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> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations). Why? Basic ari

> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations). Why? Basic arithmetic is almost entirely useless as a skill. Why should I spend my time learning something which computers will always be able to do more reliably and faster than me?

JoeAltmaier 10y ago
...so that you understand what it does. Else it will remain magic, and you may entertain other magical thinking as well. Like Astrology or Numerology or even that maybe you could win the lottery. Its important to have a good understanding at a very basic level of what math, statistics and physics are about.
- morgante 10y ago
  I never said you shouldn't understand what it does. It's just that I think it's useless to drill on arithmetic. I know very well what a computer is doing when I tell it to divide 188416 by 20148. That doesn't mean it's useful for me to be able to mentally do it. Mental arithmetic is incredibly overvalued and useless as a skill, especially since it's largely uncorrelated with actual depth of mathematical understanding.
  - rohit89 10y ago
    I believe the OP's exercise was to do the division manually not mentally. Basic mental arithmetic is probably the most used in day-to-day life. It feels weird having to whip out a calculator/phone every time you need to make a quick estimate.
    - morgante 10y ago
      > I believe the OP's exercise was to do the division manually not mentally. That's equally useless. Why would I try to figure out the result manually when I have a computer in my pocket at all times? If anything, doing things manually when we have computers seems weirder.
      - JoeAltmaier 10y ago
        With only a little practice, I found I can add up a column of 4-digit numbers in seconds. Faster than you can whip out your calculator app. Its the impression that computers are easier, that gets me. Why not practice for 2 minutes and learn a better way? Instead of limping along with the computer all your life.
        morgante 10y ago
        Good for you. Do whatever you want. I have a phone with me at all times. It's hardly an inconvenience to use it.
        JoeAltmaier 10y ago
        Its not a point of pride, you know, to remain unskilled in the ordinary things of life. It takes only a few minutes to learn these things. I wonder why anyone would resist?
      - rohit89 10y ago
        The point of that exercise was to show whether you knew how to do it. Things like division and multiplication etc are so basic that you should know how to do it even if you haven't done it for years. As for mental arithmetic, its main advantage is speed. Faster to mentally solve and continue along your train of thought/flow of conversation than to pull out a calculator. Physical actions will never be faster than speed of thought.
mamcx 10y ago
Ok, so what could be the true "base-skill" in math? And is possible to achieve knowledge of it, without a strong foundation of arithmetic? Truly, I don't know, as I say I'm bad at math. However, the point is that without strong basics the rest is a lost cause (IMHO). What is the basic, I'm open to know, however, I think arithmetic is part of it...
- nzp 10y ago
  Nope. There are people (I'm one of them) who have sometimes extreme difficulty doing basic arithmetic manually and in the head. In my case it's not the full-blown dyscalculia[1] but to this day I haven't been able to learn full multiplication table for example, so forget about multiplying numbers in my head. I can do it on paper, but the whole process looks like a computer under heavy swapping. I even have hard time adding and subtracting numbers mentally. If I'm expected to produce a numerical result while being watched it all becomes a catastrophe because then I also get substantial anxiety for not being able to do what for most people is a simple thing. There's something about operations with concrete numbers (although I have no problem with numbers themselves) that turns my mind into mush. OTOH, I have basically little problem with any other branch of mathematics. The more advanced the better, actually. In school it got easier as it got more advanced (although geometry was always easy no matter what level). Getting calculus in high school felt like I could suddenly breathe with full lungs. And I studied theoretical physics later at university. Apart from the basic reality that the math required is hard and needs a lot of work no matter how smart/gifted/whatever you are, I had no substantial problem with most of it. Abstract algebra, group theory, vector spaces and manifolds... oh the joys! Because none of it requires you to do any kind of mental arithmetical computation. This is not a unique experience, I once saw a TV report on a young successful astrophysicist with basically the same problem: Calculus on manifolds, GR field equations? Pfff... All day and every day. But, give her some numbers on a blackboard to multiply and she gets completely lost. [1]: https://en.wikipedia.org/wiki/Dyscalculia https://en.wikipedia.org/wiki/Dyscalculia

