5 ms·

The big issue here, since most reading this are probably of the generation in question, is found in the first comment: As a result they have no quantitative in

The big issue here, since most reading this are probably of the generation in question, is found in the first comment: As a result they have no quantitative intuition, which means they have no idea if their arithmetic results (achieved by simply hitting buttons on a keypad) even make sense. That's scary. It'll be quite difficult to teach my kids math if their own schools don't see it as a requirement.

silvestrov 15y ago
I think we should aim for "quantitative intuition" by teaching how to do rough calculations instead of spending time teaching precise calculations. There is a lot of "cheats" possible when calculating approximations that makes it much easier to learn/perform. In real life there is often so many uncertainties in the source numbers that a 'precise' answer is not meaningful anyway. Many people think that all the digits displayed in the calculator are significant/meaningful. If you are a painter that estimates an offer price to the customer, you don't need to be able to work out in your head that 10.5 * 21.5 is 225.75, the estimate 'approx 215-230' is almost always good enough.
- run4yourlives 15y ago
  I think we should aim for "quantitative intuition" by teaching how to do rough calculations instead of spending time teaching precise calculations. This is like saying we should teach children how to swim by letting them splash around in the wading pool. In real life there is often so many uncertainties in the source numbers that a 'precise' answer is not meaningful anyway. Math is precise. That's the whole point of it. I don't want my banker, accountant, civil engineer, pilot, cartographer, or architect working on "good enough". I want them to be precise. Consistently.
  - jerf 15y ago
    "Math is precise." Your brain is not. I've seen a lot more evidence of people bootstrapping from intuition up to mathematical precision than simply starting with mathematical precision. Taken to its logical conclusion (and I do mean that I believe this is the logical conclusion), this leads to trying to teach number and set theory to kindergarteners, berating them for failing to get it, throwing your hands up and declaring they just aren't suited for math. You have to start with quantitative intuition, the alternative is not to teach math at all. There isn't a "start them out on correct pedagogy immediately" choice. You can and should argue about what tradeoffs are best, but you will have to have tradeoffs.
    - run4yourlives 15y ago
      I don't seen how quantitative intuition and precision are somehow opposed to each other. 4*5 is 20. Not 21. Not 18. 20. That is logical, and it's vitally important in the understanding of all future concepts. You don't need to understand advanced calculus to grasp the concept that 2 3/4 oranges + 2 1/3 oranges is not 5 oranges altogther, but actually more, and that left over bit is in fact meaningful and relevant. It's when you start to play with abstractions that mathematics becomes confusing, not when you are being precise.
      - lurker14 15y ago
        When is the last time you had a use for exactly 1/12 oranges? "some bit more than 5" is plenty of precision for nearly any conceivable situation in which your example could appear. https://secure.wikimedia.org/wikipedia/en/wiki/Significant_figures https://secure.wikimedia.org/wikipedia/en/wiki/Significant_f...
        run4yourlives 15y ago
        I think you misunderstood my example. My point was that knowing that there is 5 1/12 oranges (as opposed to 5) is the important precision, and it works logically to a child's mind. It's quite a bit more complex to expect the child to discard the 1/12 and suggest there are 5 oranges. It's not that the 1/12 is useful for anything, it's the fact that it exists, and is accounted for.
  - more_original 15y ago
    > Math is precise. No, this statement is too strong. There are many examples in mathematics where one cannot exactly calculate a result (e.g. because one doesn't know all inputs), but one can give an estimation and prove that it is good enough for a certain purpose. Example: Chebyshev's inequality in probability theory: http://en.wikipedia.org/wiki/Chebyshev%27s_inequality http://en.wikipedia.org/wiki/Chebyshev%27s_inequality
    - run4yourlives 15y ago
      Certainly, but in order to properly appreciate these more advanced aspects, you need to have an appreciation of the precision and logic of more basic math. More importantly, I'd suggest that you need to know very basic math (simple addition, subtraction, multiplication and division) on the same level that you can type at your keyboard or drive a stick shift. If you're spending brain effort on the basics, you've got less of it left for the complexities, making the entire exercise much more difficult.
jerf 15y ago
Math is one of the huge things leading me to home school rather than sending the kids to school. It's bad enough that schools teach "calculation" rather "math", but now they're not even teaching "calculation"‽ It's a lot of work but it has gotten to the point that I feel like I'd be screwing my kids over to send them to school. Changes are in play that may make me comfortable with them sending their children to a 21st century school, but I can't stomach the thought of sending them to these 19th century monstrosities in their final days.
sn 15y ago
I have little quantitative intuition, which typically leads me to have to work through everything rather than give an off-the-cuff answer and checking my results multiple times.

