Graphs of the words Montessori and muddle created with Google Ngram.

If you take all the books ever written and draw a graph showing which words were used when, you’d end up with something like Google’s Ngram. Of course I thought I’d chart “Montessori” and “muddle”.

The “Montessori” graph is interesting. It seems to show the early interest in her work, around 1912, and then an interesting increase in interest in the 1960’s and 1970’s. Like with all statistics, one should really be cautious about how you interpret this type of data, however, I suspect this graph explains a lot about the sources of modern trends in Montessori education. I’d love hear someone with more experience thinks.

Another nice resource that provides neat graphs of real data that are easy for students to understand is Pollster.com. The graphs of survey results are constantly updated and, if you want to, you can go into how they were created (survey questions, averages etc.). They’re great for current event discussions and research projects.

In addition to the national polls, like the president’s job approval (see below), the site also has charts for state level races, like for governor, which are handy around election time.

Pollster.com aggregates polls, because, depending on how a question is phrased, each poll will have it’s own bias. However, since not all of the poll data is freely available to the public, the sites of the major polling organizations, like GALLUP, are also quite useful. The polling organizations tend to have a much wider variety of poll results available. Gallup in particular provides some very nice graphs.

Normal distribution with 95% unshaded. Adapted from Wikimedia Commons.

A discussion of statistical significance is probably a bit above middle school level, but I’m posting a note here because it is a reminder about the importance of statistics. In fact, students will hear about confidence intervals when they hear about the margin of error of polls in the news and the “significant” benefits of new drugs. Indeed, if you think about it, the development of formal thinking skills during adolescence should make it easier for students to see the world from a more probabilistic perspective, noticing the shades of grey that surround issues, rather that the more black and white, deterministic, point of view young idealists tend to have. At any rate, statistics are important in life but, according to a Science Magazine article, many scientists are not using them correctly.

One key error is in understanding the term “statistically significant”. When Ronald A. Fisher came up with the concept he arbitrarily chose 95% as the cutoff to test if an experiment worked. The arbitrariness is one part of the problem, 95% still means there is one chance in twenty that the experiment failed and with all the scientists conducting experiments, that’s a lot of unrecognized failed experiments.

But the big problem is the fact that people conflate statistical significance and actual significance. Just because there is a statistically significant correlation between eating apples and acne, does not mean that it’s actually important. It could be that this result predicts that one person in ten million will get acne from eating apples, but is that enough reason to stop eating apples?

It is a fascinating article that deals with a number of other erroneous uses of statistics, but I’ve just spent more time on this post than I’d planned (it was supposed to be a short note). So I’d be willing to bet that there is a statistically significant correlation between my interest in an issue and the length of the post (and no correlation with the amount of time I intended to spend on the post).