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I still would argue that method of teaching is perfectly fine. You cannot simply explain to someone complex stuff - best way is to let people grind through to

by ozim 3y ago

I still would argue that method of teaching is perfectly fine. You cannot simply explain to someone complex stuff - best way is to let people grind through to build their own understanding. Parent poster wrote that "it’s useful for determining the similarity of two vectors" - now I would ask why do I need to determine similarity of two vectors as it does not mean much to me - if I would be grinding through math problems I would most likely find out why, but there is no way I could understand and retain it when someone would just tell me.

jampekka 3y ago
I think more intuitive/holistic ways of teaching would be a lot better. But it's hard to do, especially in dead tree format. To get someone understand something holistically, as in link to their previous knowledge base, requires knowledge of what their knowledge base is. Traditionally this has been done with structuring the teaching with prerequisites etc and hoping it works. I struggle with this quite a bit when I teach students with heterogeneous background. To be effective, one has to first probe what the students already knows to be able to relate the new stuff to that, and this requires interaction. Hypertext is/would be helpful for self-learning, but it's sadly very underutilized. LLMs may be better. But probably even those can't at least in the current form replace interactive human teaching as they don't really form/retain a model of what the user knows.
z3phyr 3y ago
> Ask why do I need to determine similarity of two vectors Simple: Start with a) Suppose you are making a video game.. b) Suppose you are determining ballistic trajectory of your missile system based on model rockets c) Suppose you are running a fighter robot group.. Or any of the stuff children are supposed to *actually* do and then take these classes with determination to do the actual creative things that they wanna do all life. There is an aspect of jest in the above comment, but it also contains some likely truth. Children love doing stuff, and these are the things that may enable them.
- kyykky 3y ago
  Take a random group of students from the general population and one of those examples (Edit: or any single given example whatsoeve). Turns out 95% are not really interested. Edit 2: The teacher probably gave some example from biology or something that you didn't care about and therefore forgot about it.
  - z3phyr 3y ago
    The core skill of the teacher lies in recognizing the interests of the pupil and then working on refining those skills so that the pupil can use those skills for at least their betterment, if not the society. And that is one of the toughest things to get right. Children are extremely curious, that's how they learn and master absolutely anything including arts, dancing, music, history, skating, catching insects, street smarts etc. It's on us as teachers to not let that curiosity wither into nothingness.
- xandrius 3y ago
  This is exactly how I would teach SO many subjects in school: take what kids are actually interested about and make them see the connection. The worst thing was to learn something just because the teacher said so. If I hadn't had the motivation not to fail, I would definitely not have gone this far in my studies and in life.
- slowmovintarget 3y ago
  If I'm writing an instruction manual for a lathe, I'm probably not going to run through all the varying things you produce with the lathe. I'm going to talk about correct use of the lathe. It won't help you understand what a lathe is for, but it will help you use the lathe correctly. I think the same goes for mathematics instruction. The thinking is that you will soon take courses that will make specific application of these tools that have broad application.
  - z3phyr 3y ago
    You will be correct for the most part. However, there is a question of motivation as well. Kids can make very cool toys with a lathe. I am not from the west, but I watched Band of Brothers. From most of the ww2 media there is always a term being used. "Why we fight?"
vasco 3y ago
> You cannot simply explain to someone complex stuff This is absolutely not true. Many times I've experienced the moment of something complex "clicking" after hearing or reading an appropriate explanation for a phenomenon - finally seeing the right visual or appropriate example or comparison. I find it hard to believe you've never experienced this other than through grinding problem sets.
- ozim 3y ago
  I don't believe something can "click" - without grinding first. I believe something "clicked" only because you were grinding or already quite familiar with the topic. There is no way to simply explain complex topic so someone would just get it or someone would "click" on after reading one book on the topic.
  - vasco 3y ago
    Like I said, I've had many of those moments. It is strange you haven't. You telling me I just wasn't aware of my own grinding is a bit strange. I've literally had examples where person A explains X and I don't get it, then 2 hours later person B explains X again and I get it. There's no grinding in the middle. There's good and bad ways to explain complex things, and the success rate will vary and the amount of "grinding" you need to do I think also varies depending on the quality of the explanations you get. Maybe I'm missing the core of your point.
    - jawilson2 3y ago
      I agree and disagree. I've definitely experienced this, but I've come to the conclusion that the problem is bouncing around in my head for those 2 hours, quietly grinding away in the background. Then, when person B explains it, my brain is more receptive to it. At work as a developer, I'll often encounter a difficult problem, and walk away for a few minutes. Then, if still stuck, I'll go to the gym. Usually when I come back I'll have the answer coded in 5 minutes. However, I've definitely had the case where person B just explains it better (for me). I still can't completely discount that my brain was primed for it by person A.
codingrightnow 3y ago
Knowing why and when to use math is equally as important as knowing it. One of the reasons I lost my love for learning it was this missing information.
- sumtechguy 3y ago
  What I found very annoying with calculus specifically was the previous 15 years I had been memorizing formulas. Formula to get the area of something remember this thing. Formula to get the volume of something remember this formula. Formula to get the angle of something remember this formula. But if I had known the way of calculus and derivatives I could make those formulas. I now have the ability to have a formula factory instead of devoting tons of mental space to keeping those formulas. I feel I wasted 15 years rote memorizing things instead of understanding the N spaces things live in and how to get the formulas.
  - ghaff 3y ago
    But you--or at least most of your classmates--probably weren't in a place to just learn calculus before taking high school physics or even simple geometry. And this happens at a lot of different levels with math, physics, chemistry, etc. There are a lot of inter-relationships and often moving forward requires taking some things on faith (for now).
  - vundercind 3y ago
    Illustrative point for the “the value isn’t explained” issue: I’ve spent two years on calculus in school plus some more time on my own and don’t know how or why I’d e.g. use it to derive the formula for the area of an oval (I think that’s the kind of thing you’re getting at?) Actually, I can count the times I’ve applied math from later than 6th or 7th grade on one hand. I’m almost 40 and have been writing code for pay since I was 15. I struggle with this with my own kids and dread their reaching those later classes because I have no compelling answer for “why do I have to learn this boring shit?”
  - financltravsty 3y ago
    How did you learn to make those formulas?
The_Colonel 3y ago
You're making a false dichotomy. Learning is a combination of guidance and own hard work. Maybe you prefer to figure out everything yourself, but you have just one lifetime, and having access to guidance while grinding will allow you to learn things faster (and thus more).
- pk-protect-ai 3y ago
  This is quite an old book. I wish I had an access to or even knew about this book during my school days 40 years ago. When I discovered this book, I was already a middle-aged engineer and was just looking for books for my kids. The first two pages blew my mind. If only I had this book back then... However, I remember now the several sleepless days and nights in sequence when I tried to make sense of finite fields at university. I could not sleep; I could not rest... And then I understood that you can create your own algebra whenever you want; you just need to follow the rules. This was so mind-blowing, and at the same time, no single teacher even tried to point out this wondrous fact that actually changed my mind in such a significant way. It could literally have saved a couple of years of my life if I had read this book back in high school. I'm not a mathematician; math exists for me only when it is applicable to what I have at hand. But you realize that you missed a HUGE AMOUNT OF TOOLS, too late in your life.
- ozim 3y ago
  What I argue is that there is no approach to guidance that will substitute for own hard work. I do not argue that guidance is not needed, it also is, but there is no shortcut that lets people skip own hard work by telling someone incantation of words or sentences in special order that will make things click.
hobs 3y ago
And you'd be dead wrong by all methods of pedagogy that we find useful! People learn best with stories and meaning, its why the ancients were able to reproduce stories of almost inhuman length via memory. Grinding through to build your own understanding when someone can just give you useful meaning and context to connect to your other parts of learning is a core teaching skill, and anyone avoiding that because its "too hard" is doing a deep disservice to their students.

