Originally Posted by SiuiS
First, I've never learned long division. I can't. No, seriously. I have the general idea, and I can do basic division in my head, or even break it into five different problems, count X units one at a time until they math up an drop the remainder into the next equation (which is ostensibly what long division is), but my brain cannot process long division. I had to relearn it every day after school for a year to get my homework done. I think it's a brain damage issue, honestly. Am I a bad guy because I find the concept of reding to divide a number into a fraction or huge decimal thingy tedious enough to just not bother?
I can't do long division either. I don't even remember ever learning division in school, which I will admit is more likely to be faulty memory but I seriously can not remember ever learning division. It's blank, it never happened as far as my memory is concerned.
I've never needed long division. We have calculators after all. You don't need to know long division to understand division, long division is for when you wish to do division of big numbers by hand, and how often do you need that in the modern age? It may also be useful in the study of some specialized areas of number theory, which I've recently found out, much to my horror.
The few times I've tried to understand long division, it has made absolutely no sense. I have no clue which hat they're pulling those numbers out of.
I've always found it funny how friends and family assume that because I study math, I'm somehow really good at numbers. I'm horrible at numbers, although I've gotten better over the years, slow and steady from constant use.
Originally Posted by SiuiS
Also, tau may be neat, but it's too elite. As a cashier, a roofer, a construction worker, a strategist, a lay-engineer, and when working out geometry for massage, pi has been simple enough to use. And none of those situations would call for tau. So, why bother teaching kids early on something they won't use, and that doesn't have an easy metric, so that if they bother getting to trigonometry (fat chance of that, since they can't even use the basics of geometry theyre getting so why bother with more stuff you don't get?) instead of reserving tau for people who need it. Kids Lear that Pi may as well be 3.14, teenagers learn that pi I'd actually a discrete number, an later, adults who go into the field can learn about tau.
The problem is that pi is an awkward choice based on a strange convention. the problem goes to the very root of pi and affects everything.
Of course, the ones most directly affected will be those who go on to study science, engineering and other mathy subjects, but that doesn't mean others are unaffected.
It's a matter of concepts, not just the specific applications (like the area formula for circles). Tau uses a natural definition and leads to intuitive results, whereas pi is simply a strange convention that is only used because it's what we've always used. And you just deal with its strangeness because you're used to it, and it still works, sure.
You could just give students a list of formulas to memorize, in which case it doesn't matter a lick which constants, notations or definitions you use, because most of the students will never learn them anyway and those who do will do so only by rote memorization. You could also just teach them to use a calculator or a computer and be done a lot faster, but you'd be doing them a terrible disservice.
Ideally you want to teach children to understand what pi (or tau) means, why it is what it is and why they use it where they do. Not because knowing this will be directly useful for most of them, in itself, or because they're likely to remember it five years on, but because the conceptual understanding is important. It is important to teach children to understand and to question what they're doing and why they're doing it, even if they forget the specifics (like what pi is) later on. Then they'll learn other specifics that do matter to their particular job or interests.
Also, tau is not more complicated to use than pi in practical problems, it's just a slightly different number, so there's really no downside. Quite the opposite for a lot of situations.
Well, I suppose because of history there's the downside that a change will require people to remember a new number and all, but that's a problem which will diminish over time.