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" The two solutions of aXX+bX+c = 0 are X=(-b+√(bb-4ac))/2a and X=(-b-√(bb-4ac))/2a ? You would convert this equation into an unrecognizable monostrosity." Fo

" The two solutions of aXX+bX+c = 0 are X=(-b+√(bb-4ac))/2a and X=(-b-√(bb-4ac))/2a ? You would convert this equation into an unrecognizable monostrosity." For any beginner this is a unrecognisable monstrosity. Having real names for the variables can give them something to hold on. Something they can relate to. So it makes sense to their brain. And later on, you can abstract it - and they are fine with it and see the benefits. (I still want programming variable names to be as descriptive as possible) You (and probably everyone else around here) are used to abstraction - a beginner to math is not! (and sadly, most people are even after 12 years of schoolmath still beginners in math) And the focus on abstraction is a huge wall, making everything harder than it needs to be. " Thus it pays off to have variable names as meaningless as possible. " I agree that this is very helpful to achieve, when you are dealing with plain math only. But I think this thinking actually lead to lots of real world harm - when variables are not meaningless factors in math - but representing real persons. Which is forgotten quite often, if some buerocrat for example just sees them as a "meaningless variable" and treats them like this. But in reality this can mean, someones existence just got crushed.

enriquto 6y ago
> 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 6y 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 6y 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 6y 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 6y 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 6y 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 ..

enriquto 6y ago

> 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 6y 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 6y 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 6y 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 6y 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 6y 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 ..