by ozim 3y ago

jampekka 3y ago

I think more intuitive/holistic ways of teaching would be a lot better. But it's hard to do, especially in dead tree format. To get someone understand something holistically, as in link to their previous knowledge base, requires knowledge of what their knowledge base is. Traditionally this has been done with structuring the teaching with prerequisites etc and hoping it works. I struggle with this quite a bit when I teach students with heterogeneous background. To be effective, one has to first probe what the students already knows to be able to relate the new stuff to that, and this requires interaction. Hypertext is/would be helpful for self-learning, but it's sadly very underutilized. LLMs may be better. But probably even those can't at least in the current form replace interactive human teaching as they don't really form/retain a model of what the user knows.

z3phyr 3y ago

> Ask why do I need to determine similarity of two vectors Simple: Start with a) Suppose you are making a video game.. b) Suppose you are determining ballistic trajectory of your missile system based on model rockets c) Suppose you are running a fighter robot group.. Or any of the stuff children are supposed to *actually* do and then take these classes with determination to do the actual creative things that they wanna do all life. There is an aspect of jest in the above comment, but it also contains some likely truth. Children love doing stuff, and these are the things that may enable them.

kyykky 3y ago
Take a random group of students from the general population and one of those examples (Edit: or any single given example whatsoeve). Turns out 95% are not really interested. Edit 2: The teacher probably gave some example from biology or something that you didn't care about and therefore forgot about it.
- z3phyr 3y ago
  The core skill of the teacher lies in recognizing the interests of the pupil and then working on refining those skills so that the pupil can use those skills for at least their betterment, if not the society. And that is one of the toughest things to get right. Children are extremely curious, that's how they learn and master absolutely anything including arts, dancing, music, history, skating, catching insects, street smarts etc. It's on us as teachers to not let that curiosity wither into nothingness.
xandrius 3y ago
This is exactly how I would teach SO many subjects in school: take what kids are actually interested about and make them see the connection. The worst thing was to learn something just because the teacher said so. If I hadn't had the motivation not to fail, I would definitely not have gone this far in my studies and in life.
slowmovintarget 3y ago
If I'm writing an instruction manual for a lathe, I'm probably not going to run through all the varying things you produce with the lathe. I'm going to talk about correct use of the lathe. It won't help you understand what a lathe is for, but it will help you use the lathe correctly. I think the same goes for mathematics instruction. The thinking is that you will soon take courses that will make specific application of these tools that have broad application.
- z3phyr 3y ago
  You will be correct for the most part. However, there is a question of motivation as well. Kids can make very cool toys with a lathe. I am not from the west, but I watched Band of Brothers. From most of the ww2 media there is always a term being used. "Why we fight?"

