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> For any beginner this is a unrecognisable monstrosity. Having real names for the variables can give them something to hold on. Can you rewrite this same equ

> For any beginner this is a unrecognisable monstrosity. Having real names for the variables can give them something to hold on. Can you rewrite this same equation using "real names" so that it becomes less monstrous? I don't think that's possible, but maybe you have something in mind.

hutzlibu 5y ago
You equation is abstract. I recognize it exactly as this: as some abstract equations - but nothing more. (am I supposed to recognize them?) There is of course no real point in adding names later on. At least not without context. I would start with a real world example. And then - yes have the equations with long names. And then after that - have the equation as abstract plain math - in the shape you posted it. But not starting with it.
- username90 5y ago
  Can you illustrate how you would teach inner product using a real world example without using mathy names like x, y and z.
  - hutzlibu 5y ago
    Not on the spot - but with some thoughts very likely yes. And like I said: nothing wrong with using x, y and z - when teaching und using abstract math. My point was and is, that this should come later. After the real world examples.
    - username90 5y ago
      Most math doesn't have real world examples though. Inner product doesn't. It is useful in many places, but all of those applications are more complicated than inner product itself and are therefore best taught after inner product.
      - hutzlibu 5y ago
        "Most math doesn't have real world examples though. " I don't think so, as you can embed allmost any math concept in a real world context. Then the numbers get meaning - then the brain accepts dealing with it easier. The first time I had real fun with math, was when I dived into computergraphic and had to come up with equations for various vector related stuff. Suddenly there was meaning to it - the equations provided real benefit. With great visual results. So I had fun improving my equations with pen and paper. I never had that doing abstract math. Only slight relief when some equation finally solved, but it remakned abstract and meaningless. So this is where I would start: a real world problem - and then to solve it, show how abstraction helps. And all the various needed math concepts along the way. But starting with abstractions or focusing too much on them, just creates more mental blocks. I certainly had some with math - and I liked science from being very young. For common persons it is much worse. Just have a look how the common people discuss numbers related to covid for example ..
        username90 5y ago
        > I don't think so, as you can embed allmost any math concept in a real world context. Not without adding a lot of complexity. What I meant is that the concepts taught in maths very rarely map directly to any real world problems. GPU programming is a good example, it uses a lot of vector related maths but the leap from not knowing about vectors to GPU programming is huge and not a good way to learn the subject, since you would have to think both about the complexity of GPU's and graphics and about the vector abstraction at the same time. The reason you had fun doing GPU programming is because you already knew about the interface of vectors so you had no problems working with them.
        hutzlibu 5y ago
        "reason you had fun doing GPU programming is because you already knew about the interface of vectors so you had no problems working with them" Actually no. I had to relearn them pretty much completely, as I forgot all the abstract lessons before. But I had fun doing so. Because my brain saw real world use.

hutzlibu 5y ago

You equation is abstract. I recognize it exactly as this: as some abstract equations - but nothing more. (am I supposed to recognize them?) There is of course no real point in adding names later on. At least not without context. I would start with a real world example. And then - yes have the equations with long names. And then after that - have the equation as abstract plain math - in the shape you posted it. But not starting with it.

username90 5y ago
Can you illustrate how you would teach inner product using a real world example without using mathy names like x, y and z.
- hutzlibu 5y ago
  Not on the spot - but with some thoughts very likely yes. And like I said: nothing wrong with using x, y and z - when teaching und using abstract math. My point was and is, that this should come later. After the real world examples.
  - username90 5y ago
    Most math doesn't have real world examples though. Inner product doesn't. It is useful in many places, but all of those applications are more complicated than inner product itself and are therefore best taught after inner product.
    - hutzlibu 5y ago
      "Most math doesn't have real world examples though. " I don't think so, as you can embed allmost any math concept in a real world context. Then the numbers get meaning - then the brain accepts dealing with it easier. The first time I had real fun with math, was when I dived into computergraphic and had to come up with equations for various vector related stuff. Suddenly there was meaning to it - the equations provided real benefit. With great visual results. So I had fun improving my equations with pen and paper. I never had that doing abstract math. Only slight relief when some equation finally solved, but it remakned abstract and meaningless. So this is where I would start: a real world problem - and then to solve it, show how abstraction helps. And all the various needed math concepts along the way. But starting with abstractions or focusing too much on them, just creates more mental blocks. I certainly had some with math - and I liked science from being very young. For common persons it is much worse. Just have a look how the common people discuss numbers related to covid for example ..
      - username90 5y ago
        > I don't think so, as you can embed allmost any math concept in a real world context. Not without adding a lot of complexity. What I meant is that the concepts taught in maths very rarely map directly to any real world problems. GPU programming is a good example, it uses a lot of vector related maths but the leap from not knowing about vectors to GPU programming is huge and not a good way to learn the subject, since you would have to think both about the complexity of GPU's and graphics and about the vector abstraction at the same time. The reason you had fun doing GPU programming is because you already knew about the interface of vectors so you had no problems working with them.
        hutzlibu 5y ago
        "reason you had fun doing GPU programming is because you already knew about the interface of vectors so you had no problems working with them" Actually no. I had to relearn them pretty much completely, as I forgot all the abstract lessons before. But I had fun doing so. Because my brain saw real world use.