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I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually,

I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually, it’s later on in one’s journey through life that appreciation for the cool applications occur. At the time of taking the class doing cool applications inspires 1, pisses off 50 because it’s too hard, and leaves 49 rolling their yes.

atoav 3y ago
Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power. You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-like freakiness I got students where their teachers told me it is hopeless sitting there participating with glowing eyes. Meanwhile in my own math education I had a teacher who made us do integrals for what felt like a year without telling us once what the hell it is needed for. I had to figure that out on my own. My colleagues who didn't care just learned it by hard and forgot it immediately after. But I guess they got thought all the material and got ok grades so their education was a success. What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep.
- skhunted 3y ago
  What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep. This is precisely what I was referring to about people who come back at a later time and relearn the stuff. They want applications. At the time a class is taken very few actually want to dive into applications. The subject has been taught the way it is taught for a reason.
  - atoav 3y ago
    I am in education and what you claim here is in contradiction with both my experience and the direct feedback of the people I educated — most of which would say they dislike math or say they are bad at it. The argument that it is like it is for a reason can be made, but it has probably more to do with the historical role of school as an institution that is meant to produce obidient workers than with school as a place that is meant to produce people able to analyze nature and the world around them with the tools of mathematics. Ever student that got a bad grade because they solved the problem, but did so using the "wrong" way can testament to this. Back when I was in school I had the luck to also have a lot of maths both physics and mechanics classes, so I had above average exposure to mathematical applications. This is what made me the most wanted maths-helper among my friends who went to other schools with a "purely theoretical"-maths approach: I could finally show them how the stuff they had a hard time with connects to the actual real world and nature around them — which contrary to your statement really their ability to grasp it. If we think about how one would go about teaching any subject in a way that creates the maximum disinterest in the field it would be done dry theory only while keeping real world connections and story telling to a minimum. Sure, you could do that and there would always be a small number of students who would excell at that anyways because their brains are wired for abstract things — but that isn't a healthy approach to to take in general education. Sometimes my feeling is that mathematicians, like many other nerds want to gatekeep and shroud their own field in an overly opaque mysticism, because they can derive a higher self value from that. So things get explained over complicated and they tell you, that you would never understand (because you are the wrong kind of person). I like to instead believe that if explained right you can nearly explain everything to everyone — provided you manage to spark their interest, keep their interest and provide a good way into the matter. This is why Feynmanns lectures are so famous. He was really good at this.
    - skhunted 3y ago
      Feynman’s lectures demonstrate my point. From Wikipedia on the lectures: As a result, some physics students find the lectures more valuable after they have obtained a good grasp of physics by studying more traditional texts, and the books are sometimes seen as more helpful for teachers than for students.[5] It does not sound to me that you have much experience with actual teaching.
cultofmetatron 3y ago
That 1 will go and actually do amazing things with it. maybe invent a new application of the mathematics or invent new mathematics. The other 49 will forget it as soon as its no longer something to learn on an exam.
homefree 3y ago
imo this is largely because of the incentives around the game of school and testing. If you must wait 20yrs before you can do interesting stuff and you’re evaluated primarily on your ability to maximize your grade then anything that gets in the way of that is an annoying distraction for most at best. Even if you’re a student predisposed to find applications and the narrative of the discovery interesting you still have to focus on guessing what the test questions will be and just doing those, spending mental cycles on other stuff is a “waste” in that environment. Once you’re finally free of school only then can you actually learn based on where your curiosity takes you, though at that point most choose not to - the curiosity having been driven out of them. Makes me think a little bit about the movie the lives of others: > “Did you know that there are just five types of artists Your guy, Dreyman, is a Type 4, a "hysterical anthropocentrist." Can't bear being alone, always talking, needing friends. That type should never be brought to trial. They thrive on that. Temporary detention is the best way to deal with them. Complete isolation and no set release date. No human contact the whole time, not even with the guards. Good treatment, no harassment, no abuse, no scandals, nothing they could write about later. After 10 months, we release. Suddenly, that guy won't cause us any more trouble. “Know what the best part is? Most type 4s we've processed in this way never write anything again. Or paint anything, or whatever artists do. And that without any use of force. Just like that. Kind of like a present.”
- skhunted 3y ago
  For the vast majority of the students the curiosity, as you put it, isn’t really there. Understanding is very hard work and most people don’t want to put in the work to acquire understanding.
  - homefree 3y ago
    Perhaps, but it isn’t helped that spending effort to understand is often in direct conflict with the work required to get a good grade. You’re not tested on understanding how stuff is derived or how it’s used, you’re tested on grinding problems, particularly ones that are easy for teachers to put on a test and easy to grade (if they even bother with that, my worst teachers didn’t create their own tests or grade them, machines did both). In English or humanities you’re tested on predicting whatever bullshit your teacher believes and then crafting an essay that leans into their cognitive bias. I got very good at school and it was mostly by trying to model the minds of my mostly bad teachers and getting good at predicting what they want to hear and what they’d ask on the exam. With that down I could focus personal time on the stuff I was truly interested in (which ironically is what actually had market value). At least in the US public school system this is further hurt by public school teachers often barely knowing the material themselves and that’s if they’re not also outwardly hostile/condescending to the kids (there are always great teachers, but they’re the exception to the rule). The system isn’t selecting for the right things and those with enough money know this and work around it.
tarkin2 3y ago
If you look at the comments in khan academy there are tonnes of people asking for real life applications—that said, they’re given in most of the material there. Inspiring students (and showing the material can help them in their lives additionally) is one of the most important but difficult parts of teaching: good explanations falling on uninspired ears rarely settle. And I’d argue the onus is on the teacher to inspire but it’s not something I can say is an easy skill to master. Succinct explanations can be hammered out but fostering inspiration is a soft skill rarely taught—-and rarely deemed important in the already inspired.
- skhunted 3y ago
  I imagine - but have no data to back me up on this - that a lot of those comments you mentioned on Khan Academy come from two types of people. Those who are relearning the subject and are amenable to applications and those who say they want the cool problems but when they are actually done fall into the 99 category I mentioned above. It sounds to me like you haven’t taught much. I could be wrong.
Ekaros 3y ago
At university level not insignificant amount of students are there because they have to. The course is mandatory. And they might only want to pass. They are not getting degree because they want education, but because it is perceived as needed in society. Now should these be ignored or not is a discussion to have.