vasco 3y ago

> You cannot simply explain to someone complex stuff This is absolutely not true. Many times I've experienced the moment of something complex "clicking" after hearing or reading an appropriate explanation for a phenomenon - finally seeing the right visual or appropriate example or comparison. I find it hard to believe you've never experienced this other than through grinding problem sets.

ozim 3y ago
I don't believe something can "click" - without grinding first. I believe something "clicked" only because you were grinding or already quite familiar with the topic. There is no way to simply explain complex topic so someone would just get it or someone would "click" on after reading one book on the topic.
- vasco 3y ago
  Like I said, I've had many of those moments. It is strange you haven't. You telling me I just wasn't aware of my own grinding is a bit strange. I've literally had examples where person A explains X and I don't get it, then 2 hours later person B explains X again and I get it. There's no grinding in the middle. There's good and bad ways to explain complex things, and the success rate will vary and the amount of "grinding" you need to do I think also varies depending on the quality of the explanations you get. Maybe I'm missing the core of your point.
  - jawilson2 3y ago
    I agree and disagree. I've definitely experienced this, but I've come to the conclusion that the problem is bouncing around in my head for those 2 hours, quietly grinding away in the background. Then, when person B explains it, my brain is more receptive to it. At work as a developer, I'll often encounter a difficult problem, and walk away for a few minutes. Then, if still stuck, I'll go to the gym. Usually when I come back I'll have the answer coded in 5 minutes. However, I've definitely had the case where person B just explains it better (for me). I still can't completely discount that my brain was primed for it by person A.

codingrightnow 3y ago

Knowing why and when to use math is equally as important as knowing it. One of the reasons I lost my love for learning it was this missing information.

sumtechguy 3y ago
What I found very annoying with calculus specifically was the previous 15 years I had been memorizing formulas. Formula to get the area of something remember this thing. Formula to get the volume of something remember this formula. Formula to get the angle of something remember this formula. But if I had known the way of calculus and derivatives I could make those formulas. I now have the ability to have a formula factory instead of devoting tons of mental space to keeping those formulas. I feel I wasted 15 years rote memorizing things instead of understanding the N spaces things live in and how to get the formulas.
- ghaff 3y ago
  But you--or at least most of your classmates--probably weren't in a place to just learn calculus before taking high school physics or even simple geometry. And this happens at a lot of different levels with math, physics, chemistry, etc. There are a lot of inter-relationships and often moving forward requires taking some things on faith (for now).
- vundercind 3y ago
  Illustrative point for the “the value isn’t explained” issue: I’ve spent two years on calculus in school plus some more time on my own and don’t know how or why I’d e.g. use it to derive the formula for the area of an oval (I think that’s the kind of thing you’re getting at?) Actually, I can count the times I’ve applied math from later than 6th or 7th grade on one hand. I’m almost 40 and have been writing code for pay since I was 15. I struggle with this with my own kids and dread their reaching those later classes because I have no compelling answer for “why do I have to learn this boring shit?”
- financltravsty 3y ago
  How did you learn to make those formulas?

The_Colonel 3y ago

You're making a false dichotomy. Learning is a combination of guidance and own hard work. Maybe you prefer to figure out everything yourself, but you have just one lifetime, and having access to guidance while grinding will allow you to learn things faster (and thus more).

pk-protect-ai 3y ago
This is quite an old book. I wish I had an access to or even knew about this book during my school days 40 years ago. When I discovered this book, I was already a middle-aged engineer and was just looking for books for my kids. The first two pages blew my mind. If only I had this book back then... However, I remember now the several sleepless days and nights in sequence when I tried to make sense of finite fields at university. I could not sleep; I could not rest... And then I understood that you can create your own algebra whenever you want; you just need to follow the rules. This was so mind-blowing, and at the same time, no single teacher even tried to point out this wondrous fact that actually changed my mind in such a significant way. It could literally have saved a couple of years of my life if I had read this book back in high school. I'm not a mathematician; math exists for me only when it is applicable to what I have at hand. But you realize that you missed a HUGE AMOUNT OF TOOLS, too late in your life.
ozim 3y ago
What I argue is that there is no approach to guidance that will substitute for own hard work. I do not argue that guidance is not needed, it also is, but there is no shortcut that lets people skip own hard work by telling someone incantation of words or sentences in special order that will make things click.

hobs 3y ago

And you'd be dead wrong by all methods of pedagogy that we find useful! People learn best with stories and meaning, its why the ancients were able to reproduce stories of almost inhuman length via memory. Grinding through to build your own understanding when someone can just give you useful meaning and context to connect to your other parts of learning is a core teaching skill, and anyone avoiding that because its "too hard" is doing a deep disservice to their students.