In my daily search for new and interesting news, I recently came across an interesting post on the site of the Carnegie Foundation for the Advancement of Teaching. It was written by a mathematician who was expanding on remarks Paul Krugman made in his blog about economics.
Krugman wrote, "I'll be using this space to present the kind of information I can't provide on the printed page -- especially charts and tables, which are crucial to the way I think about most of the issues I write about." Krugman then introduces a graph that presents a picture of income distribution in the country by displaying the share of total income earned by the richest 10 percent of Americans.
The mathematician, Michael C. Burke, then goes into an interesting discussion about Krugman's observations on the seemingly idyllic period of the 1950s -- the time during which "Middle Class America" became the symbol that it was for much of the '70s and '80s and into the '90s. America's golden period of equality. Krugman had supplied a chart of income distribution, which showed a relative flat period in which income was more equitably shared. In case anyone was unclear, such equality no longer exists in America. Since the 1980s -- the late '80s especially (and I suspect that has a lot to do with the tax reform act of 1986, though I'm no economist) -- the United States has seen its share of income diverge quickly. To show that this isn't simply about which party is in power, the Democrats were in power in Congress during the late '80s and the Republicans had their Newt Revolution in the mid '90s, when Krugman's "Great Divergence" occured; moreover, Reagan and Clinton were the presidents at those respective times.
But Burke has a broader comment to make. He calls for teachers -- especially college professors -- to redesign their curricula.
[M]y larger point here is that the content of our thoughts and the depth of our understanding are dependent on the tools we bring to the task. What we think is intertwined with how we think. And the ability to think in terms of quantitative data, in terms of tables and graphs, is indispensable for understanding our modern world. This should be part of what we teach all our students -- not just students in selected courses or selected majors.
With that aim in mind, I would propose that we begin by redesigning our freshman and sophomore writing programs in order to place a significant emphasis on working with quantitative data, and on the visual representation of that data. We write, after all, to figure out what we think. And we ask our students to write so that they will learn how to think.
This is not the first time I've heard this argument, but I think Burke proposes it well. I don't work as a professor, though I was trained as a teacher, and I've toyed with the idea of tutoring math and English on the side -- perhaps as soon as next fall. Burke is right, in my opinion, but I'm not sure whether his direction is the right one; I think he's right that we need to inform our youth better about how to think and how to recognize absurdities in mathematical "answers." But I think it goes beyond teaching freshman.
I heartily recommend that everyone read John Allen Paulos's book Innumeracy. He cleverly points out how badly most Americans -- not simply students -- handle simple math problems. Percentages, probabilities. He helps readers recognize the flaws in their reasoning. If we can teach a couple generations of Americans how to reason, boy that would help improve our state in the world.
