good math education

In case some of the two or three people who read this blog don't also read Crooked Timber, I highly recommend Lane Kenworthy's post on how to visually display income inequality levels over the last 40ish years. To me, this is a more mathematically complex version of what I would like students to be learning in math classes: how to represent real-world information in abstract terms so that the information is communicated clearly and can be understood and analyzed better than it could with a verbal description. Kenworthy also articulates the representational choices he made, notes other possibilities, and explains why he showed the information as he did.

If you can do that - which practically none of my students, and damn few adults I know can do - you're less vulnerable to bad data or misleading claims in news accounts; and you can have some idea how to break down public information to find what's noteworthy about it. Of course, Kenworthy's a professional, so maybe he shouldn't count.

If I could have a couple of ideas stuck in every math student's head, here's what they'd be:

1. Numbers only mean something in context, and that context has to be meaningful. If 121 Iraq and Afghanistan veterans committed or charged with murder, is that great or catastrophic news given the general homicide rate? Given the homicide rate for veterans of previous wars? Given the homicide rate among non-combat veterans? Nobody knows from that article. As a subset of this, you need to read the context and justification for any data - including rates - that you read. Should incarceration rates be of US adults? Of all residents?

2. Dollars are an arbitrary unit whose value varies. Same with other currency. You need to adjust for inflation to understand any economic data.

3. Translating real-world information into mathematical terms always involves some simplification. It's important to check what simplifications happen, and whether you buy into them. Do you count someone as unemployed if they're not looking for work because they got sick of it? Current answer: no. What if they're working part-time and want a full-time job? Current answer: still no. These simplifications are incredibly helpful, but they can also be really tricky.