Nothing is quite as fun as getting stuff. Especially stuff in quantity. I’m sure exactly how I will use these—the obvious is to do a hands-on simulation of exponential decay, but I bet I can come up with something cooler.
A first draft: “We’ve taked about craps, a game that uses two dice. Most games with dice use two dice. Suppose you wanted to design a game that used two hundred dice. What could it be?”
Anyway, I’ve had it on my list to buy dice because I just think I ought to have a lot of them for this class. You veterans probably already have your dice in vast quantities, but for the record, in Summer 2010, the best deal I coud find was at, of all places, Amazon. $11.70 per hundred. These are the translucent, full-sized red ones in the photo. A little more expensive, but with more variety, is a product from Chessex (also cheapest at Amazon in my searching) called “pound-o-D6,” which incudes about 100 dice (seconds, but who cares?) in various colors and sizes, mostly a little smaller than the red ones.
I’ve recently been reading a new edition of a major AP stats book. Let me stipulate that the book is good: it covers the material thoughtfully. It’s well-written. It has good problems. And when I read it, I get seduced: I start to think that my course ought to be just like it. For example, I start to think that when I introduce distributions of continuous data, students ought to attend to shape, center, spread, and outliers, and that they can remember this by thinking, “don’t forget your SOCS.”
But the truth is, I don’t even want to “introduce distributions.” I want to introduce situations and then notice when distributions show up. But as I read the book, my resolve starts to soften. Should I be so relentlessly new-age-constructivist-progressive-touchy-feely in my attitude towards curriculum, or should I just get real and teach distributions? This spinelessness gets worse as we get into parts of the course I haven’t thought of as carefully: gee, if I’m not sure how to teach this, maybe I should go with the book. And more insidiously, I’m not sure whether to teach this; but it’s in the book, so maybe it’s important.
I need a good system to deal with those moments when you’re reading the news or listening to NPR and they bring up something that could fit into an actual lesson, connecting math to everyday life. This probably happens more when thinking about teaching stats than with other areas of math. Of course I have thought of clipping the article, and I have several folders on my computer, but I can never find them. Here is another attempt: blog about them! And we get a new category, Data in the News.
Onward! Yesterday’s NYT prints what appears online as a blog post by Carl Richards. It makes the point that we often assume erroneously that everything is normally distributed (yay!) and that this affects our expectations about, for example, investing. The outliers, he says, are much more salient than we think they would be. And then we get this delicious passage:
If you take the daily returns of the Dow from 1900 to 2008 and you subtract the 10 best days, you end up with about 60 percent less money than if you had stayed invested the entire time. I know that story has been told by the buy-and-hold crowd for years, but what you don’t hear very often is what happens if you were to miss the worst 10 days. Keep in mind that we are talking about 10 days out of 29,694. If you remove the worst 10 days from history, you would have ended up with three times more money.
This is interesting in itself, but in terms of my desire for kids to get data goggles and to look at claims and cry, “evidence please!” this is perfect. Because we can do just that: go online, get the data he’s talking about, load it into Fathom, and see if this claim is correct.
This is another topic I want to write about. I did speak about it a few years ago at Asilomar, but it’s still kinda half-baked and is worth revisiting here because of how it fits with what I want to do in class this year. It will be interesting to look back in May and see what its role was. So, here we go:
Like many math educators, I used to dismiss the “measurement” strand. I thought of it as the weak sister of the NCTM content standards, nowhere near the importance of geometry or algebra, or even the late lamented discrete math. But I have seen the light, and now it’s one of my favorites. Not for how NCTM represents it, but for the juicy stuff that got left out.
I like the “rule of three” slogan of the title: Invented, inexact, and indirect. Oddly, I have trouble remembering it, and I created it. This suggests that something is wrong—but for now, let’s proceed as if it were perfect.
For me, well, none of them are in statistics yet, but maybe that’s a place where I can contribute when I make that list.
So I tried to get started. One place to look for statistics standards is in the GAISE materials. That’s Guidelines for Assessment and Instruction in Statistics Education, put out by the American Statistical Association (ASA) and designed to elaborate on the NCTM Standards. These guidelines come in two downloadable pdf books, one for pre-college (that’s us!) and another for postsecondary. In our book, they define three levels, named A, B, and C. These do not correspond to elementary, middle, and secondary; many high-school students (not to mention adults, not to mention me) have not fully mastered the ideas in levels A and B.
Tyranny of the Center: a favorite phrase of mine that I keep threatening to write about. Here is a first and brief stab, inspired by my having recently used it in a comment on ThinkThankThunk.
In elementary statistics, you learn about measures of center, especially mean, median, and mode. These are important values; they stand in for the whole set of data and make it easier to deal with, especially when we make comparisons. Are we heavier now than we were 30 years ago? You bet: the average (i.e., mean) weight has gone up. Would you rather live in Shady Glen than Vulture Gulch? Sure, but the median home price is a lot higher.
We often forget, however, that the mean or median, although useful in many ways, does not necessarily reflect individual cases. You could very well find a cheap home in Shady Glen or a skinny person in 2010. Nevertheless, it is true that on average we’re fatter now—so when we picture the situation, we tend to think that everyone is fatter.
One of my goals is to immunize my students against this tendency to assume that all the individuals in a data set are just like some center value; I think it is a good habit of mind to try to look at the whole distribution whenever possible. Let’s look at a couple situations so you can see why I care so much.
I am not quite done with jet lag. I think I’m trying to hang onto being away, it was so delicious.
I love travel. In my other life as a freelance science-and-math educator, I attended conferences and traveled a lot. Now the schedule does not permit it much, so I guard my opportunities carefully. Summer is the big chance.
So: ICOTS. The International Conference On Teaching Statistics. Held every four years. 2010 was in Ljubljana. (Huh? The capital of Slovenia. Oh. You mean Slovakia? No, Slovenia. Just to the right of the top of Italy. Under Austria. Part of the former Yugoslavia. Forests. Mountains. Caves. Castles. Gelato. Tied USA 2-2 in the World Cup even though we maybe shoulda won.)