Originally Posted by Deadly
1. So ... you want to confuse them a hundred times more when they get to radians and trigonometry and all the other stuff where tau really shines and makes everything so much neater? Wouldn't it be better to accept a tiny bit of possible confusion in one area to eliminate a much bigger and more pervasive confusion elsewhere?
2. Getting a good grip on division is something I'd say is important for kids at that age. If they are scared by having to halve something when they get to circles and areas, then their education has failed them massively! If we were talking about stranger fractions rather than simply halving stuff, then maybe. If squaring something is not scary, then division by 2 should not be.
If children are intimidated by simple fractions, it is not the fault of the fractions (or the children), but of their teachers, parents, educational system and/or society as a whole.
3. You could write it as 2A=tau * r^2 if you really wanted to avoid obvious fractions. Perhaps there's even an opportunity for some lesson or (possibly visual) aid to help them better understanding the formula or division itself. As a teacher I'd probably see an opportunity for some discussion here.
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?
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.
Temperature is a state of a system base on energy and entropy, whee the higher the temperature, the more energy you feed into the system the more entropy you get. No one from age 0-17 will make heads or tails of that. They will understand hot and cold. So teach them hot an cold, and teach them the more rigorous science when they need it. Teach both!
Don't throw the baby out with the bath water.