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It's not just the books it is the whole method of teaching. I remember learning the steps to calculate an eigenvector without a single comment on why one would

It's not just the books it is the whole method of teaching. I remember learning the steps to calculate an eigenvector without a single comment on why one would ever want to do that. I think it is done so that the educator can claim "this course teaches all of calculus and linear algebra and quantum mechanics". To actually explain things properly would require more modest course goals.

aerhardt 2y ago
I was taught linear algebra and multivariate calculus as a business major. They could hardly justify why they were teaching it in that context - they were weeder courses - but I always wished they had at least tried to give us a hint of applications. Nothing, it was all algebra for the sake of algebra. Atrocious.
- klysm 2y ago
  I think the concepts of linear systems and multivaribale calculus are important for just understanding systems in general. Even without applying them all the time you can think about dynamics with them
  - aerhardt 2y ago
    Multivariate calculus is also useful in probability, which in my degree was rigorous too, and is broadly useful in business, so perhaps I’m being unfair about all that math not being useful in business management. I’m grateful because later I got a degree in software engineering… But the point about math being taught like shit stands; if calculus and algebra can be useful in thinking about systems they should make an effort to show it.
    - klysm 2y ago
      100% agree that mathematical pedagogy in the USA is in terrible shape. It’s a hard problem, but we can do so much better
      - aerhardt 2y ago
        This was in Spain, but I have no problem believing it's roughly the same everywhere in the world, with few exceptions.
- deleted 2y ago
  [deleted]
- ozim 2y ago
  I still would argue that weeder courses are fine. If you start as a major whatever the field is - you should be interested in the field enough to plow through. Otherwise at the end you get people dissatisfied they cannot get job but they have a degree.
vasco 2y ago
I think I only learned linear algebra about 3 or 4 years after I graduated. I learned how to do the computations during the course but the teacher was so bad I had no idea what anything was for. Could've been an IQ test course for all it mattered. Here transpose this matrix now. Ok.
- klysm 2y ago
  Pretty common with lin alg and diffeq unfortunately. Many schools teach it as a toolbox instead of for understanding.
  - slowmovintarget 2y ago
    Math like words are tools. When you want application instead of tool operating instructions, go into physics or computer science (or both).
    - klysm 2y ago
      I disagree from a pedagogical standpoint. Math can be used as a tool, but that’s not the most effective way to teach math. I’m assuming the goal is to teach comprehension and understanding.
ozim 2y 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 2y 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 2y 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 2y 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.

aerhardt 2y ago

I was taught linear algebra and multivariate calculus as a business major. They could hardly justify why they were teaching it in that context - they were weeder courses - but I always wished they had at least tried to give us a hint of applications. Nothing, it was all algebra for the sake of algebra. Atrocious.

klysm 2y ago
I think the concepts of linear systems and multivaribale calculus are important for just understanding systems in general. Even without applying them all the time you can think about dynamics with them
- aerhardt 2y ago
  Multivariate calculus is also useful in probability, which in my degree was rigorous too, and is broadly useful in business, so perhaps I’m being unfair about all that math not being useful in business management. I’m grateful because later I got a degree in software engineering… But the point about math being taught like shit stands; if calculus and algebra can be useful in thinking about systems they should make an effort to show it.
  - klysm 2y ago
    100% agree that mathematical pedagogy in the USA is in terrible shape. It’s a hard problem, but we can do so much better
    - aerhardt 2y ago
      This was in Spain, but I have no problem believing it's roughly the same everywhere in the world, with few exceptions.
deleted 2y ago
[deleted]
ozim 2y ago
I still would argue that weeder courses are fine. If you start as a major whatever the field is - you should be interested in the field enough to plow through. Otherwise at the end you get people dissatisfied they cannot get job but they have a degree.

vasco 2y ago

I think I only learned linear algebra about 3 or 4 years after I graduated. I learned how to do the computations during the course but the teacher was so bad I had no idea what anything was for. Could've been an IQ test course for all it mattered. Here transpose this matrix now. Ok.

klysm 2y ago
Pretty common with lin alg and diffeq unfortunately. Many schools teach it as a toolbox instead of for understanding.
- slowmovintarget 2y ago
  Math like words are tools. When you want application instead of tool operating instructions, go into physics or computer science (or both).
  - klysm 2y ago
    I disagree from a pedagogical standpoint. Math can be used as a tool, but that’s not the most effective way to teach math. I’m assuming the goal is to teach comprehension and understanding.

ozim 2y 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 2y 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 2y 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 2y 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.