We need pedagogical research on τ (tau) versus π (pi)!

After reading a bit of a wikipedia talk page (which I may or may not continue to read), I have a thought:

I'd like to see a relatively-large-scale study done comparing the pedagogical success of "π" (pi) versus "τ" (tau) with students learning the relevant mathematics (trigonometry; perhaps other things?) for the first time.

Because it seems to me there's a hypothesis that's been proposed: that τ is a better pedagogical tool for teaching the relevant trigonometric concepts than π is.  There's a bit of anecdotal evidence for this, but anecdotal evidence is at the very bottom of the hierarchy of evidence, so it seems to me we can do better.

So I'd like to see us go up the hierarchy at least as far as a cohort study (the middle of the hierarchy as listed), with a cohort divided into groups that learn π, and groups that learn τ, and see how they do, both initially and over a more extended period of time, in their skills in the various mathematical concepts.

I can immediately think of 4 main possible outcomes (perhaps there are more?):

1. There is strong support for the hypothesis within the cohort;
2. There is strong evidence _against_ the hypothesis within the cohort;
3. There is strong evidence that it makes little difference; or
4. The evidence is not strong, in any particular direction.

My (admittedly biased) hope and estimation is that #1 would be the outcome, but I'd honestly be happy to learn of #2 or #3, provided I thought the study was well-designed and well-executed.

For any of the first 3 outcomes, though, it strikes me as something that could settle the debate a bit.  And for the 4th outcome, hopefully that would also come with insights into how to improve future research in the area.

Now, I'm not a researcher, and I'm not particularly learned in pedagogy, especially as relates to childhood mathematics instruction, so... I don't feel prepared to do much with this.  But perhaps I could help facilitate it some way?  If someone with more relevant skills wants to collaborate with me, I'd be happy to do some work towards putting together a crowd funding campaign, or some such thing.

Anyway, I hope you all had a nice half-circumference / radius day.  Because pi is (still) wrong, and, while I'm failing to find the source for this at the moment (hopefully I will at some point, and can update this post), so is the notion that π became "3.14..." by being the ratio of circumference divided by the diameter.  My understanding (based on the source I'm failing to find) is that it was actually defined as the ratio of the half-circumference divided by the radius.  So, even Vi Hart's above-linked video is a little bit wrong (though mostly it's just a wonderful work of rant-art).  C/2r isn't C/D, it's (C/2)/r... hopefully I'll find the reference to prove it.  (Not that it's not also C/D, just that that's not how π was defined in the article that popularized π as a symbol referring to that particular constant.)

Let's take a new τurn, shall we?

The world will be better if I share my ideas...

I've come, just moments ago, to a conclusion: The world will be better if I share my ideas (with the world). This means I'm going to blog here about some ideas that I've long been considering to be more or less "trade secrets" or something. Inventions of mine, in concept, that I think the world should have. And frankly, I'm never going to make all of them happen. And I'm also never (until I die, that is), or at least I hope I'll never, stop having more of them. So sharing some now won't preclude me from making a billion dollars off them later. Well, it might keep me from making a billion dollars off the one I share, because someone else might go do them before I do. But if I'm not going to do all of them anyway, I might as well let that happen, and hope that my life can be improved for having access to the thing I wanted enough in the first place to dream it up. That said, if I happen to get any readers that are in a position to fund a startup to make some of these ideas fly, I'd be happy if you'd drop me a line before starting something going. Chances are good that I've thought about this (whatever idea it happens to be) in more depth than has made it to the blog, and perhaps for some stock in a startup, I'd be happy to be on an advisory board or something. Or maybe, for some of the ideas, I'd even be up for launching the company myself, with the help of your financial resources (and, then, by hiring the requisite number of Really Smart People to make it all happen -- hopefully, the Done, and Gets Things Smart sort of people. Sorry I keep picking on you, Steve). But really, I think the world will benefit just as much, and probably more, from someone else taking these ideas and running with them, than by helping me to run with them. I'm overburdened or something. (Which goes into a whole different story, which will likely find its way into this blog in some form or other over time. Today is not that time.) So yeah. Any idea that I don't have an expectation that I'm particularly likely to try to put into practice on my own is now fair game for me to blog about. Here's hoping the world will benefit from it. This all begins with the next post.