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It's difficult tho, the idea is the student should want to learn that they learn no matter how boring because the teacher/institution says so. I remember when

It's difficult tho, the idea is the student should want to learn that they learn no matter how boring because the teacher/institution says so. I remember when I got introduced to matrix in high school, it felt pointless and stupid. Why would I want to transform matrix? I hated the entire thing, sure I could solve it but for what purpose? Then I learned I could use it for 3D engine, and I could load my object in a matrix and transform to move things around, that got my attention. However, a student that has no interest in 3D engines won't care. How then do you make it exciting? It's not enough to make the problem concrete, but the student will also need to be interested in the concrete application of the subject. Teaching is hard!

at_a_remove 5y ago
Absolutely. As a private tutor, finding applicability and motivation for students was quite a challenge. I spent a lot of time reformulating problems in terms of things they might care about.
laichzeit0 5y ago
Maybe it was taught in the wrong order. Matrix multiplication makes perfect sense if you see (a) that linear transformations can be represented as matrices, I.e A = f, B = g and (b) you define matrix multiplication so that the composition of linear transformations I.e. f(g(x)) = ABx gives the same result. That’s a pretty cool idea, that you can represent a function by a matrix and that you can compose those functions and the composition is the same as multiplying the matrices together. So let’s say f(x) computes the derivative of a polynomial, and you have a matrix representation for that, say A. Now what if I want the second derivative? That would be f(f(x)) or just AAx. I suppose I would tell a student that asks “why would I want to remember the stupid rule for multiplying matrices together in that way?” to try and figure out a rule for multiplying two matrices together such that you could represent functional composition by it, and they would self-discover the matrix multiplication rule and see why it would be useful to do it that way.
- segmondy 5y ago
  It's not that it didn't make sense, it's that it was boring! Of what use is it? Sure, you have composition of linear transformations, but of what use is it again? If there's no use, it's boring. Pure math is like a puzzle, some people really love to solve the puzzle. The joy is in the solving the puzzle, and then for some people the joy only manifests if it's applied. Point of the original post being that math is harder for students to accept in its pure form if not applied.
  - zoomablemind 5y ago
    Matrix calc organically fits with systems of linear equations. Hard not to appreciate its expessiveness and beauty. If one was already exposed to the need of solving the linear systems, then the matrix calc becomes of a direct utility.
_carbyau_ 5y ago
A good teacher can make a great difference but as you say, the pupil needs some motivation - some reason to want to learn it. I took exactly one class of 2nd year physics and couldn't see the point of it. I walked out, quit physics altogether and came back the following year to do CS.

at_a_remove 5y ago

Absolutely. As a private tutor, finding applicability and motivation for students was quite a challenge. I spent a lot of time reformulating problems in terms of things they might care about.

laichzeit0 5y ago

Maybe it was taught in the wrong order. Matrix multiplication makes perfect sense if you see (a) that linear transformations can be represented as matrices, I.e A = f, B = g and (b) you define matrix multiplication so that the composition of linear transformations I.e. f(g(x)) = ABx gives the same result. That’s a pretty cool idea, that you can represent a function by a matrix and that you can compose those functions and the composition is the same as multiplying the matrices together. So let’s say f(x) computes the derivative of a polynomial, and you have a matrix representation for that, say A. Now what if I want the second derivative? That would be f(f(x)) or just AAx. I suppose I would tell a student that asks “why would I want to remember the stupid rule for multiplying matrices together in that way?” to try and figure out a rule for multiplying two matrices together such that you could represent functional composition by it, and they would self-discover the matrix multiplication rule and see why it would be useful to do it that way.

segmondy 5y ago
It's not that it didn't make sense, it's that it was boring! Of what use is it? Sure, you have composition of linear transformations, but of what use is it again? If there's no use, it's boring. Pure math is like a puzzle, some people really love to solve the puzzle. The joy is in the solving the puzzle, and then for some people the joy only manifests if it's applied. Point of the original post being that math is harder for students to accept in its pure form if not applied.
- zoomablemind 5y ago
  Matrix calc organically fits with systems of linear equations. Hard not to appreciate its expessiveness and beauty. If one was already exposed to the need of solving the linear systems, then the matrix calc becomes of a direct utility.

_carbyau_ 5y ago

A good teacher can make a great difference but as you say, the pupil needs some motivation - some reason to want to learn it. I took exactly one class of 2nd year physics and couldn't see the point of it. I walked out, quit physics altogether and came back the following year to do CS.