atoav 3y ago

Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power. You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-like freakiness I got students where their teachers told me it is hopeless sitting there participating with glowing eyes. Meanwhile in my own math education I had a teacher who made us do integrals for what felt like a year without telling us once what the hell it is needed for. I had to figure that out on my own. My colleagues who didn't care just learned it by hard and forgot it immediately after. But I guess they got thought all the material and got ok grades so their education was a success. What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep.

skhunted 3y ago
What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep. This is precisely what I was referring to about people who come back at a later time and relearn the stuff. They want applications. At the time a class is taken very few actually want to dive into applications. The subject has been taught the way it is taught for a reason.
- atoav 3y ago
  I am in education and what you claim here is in contradiction with both my experience and the direct feedback of the people I educated — most of which would say they dislike math or say they are bad at it. The argument that it is like it is for a reason can be made, but it has probably more to do with the historical role of school as an institution that is meant to produce obidient workers than with school as a place that is meant to produce people able to analyze nature and the world around them with the tools of mathematics. Ever student that got a bad grade because they solved the problem, but did so using the "wrong" way can testament to this. Back when I was in school I had the luck to also have a lot of maths both physics and mechanics classes, so I had above average exposure to mathematical applications. This is what made me the most wanted maths-helper among my friends who went to other schools with a "purely theoretical"-maths approach: I could finally show them how the stuff they had a hard time with connects to the actual real world and nature around them — which contrary to your statement really their ability to grasp it. If we think about how one would go about teaching any subject in a way that creates the maximum disinterest in the field it would be done dry theory only while keeping real world connections and story telling to a minimum. Sure, you could do that and there would always be a small number of students who would excell at that anyways because their brains are wired for abstract things — but that isn't a healthy approach to to take in general education. Sometimes my feeling is that mathematicians, like many other nerds want to gatekeep and shroud their own field in an overly opaque mysticism, because they can derive a higher self value from that. So things get explained over complicated and they tell you, that you would never understand (because you are the wrong kind of person). I like to instead believe that if explained right you can nearly explain everything to everyone — provided you manage to spark their interest, keep their interest and provide a good way into the matter. This is why Feynmanns lectures are so famous. He was really good at this.
  - skhunted 3y ago
    Feynman’s lectures demonstrate my point. From Wikipedia on the lectures: As a result, some physics students find the lectures more valuable after they have obtained a good grasp of physics by studying more traditional texts, and the books are sometimes seen as more helpful for teachers than for students.[5] It does not sound to me that you have much experience with actual teaching.

