimes people figure out a nice solution, but when you tell them "great, and now do this in every village" the problem becomes obvious. But there are kids in that village, too, and you want them to know reading and math and hopefully also something more.
  - mschuster91 2y ago
    > Education has a problem with scaling, especially at the elementary level. Not if you actually provide the money. Europe gets this down decently well - although I'll admit, in rural areas in Germany we got some serious consolidation issues thanks to urban flight. But at least our teachers are well paid government jobs and the job is decently attractive.
    - vacuity 2y ago
      There's plenty of money thrown at schools in the US, but the issue is that the students that live in poor socioeconomic conditions tend to not do well. The "simple answer" that addresses the root cause would make individuals not subject to poverty and whatnot. But throwing money at institutions is already on the ropes in the US, let alone throwing money at the "undeserving". (Yes, this is a political opinion. No, do not blame me for that. Politics does not come wrapped up neatly with a bow tie in a box. If you want to debate the veracity of my claim, go do that instead.)
      - mschuster91 2y ago
        > If you want to debate the veracity of my claim, go do that instead. I'd do no such thing because you are completely correct - the only thing I'd add is that poverty, while being very dominant, isn't the only issue that desperately needs to be fixed.

somenameforme 2y ago

This becomes even more true in higher level maths where programming language style functions would make everything vastly more clear, and easily typeable, than the traditional Greek symbols. sum(x+3, 1, 4) is just so much more clear (and consistent when generalized across other operations) and practically as concise as the mathematical way of expressing that which I cannot even type. Multiple variables would be a bit dirtier, but still much cleaner than the formal expression. Interestingly mathematical symbols in the past also regularly evolved. Then at some point we just stopped doing that and get stuck in a time which is arguably no longer especially appropriate. So we're left with rather inconsistent symbols, oft reused in different contexts, and optimized for written communication.

serbuvlad 2y ago
My first thought when I read sum(x+3, 1, 4) was x+3+1+4. Also it should be sum(x+3, x, 1, 4) since you need to encode what the iterator variable is as well.
- Izkata 2y ago
  I thought that was it too, but you're saying it's not..? I've been thinking about it for a few minutes now and I still can't figure out what other meaning it could have. Edit: Oh wait, someone else mentions map/filter, did they mean this as a combination of range->map->sum and the latter two numbers are the range portion, like sum(map(x+3, 1..4)) ? Edit2: And now I'm remembering sigma. I think it would have been more obvious to me if the order was flipped and your issue handled the way it is in that notation: sum(x=1, 4, x+3), though I'd still prefer the range notation: sum(x=1..4, x+3)
  - serbuvlad 2y ago
    Yep. I agree and now we've basically reinvented sigma. Take the x=1 and put it below, take the 4 and put it above take the x+3 and put it to the right. Granted I always found sigma a bit quirky for separating the range ends like that. Either x below and 1..4 above, or x=1..4 below/above would have been more intuitive. But it's just a notation you learn once and then you know it.

maccard 2y ago

I don’t recall the exact age, but when I was doing math in primary school (somewhere around age 9/10) we were absolutely using symbols - “Paul has two apples, and the basket can hold 10 apples. How many more apples can Paul put in the basket” is the same as 2 + x = 10 We did these sorts of problems for a long time, with addition/multiplication/fractions, and even when we started doing actual algebra the problems were introduced the same way “let’s look at a problem we’ve solved already, and write it in a different way”.

HdS84 2y ago

I will die on the hill that most of math would benefit from better naming, less short names and longer format. Yes, the crack math guys have no problems with terse symbols. But most people do. Good example is Greek letters for geometry. They are not really taught in school so an easy formula gets 'weird squiggly thing times another squiggly thing....' and that does not help understanding at all

ndriscoll 2y ago
For any given problem, you usually know what it is your studying, so writing out names doesn't have much benefit. On the other hand, a more visual language (which is what mathematical writing is) lets you easily look at specific portions of the picture and read off how it behaves, which is very useful. Basically, getting hung up on names means you're reading it wrong.
globular-toast 2y ago
This is like trying to change English or arguing that we should all speak Esperanto. Mathematical notation isn't the way it is to save ink or make it look difficult. It's that way because it works. Notation isn't set by committee, it's just a way of communication that works. If you read cutting edge research you'll find notations being invented all over the place. Most of them will never go anywhere, some will become standard in their field (like big-O) and others will become universally used (like dropping the multiplication symbol and using epsilon for a small number).
- tenacious_tuna 2y ago
  I think this is a very limited take for a hacker forum. We talk about how useful accurate names for variables are all the time, or generally how working to encode more natural/context-related semantics to code helps anyone reading it understand what the goal is better than an extremely terse symbology. Yeah, lots of existing math texts will forever exist with greek alphabet soup, but we don't have to rely on those as our be-all-end-all teaching tools. To operate at a high level in mathematics I would agree that having the skill of easily abstracting complex things into compact symbols is a necessary skill, just as I would agree to the same concept applied to software engineering or really any complex engineering system; by the same token, we don't have to START on hard mode with all of our students. Math is infamously difficult for some, largely (I think) because we make it unnecessarily opaque out of some misguided sense of traditionalism. If we want to have lots of people who are good at math we should embrace whatever pedagogy is effective.

amluto 2y ago

One answer: sometimes you need a name, especially because there’s more than one of them. Suppose you’re looking for one digit numbers like this: 10•_ + _ = 73 Now try saying the answer: “7 and 3”. This gets vague quite quickly —- which blank is 7 and which is 3?

carabiner 2y ago

Reminds me of how the Σ symbol in math is just a for-loop.

florbnit 2y ago

> People just want to know why it's x and not something else or how a letter can have value. The way I was taught it and the way that worked now for my now 3 year old is just to say pirates buried a number under the X, and that we need to guess what they buried. If the concept of a number being hidden is a barrier to understanding for anyone they have seriously bad teachers.