Chapter 79.9: Innumeracy, Thy Name is Chucklehead

Thank God I'm not the only person who complains about innumeracy! In a recent column in Forbes, Rich Karlgaard rails against the "American math chuckleheads" who thought that instead of an $85 billion bailout for AIG, each Amerian adult should get their share of that amount. The problem is they don't know how to do math. While they thought the simple division meant the 200 million American adults would receive $425,000 each, it actually breaks down to $425 each.

I mean, come on, wasn't it obvious that $425,000 simply couldn't be right and that they needed to punch the numbers back into the calculator to do things over, only this time with the right number of zeroes?

Unfortunately, using chucklehead math, there's simply not enough money in the world to pay for all the math tutors required to retrain math-challenged Americans. Here's a low-cost alternative: Read John Allen Paulos's book Innumeracy and learn how to think logically. These days, we could all use a little help in the wallet.

Here's a math problem to get you started: If a coffee costs $2 at the corner store and you drink two cups a day each day of the work week, how much do you spend on coffee per month? Per year?

Short answer, too much. Long answer is $20 per week, $80-$100 per month, and $1000 per year (assuming two weeks off for vacation). Wouldn't you like to have another thousand dollars in your pocket? This is why I drink the free stuff at the office.

Thank God I don't smoke!

Chapter 69.8: A Mathematician's Proposal

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.

Chapter 60.7: The 300; New Liberal Arts

Ok, this will be a disjointed post because I seem to be citing a recent movie (that I haven't seen) and combining it with a phrase that in that context makes no sense. So let me explain: this is my 300th post since starting this blog in 2004. More than some people, a lot few than many others. Self-congratulation is now over.

As for "the new liberal arts," that comes from an interesting post I saw at MIT Online, a publication at the Massachusetts Institute of Technology. The writer, who is from the university's class of 2007, discusses social entrepreneurism and the importance of the priveleged to give something back to sociey -- not simply make buckets of money. And he recounts an alumnus who told him "Engineering is the liberal arts of the 21st century."

What an interesting comment; it might even be true. I'm becoming more and more convinced that the state of education -- particularly math and science -- is at a dangerous low in this country. I've spoken with people from Microsoft and the former governor of a major manufacturing state as well as others who have similar concerns, and they believe that American students -- and their parents -- have no idea how poor their math and science skills are.

The liberal arts comment points to how broadly necessary those skills are and will become. Technology is at the heart of nearly everything we use today -- this computer I'm typing on, the cash register at the coffee shop where you bought your cup this morning, the blinking voice mail like reminding your co-worker that she's ignoring a client -- and our future is spending it on their hand-held game or their cell phone, oblivious to irony.

We are far from a tipping point, unless it's already tipped to the negative. Getting through to the kids will not be easy. And it's entirely possible they don't care and will blame us for letting their world fall apart. It's not enough that we've taught them to read; we need to help them learn how to think. That requires math and science as certainly as it requires art and literature.

Chapter 58.314159: Good Math

Recently, the Seattle Post-Intelligencer posted a commentary calling for a commitment to emphasizing math in the schools. This call is certainly necessary, and long overdue. However, my pessimism may be getting the better of me. I'm not sure we can expect much. As the commentary states, we need better professional development of teachers, with a goal of training them to be more confident in their role. This takes time. No time like the present to start, but I think what we need to do is get math into more subjects; find where math fits into the history class, perhaps. Or make the examples in math class more accessible to kids: you have 500 songs on your iPod, what percentage of the memory is still available for more songs?

I'm not convinced the math block for many students is due to the subject matter. I think a big part of the problem is that math isn't cool. Maybe each student can have a team in a free fantasy league; each kid must keep their team under a salary cap. Work the numbers.

Easy for me to say -- I'm not teaching. Students who are bored are potentially disruptive, and one of the major challenges for education is classroom management. It takes more than teachers who are confident in their abilities to teach math, it takes teachers who are enthusiastic about teaching -- period. That involves a strong educational environment, a supportive administration, etc.

I'm all for emphasizing math, and I agree with Seattle -- home of the Bill & Melinda Gates Foundation -- being at the vanguard of a movement. But this will be a long slog, and the kids will need to see the light at the end of the tunnel. Kids don't implicitly care that the United States' position as an economic leader is imperiled without better math, science, and engineering education. They want to know what it means to them. Once that's been solved, you'll find more eager children.

Chapter 54.5: Quality Counts

A new report has me more concerned about the state of education in this country than I already was. I’ve always appreciated that I grew up in an educated, inquisitive family in an area that was also well-educated and populated with folks who had a similar educational foundation. In short, I grew up with a lot of smart people.

While I understand intellectually that not everyone is as fortunate as I am in this regard, the findings of Quality Counts 2007 are staggering. It’s bad enough that the state-by-state analysis shows that the luck of the draw can hamstring a child’s development (God forbid you grow up in the beautiful state of New Mexico, it seems to say), but what’s worse is that even some states that “excel” relative to the others don’t always post impressive numbers. The top state in middle-school math, for example, is Massachusetts, where less than half of students meet NAEP (National Assessment of Educational Progress) standards. In Washington, D.C., the figures are abysmal – less than 7 percent!

I fear the level of mathematics knowledge has dwindled to near innumeracy. Ask most kids the difference between the mean and the median and you might consider yourself lucky if they knew one of them meant "the average." The strong students are better educated; for the average ones, it seems to be a matter of where you live and whether you had a strong enough grammar school experience to create an academic foundation for the future. And with the state of public education in many areas of the country being so horrible, we're in danger of developing an enormous number of youth in this generation who don't know how to think through problems far more challenging than what a statistical midpoint is called.

I’m not afraid for the smart students, the kids on the far end of the bell curve. I’m afraid for those in the middle. They are by definition the majority of students, and if we can’t educate them better, then the consequences for the future are harrowing.

Who or what is to blame? Is the curriculum too hard? I doubt it –- life is only getting more complicated as we strive to create more convenience for ourselves. Are teachers worse? Perhaps, but they’re also products of our education system -– it’s a chicken/egg argument that isn’t feeding anyone’s imagination to solve the problem. Public policy? State initiatives? Federal initiatives? Yes to all, but it’s still not enough. The thing that galls me most is there are a lot of smart people trying to solve this problem, and no one has an answer that doesn’t involve leaving a lot of children and young adults educationally destitute. I’m open to suggestions. Personally, I’m going to learn how to tutor someone and start there.