Near the bottom

An interesting new theory on “what’s the matter with Kansas”: voters who feel they are near the bottom of the economic pyramid worry that income redistribution will help those who are even worse off (based on a study discussed by The Economist; via daringfireball.)

But this is not really so different than the idea that no one wants to admit (to themselves or anyone) that they’re amongst the worst off in America.

The nuance here is that if you suspect you’re near the bottom, your situation feels the most precarious, because a re-shuffling could easily put you at the bottom. For the middle class, that’s less of a worry. But it’s there. After all, any change to the status quo is scary.

Concerns about math games

Explorations in Math is an interesting Seattle organization that I have been learning about recently. I went to their volunteer training last week and have been discussing my thoughts with family and friends ever since. Those conversations have hugely helped to clarify my concerns. The conclusions deserve to be written down.

This is the draft of a letter to Explorations in Math:


What I Like

That’s easy — I fully share your mission to help all elementary students succeed in math. I think this is one of the most important goals there is. You are clearly making a difference and changing attitudes and that is awesome.



These concerns are largely spurred by books I have read about education psychology. They make me nervous that some aspects of Explorations in Math’s approach could be counterproductive.


1. Losing games may perpetuate students’ assumptions that they are bad at math.

Most of the math games have winners and losers. If a student consistently loses the games, doesn’t that reinforce the notion that they are bad at math? Weaker students can be paired with other weaker students so that they do not always lose. But kids know what is going on. They know they are in the “dumb group”. Even if they still enjoy playing the games, do they gain any confidence in their math abilities? One of the success stories that Explorations in Math gives is the observation that kids start playing math games of their own accord while waiting in lines. Are all of the kids playing? Or only the ones who consistently win?


2. Sugar-coating may perpetuate the idea that real math is hard and boring.

I don’t doubt that games are a good way to teach and learn some math concepts. But I worry that it sends the underlying message that math needs to be sugar-coated in order to be fun. After all, we don’t need to resort to games to teach reading. Instead, we give students reading materials of increasing difficulty level, with content that is interesting to them, and help them progress. We can do the same in math with well-designed curricula, teaching students how to solve math problems on topics that interest them, at gradually increasing levels of difficulty as they master each concept.


3. Arithmetic is one of the least interesting parts of math.

Most of the math games center around mental math and memorizing multiplication tables. These are important building blocks. But the really interesting aspect of math is the ability to answer a wide range of questions with just a few simple tools (such as fractions and algebra). Mental math helps students understand these tools by allowing them to solve problems quickly, without a calculator. But in the real world, we use calculators and computers to do the calculations, and the important skill is being able to translate everyday problems into math problems. The further you progress in math, the more uncommon it is to see actual numbers. Instead, you work to understand abstractions and learn how to model the world and make precise predictions.


4. I don’t see any hard evidence of results.

The Explorations in Math website includes great testimonials and anecdotes. But have math test scores improved in the schools you have worked with? In particular, have scores gone up among disadvantaged and historically weaker students? I’m as disillusioned with “teaching to the test” as anyone, but the tests do measure students’ math ability. If you are improving attitudes but having no effect on test scores, what has really been accomplished? The recent documentary Waiting for Superman points out that American students score among the lowest of developed countries in math scores, but score higher than anyone in confidence. Confidence is only useful if it is backed by reality.


It may be that the real problem is that all of our hands are tied by the school board’s mandated, poor choices of math curricula. Is Explorations in Math designed to be a side-run around that very stubborn obstacle? Is it designed as the best approach given the constraints?

Another good question

As a teacher, you are in the business of helping our children learn, grow and change. If you are not also willing to learn, grow, and change, then what reason do we have to believe that you will be a good teacher?


“I was on the side of righteousness, and like any fundamentalist, I could only stay there by avoiding information.”

-Lierre Keith, The Vegetarian Myth

Wikipedia trivia

“Wikipedia trivia: if you take any article, click on the first link in the article text not in parentheses or italics, and then repeat, you will eventually end up at ‘Philosophy’.”


It’s true. I tried it. I couldn’t resist.

Technological transitions lead to income inequality

“After a great technological revolution or a major economic transition, as when America changed from a nation of farmers to an urban industrial one, there is often a period of great concentration of wealth, and with it, a concentration of power in the wealthy. That’s what we saw in 1928, and that’s what we see today. At some point that power is exercised so injudiciously, and the lives of so many become so unbearable, that a period of reform ensues.”

“[There is no reform when] it is not public opinion but the opinions of the wealthy that predict the votes of the Senate.”

-Drew Westen, What Happened to Obama? (NYTimes, Aug 6, 2011)


From one of the most important slides I’ve seen on computer security:

“Security dialogs are a black box; clicking Permit or Allow maximizes the likelihood of getting work done.”

From WWDC ’11, session 203, 10:47, by Ivan Krstic.