Sometimes I think I could argue that it's not OK to beat up old ladies, and everyone would still push and shove to get first in line to argue that we should totally go beat up all the old ladies for lulz. Is there some kind of lets-argue-with-Deadly conspiracy? Do you do it on purpose?
Well, the gauntlet is down, then! Tell me what your stance on beating old ladies is. Go on, tell me I'm wrong.
Alright, alright, I'm joking But seriously, doesn't anyone ever agree with me on any of my major points?
The only argument I can see for dismissing tau is the status quo, that we don't want to bother about something new because it's not big enough to worry about, that it's not significant enough, and that's not a good argument. That's the kind of argument that leaves everything stagnant and prevents progress.
When I speak of long division specifically, I think of a particular algorithm used to calculate one number divided by another and nothing more (it is not the only such algorithm, by the way). I do not talk about division itself, or about fractions, and certainly not percentages, all of which I will agree are immensely important for kids to have a good relationship with, for the reasons you outlined.
I do not have the experience or knowledge to say whether long division is helpful or hurtful for some students in some areas, or whether some other division algorithm might be better to teach. Maybe it helps, maybe it's good practice, there are plenty of ways I can see that long division might be an aid. There are also ways in which I can see it might be hurtful and put students off division, where perhaps a different algorithm could help them. This is an area where I think the teacher's own wisdom and judgment ought to be applied, in each individual case. Sadly that's somewhat utopian, of course, but I am an idealist.
What I believe is that if a kid doesn't know long division (the particular algorithm), it is not the end of the world for them and will probably not impair their ability to understand division, fractions, percentages, algebra or anything else except maybe certain topics in number theory.
That doesn't mean long division can't be an aid or a good thing to teach, and it most certainly does not mean we should not teach kids division, fractions and all the other good things.
I hope that sets my position straight.
A teacher could simply draw a circle and say "this is a circle, it is this long around, it is this wide, now calculate!" No doubt that's how it goes often enough, and kids are familiar enough with the intuitive, common-sense notion of a circle as something round that they probably won't struggle with that.
But what if you draw an ellipse and ask, is this a circle? They may eagerly raise their hands and answer yes (or maybe they will be smart and say no), and then you'll have to say, no this is an ellipse because it's kinda less round. And sure, they'll get that too and not even blink.
But a circle is not defined as "something round that is not slightly squeezed, because then it's an ellipse". If you just want to teach kids raw calculation, as in fact is what is taught most of the time, then it's fine to just leave them with their every-day idea of what a circle is.
A circle is defined as a distance from a point, everything that lies exactly that distance from that point. It would be awkward to define a circle by its diameter, and would probably involve a sneaky radius anyway, no matter how you twist it. By the definition of a circle it is certainly more natural to use the distance from the center rather than arbitrarily doubling it when you wish to define the circle constant. And that gives you tau.
Teach kids what a circle is, not just how it looks. Save the diameter for later, because the diameter is a derived feature from the definition. That's math rather than calculation.
If you didn't have a problem with pi, I can not imagine you would have had a problem with tau either, had history looked different. But someone who struggles with pi (especially later on) may benefit tremendously from switching to tau instead, and it would be even better if they didn't have to make that switch (until they're comfortable enough with it). Therefore, start with tau!
I have never argued that we should throw out pi and never, ever use it. I've never argued that you can't use the number/symbol/name pi if you wish.
What I argue is that tau has an educational, academic, aesthetic and logical value and should replace pi as the base definition of the circle constant for both clarity and correctness.
I do not care if an engineer uses pi in their calculations, or a programmer has a constant called pi in their code, or someone memorizes a thousand digits of pi for fun. But when you teach circles and radians and other related subjects, tau ought to be the base definition from which you proceed, unless you're making a point or has some other reason to use pi in a particular example.
And there are plenty of reasons you might do that, because pi is still interesting because of how it relates to tau. I leave you with a quote from the manifesto I linked earlier, because I felt it put it well:
A lot of people think math is this sort of fixed, unchanging monument, a list of formulas to learn by rote or apply to the same old kinds of problems, that nothing new ever happens. That could not be further from the truth. A change from pi to tau could be an opportunity to teach not just the math, but also the history of math and how math is a subject in constant change where you can still discover new or better ways to do things. That would be a very positive thing to teach kids.Finally, we can embrace the situation as a teaching opportunity: the idea that pi might be wrong is interesting, and students can engage with the material by converting the equations in their textbooks from pi to tau to see for themselves which choice is better.