silvestrov 15y ago

I think we should aim for "quantitative intuition" by teaching how to do rough calculations instead of spending time teaching precise calculations. There is a lot of "cheats" possible when calculating approximations that makes it much easier to learn/perform. In real life there is often so many uncertainties in the source numbers that a 'precise' answer is not meaningful anyway. Many people think that all the digits displayed in the calculator are significant/meaningful. If you are a painter that estimates an offer price to the customer, you don't need to be able to work out in your head that 10.5 * 21.5 is 225.75, the estimate 'approx 215-230' is almost always good enough.

run4yourlives 15y ago
I think we should aim for "quantitative intuition" by teaching how to do rough calculations instead of spending time teaching precise calculations. This is like saying we should teach children how to swim by letting them splash around in the wading pool. In real life there is often so many uncertainties in the source numbers that a 'precise' answer is not meaningful anyway. Math is precise. That's the whole point of it. I don't want my banker, accountant, civil engineer, pilot, cartographer, or architect working on "good enough". I want them to be precise. Consistently.
- jerf 15y ago
  "Math is precise." Your brain is not. I've seen a lot more evidence of people bootstrapping from intuition up to mathematical precision than simply starting with mathematical precision. Taken to its logical conclusion (and I do mean that I believe this is the logical conclusion), this leads to trying to teach number and set theory to kindergarteners, berating them for failing to get it, throwing your hands up and declaring they just aren't suited for math. You have to start with quantitative intuition, the alternative is not to teach math at all. There isn't a "start them out on correct pedagogy immediately" choice. You can and should argue about what tradeoffs are best, but you will have to have tradeoffs.
  - run4yourlives 15y ago
    I don't seen how quantitative intuition and precision are somehow opposed to each other. 4*5 is 20. Not 21. Not 18. 20. That is logical, and it's vitally important in the understanding of all future concepts. You don't need to understand advanced calculus to grasp the concept that 2 3/4 oranges + 2 1/3 oranges is not 5 oranges altogther, but actually more, and that left over bit is in fact meaningful and relevant. It's when you start to play with abstractions that mathematics becomes confusing, not when you are being precise.
    - lurker14 15y ago
      When is the last time you had a use for exactly 1/12 oranges? "some bit more than 5" is plenty of precision for nearly any conceivable situation in which your example could appear. https://secure.wikimedia.org/wikipedia/en/wiki/Significant_figures https://secure.wikimedia.org/wikipedia/en/wiki/Significant_f...
      - run4yourlives 15y ago
        I think you misunderstood my example. My point was that knowing that there is 5 1/12 oranges (as opposed to 5) is the important precision, and it works logically to a child's mind. It's quite a bit more complex to expect the child to discard the 1/12 and suggest there are 5 oranges. It's not that the 1/12 is useful for anything, it's the fact that it exists, and is accounted for.
- more_original 15y ago
  > Math is precise. No, this statement is too strong. There are many examples in mathematics where one cannot exactly calculate a result (e.g. because one doesn't know all inputs), but one can give an estimation and prove that it is good enough for a certain purpose. Example: Chebyshev's inequality in probability theory: http://en.wikipedia.org/wiki/Chebyshev%27s_inequality http://en.wikipedia.org/wiki/Chebyshev%27s_inequality
  - run4yourlives 15y ago
    Certainly, but in order to properly appreciate these more advanced aspects, you need to have an appreciation of the precision and logic of more basic math. More importantly, I'd suggest that you need to know very basic math (simple addition, subtraction, multiplication and division) on the same level that you can type at your keyboard or drive a stick shift. If you're spending brain effort on the basics, you've got less of it left for the complexities, making the entire exercise much more difficult.

jerf 15y ago

Math is one of the huge things leading me to home school rather than sending the kids to school. It's bad enough that schools teach "calculation" rather "math", but now they're not even teaching "calculation"‽ It's a lot of work but it has gotten to the point that I feel like I'd be screwing my kids over to send them to school. Changes are in play that may make me comfortable with them sending their children to a 21st century school, but I can't stomach the thought of sending them to these 19th century monstrosities in their final days.

sn 15y ago

I have little quantitative intuition, which typically leads me to have to work through everything rather than give an off-the-cuff answer and checking my results multiple times.