JoeAltmaier 10y ago

...so that you understand what it does. Else it will remain magic, and you may entertain other magical thinking as well. Like Astrology or Numerology or even that maybe you could win the lottery. Its important to have a good understanding at a very basic level of what math, statistics and physics are about.

morgante 10y ago
I never said you shouldn't understand what it does. It's just that I think it's useless to drill on arithmetic. I know very well what a computer is doing when I tell it to divide 188416 by 20148. That doesn't mean it's useful for me to be able to mentally do it. Mental arithmetic is incredibly overvalued and useless as a skill, especially since it's largely uncorrelated with actual depth of mathematical understanding.
- rohit89 10y ago
  I believe the OP's exercise was to do the division manually not mentally. Basic mental arithmetic is probably the most used in day-to-day life. It feels weird having to whip out a calculator/phone every time you need to make a quick estimate.
  - morgante 10y ago
    > I believe the OP's exercise was to do the division manually not mentally. That's equally useless. Why would I try to figure out the result manually when I have a computer in my pocket at all times? If anything, doing things manually when we have computers seems weirder.
    - JoeAltmaier 10y ago
      With only a little practice, I found I can add up a column of 4-digit numbers in seconds. Faster than you can whip out your calculator app. Its the impression that computers are easier, that gets me. Why not practice for 2 minutes and learn a better way? Instead of limping along with the computer all your life.
      - morgante 10y ago
        Good for you. Do whatever you want. I have a phone with me at all times. It's hardly an inconvenience to use it.
        JoeAltmaier 10y ago
        Its not a point of pride, you know, to remain unskilled in the ordinary things of life. It takes only a few minutes to learn these things. I wonder why anyone would resist?
    - rohit89 10y ago
      The point of that exercise was to show whether you knew how to do it. Things like division and multiplication etc are so basic that you should know how to do it even if you haven't done it for years. As for mental arithmetic, its main advantage is speed. Faster to mentally solve and continue along your train of thought/flow of conversation than to pull out a calculator. Physical actions will never be faster than speed of thought.

mamcx 10y ago

Ok, so what could be the true "base-skill" in math? And is possible to achieve knowledge of it, without a strong foundation of arithmetic? Truly, I don't know, as I say I'm bad at math. However, the point is that without strong basics the rest is a lost cause (IMHO). What is the basic, I'm open to know, however, I think arithmetic is part of it...

nzp 10y ago
Nope. There are people (I'm one of them) who have sometimes extreme difficulty doing basic arithmetic manually and in the head. In my case it's not the full-blown dyscalculia[1] but to this day I haven't been able to learn full multiplication table for example, so forget about multiplying numbers in my head. I can do it on paper, but the whole process looks like a computer under heavy swapping. I even have hard time adding and subtracting numbers mentally. If I'm expected to produce a numerical result while being watched it all becomes a catastrophe because then I also get substantial anxiety for not being able to do what for most people is a simple thing. There's something about operations with concrete numbers (although I have no problem with numbers themselves) that turns my mind into mush. OTOH, I have basically little problem with any other branch of mathematics. The more advanced the better, actually. In school it got easier as it got more advanced (although geometry was always easy no matter what level). Getting calculus in high school felt like I could suddenly breathe with full lungs. And I studied theoretical physics later at university. Apart from the basic reality that the math required is hard and needs a lot of work no matter how smart/gifted/whatever you are, I had no substantial problem with most of it. Abstract algebra, group theory, vector spaces and manifolds... oh the joys! Because none of it requires you to do any kind of mental arithmetical computation. This is not a unique experience, I once saw a TV report on a young successful astrophysicist with basically the same problem: Calculus on manifolds, GR field equations? Pfff... All day and every day. But, give her some numbers on a blackboard to multiply and she gets completely lost. [1]: https://en.wikipedia.org/wiki/Dyscalculia https://en.wikipedia.org/wiki/Dyscalculia