cultofmetatron 3y ago

That 1 will go and actually do amazing things with it. maybe invent a new application of the mathematics or invent new mathematics. The other 49 will forget it as soon as its no longer something to learn on an exam.

homefree 3y ago

imo this is largely because of the incentives around the game of school and testing. If you must wait 20yrs before you can do interesting stuff and you’re evaluated primarily on your ability to maximize your grade then anything that gets in the way of that is an annoying distraction for most at best. Even if you’re a student predisposed to find applications and the narrative of the discovery interesting you still have to focus on guessing what the test questions will be and just doing those, spending mental cycles on other stuff is a “waste” in that environment. Once you’re finally free of school only then can you actually learn based on where your curiosity takes you, though at that point most choose not to - the curiosity having been driven out of them. Makes me think a little bit about the movie the lives of others: > “Did you know that there are just five types of artists Your guy, Dreyman, is a Type 4, a "hysterical anthropocentrist." Can't bear being alone, always talking, needing friends. That type should never be brought to trial. They thrive on that. Temporary detention is the best way to deal with them. Complete isolation and no set release date. No human contact the whole time, not even with the guards. Good treatment, no harassment, no abuse, no scandals, nothing they could write about later. After 10 months, we release. Suddenly, that guy won't cause us any more trouble. “Know what the best part is? Most type 4s we've processed in this way never write anything again. Or paint anything, or whatever artists do. And that without any use of force. Just like that. Kind of like a present.”

skhunted 3y ago
For the vast majority of the students the curiosity, as you put it, isn’t really there. Understanding is very hard work and most people don’t want to put in the work to acquire understanding.
- homefree 3y ago
  Perhaps, but it isn’t helped that spending effort to understand is often in direct conflict with the work required to get a good grade. You’re not tested on understanding how stuff is derived or how it’s used, you’re tested on grinding problems, particularly ones that are easy for teachers to put on a test and easy to grade (if they even bother with that, my worst teachers didn’t create their own tests or grade them, machines did both). In English or humanities you’re tested on predicting whatever bullshit your teacher believes and then crafting an essay that leans into their cognitive bias. I got very good at school and it was mostly by trying to model the minds of my mostly bad teachers and getting good at predicting what they want to hear and what they’d ask on the exam. With that down I could focus personal time on the stuff I was truly interested in (which ironically is what actually had market value). At least in the US public school system this is further hurt by public school teachers often barely knowing the material themselves and that’s if they’re not also outwardly hostile/condescending to the kids (there are always great teachers, but they’re the exception to the rule). The system isn’t selecting for the right things and those with enough money know this and work around it.

tarkin2 3y ago

If you look at the comments in khan academy there are tonnes of people asking for real life applications—that said, they’re given in most of the material there. Inspiring students (and showing the material can help them in their lives additionally) is one of the most important but difficult parts of teaching: good explanations falling on uninspired ears rarely settle. And I’d argue the onus is on the teacher to inspire but it’s not something I can say is an easy skill to master. Succinct explanations can be hammered out but fostering inspiration is a soft skill rarely taught—-and rarely deemed important in the already inspired.

skhunted 3y ago
I imagine - but have no data to back me up on this - that a lot of those comments you mentioned on Khan Academy come from two types of people. Those who are relearning the subject and are amenable to applications and those who say they want the cool problems but when they are actually done fall into the 99 category I mentioned above. It sounds to me like you haven’t taught much. I could be wrong.

Ekaros 3y ago

At university level not insignificant amount of students are there because they have to. The course is mandatory. And they might only want to pass. They are not getting degree because they want education, but because it is perceived as needed in society. Now should these be ignored or not is a discussion to have.