Data manipulation

To plan a statistical hypothesis test, specify the model you will use to test the null hypothesis and the parameter of interest. Of course, all models require assumptions, so you will need to state them and check any corresponding conditions.

When the conditions fail, you might proceed with caution, explicitly stating your concerns. Or you may need to do the analysis with and without an outlier, or on different subgroups, or after re-expressing the response variable. Or you may not be able to proceed at all.

Intro Stats (De Veaux, Velleman, Bock)

Science is not intuitive

From the trenches of science, it’s easy to label evolution deniers and global warming skeptics as dumb or at least uninformed. But we should remember that the scientific method is not an intuitive process, and takes a lot of time to learn.

For one thing, the scientific method is based on probabilities, which humans famously misunderstand. We play the lottery because we have a chance of winning, even though that chance is vanishingly small. We tend to think of very large or small probabilities as less extreme than they actually are, so when scientists say there is a 95% chance (or even a 99.9% chance) that, say, smoking causes cancer, it is easy for us to simply hear “they’re not sure.” Intuitive science is based on stories and anecdotes, rather than quantifiable statistics. We might pray and then find out that our friend returned to health. So there’s “a good chance” that the one caused the other. Isn’t that the same as scientists saying “there’s a good chance” that antibiotics were the cause of her recovery?

For another thing, it’s not immediately obvious that we need controls and placebos. If we want to find out whether an intervention works, why would we do an experiment that doesn’t actually use the intervention? Worse, isn’t it morally wrong in many cases to not give the intervention? In order to prove that an educational or healthcare strategy is effective, we have to not use the strategy in some classrooms and hospitals. Scientists are monsters!

These are just the first few tricky aspects of science that come to mind. As I re-read the Intro Stats textbook, I’m reminded how subtle a lot of this is, and how even professional scientists can sometimes get it wrong. That doesn’t mean we should be skeptical of science as a whole, though science itself relies on a healthy skepticism of individual results (another subtle distinction!). It does mean that scientists and journalists should try to explain the scientific process, over and over, day after day, when presenting results to the public. Because if you’re not doing science every day, it’s easy to forget how it works.

I hope to do what I can to help everyone do more science every day.

Three Cups of Tea

Apparently, a lot of people have read Three Cups of Tea, the book about Greg Mortenson’s work building schools in rural, mountainous Pakistan. Many have written reviews, and some have disputed his details (though not the broader story).

The normal reaction is to be amazed and inspired by the tenacity and success of this unusual character. And I don’t want to downplay that too much. But I look at the story from the perspective of Malcolm Gladwell’s Outliers; Carol Dweck’s Mindset; and Dan and Chip Heath’s Made to Stick (among other important books).

From those perspectives, here is a very unusual American who is most comfortable living with and working to help rural, mountainous tribes halfway across the world. It is no great mystery why he is good at that; Mortenson grew up in a foreign country with both parents dedicating their working lives to charity projects. He served in the army, learning to cope with discomfort and yet more foreign cultures and situations. He went to nursing school, learning to listen and care for patients. And finally, he spent many years practicing rock climbing and mountaineering, learning to survive in that sparse, rugged landscape. When he stumbles into Haji Ali’s village, he finally, miraculously, finds himself at home.

From that perspective, here is the story of a man who desperately, tenaciously tries to find a way to return to what he is most comfortable with. Psychologically, he is not unusual. What’s unusual is his exotic set of skills.

It’s easy for us to read this story and think about how hard it would be to leave home, live in medieval conditions for months, and organize the building of schools in hostile political and geographical terrain. But that is because we, unlike Mortenson, do not have extensive training doing charity work in primitive and hostile environments, and we do not feel at home in foreign countries.

From this perspective, I think the most interesting (and entertaining) aspects of the story are what he is not good at.

First, fundraising. He writes five hundred letters to celebrities he has never met. Later, he gives slideshow after slideshow all across the country to audiences essentially at random. He certainly understands tenacity; that’s how you win at rock climbing. But the way you win at fundraising is through connections and the media. The only significant money Mortenson ever received was accidental. A friend with connections to the mountaineering society writes an article for their newsletter, which is noticed by a wealthy ex-climber. Later, soon after 9/11, a journalist friend passes the story to a leading magazine, whose editors for the first time figure out how to describe the charity in a way that sticks: “books, not bombs.” Their cover story finally generates widespread donations. In all, Mortenson wastes years of time doing poorly thought out fundraising that has a minuscule probability of success. He read countless books on southeast asian culture and politics, but no books on effective fundraising. He should have responded to his failure by learning more or asking for help. He worked hard, where he should have worked smart.

Second, delegating. Here, Mortenson gradually improves over the course of the story. He delegates tasks that he is obviously not prepared for, such as driving, bargaining, and translating. But he only stops micromanaging the construction of the schools after Haji Ali (his most trusted mentor) walks him up a mountain and forces him to relent. And throughout the story he continues to insist on personally overseeing all of the projects that the organization undertakes. The board eventually convinces Mortenson to hire a few assistants for donor relations, website, etc., but he never hires another person to do the core work of overseeing the charity projects. In other words, he is ineffective at scaling the organization beyond what is essentially a one-man show. Again, this is not surprising, given that Mortenson has no training or experience in management. But he does not study management nor hire managers to make up for this shortcoming. Instead, he keeps the organization small.

If Mortenson’s true goal was to serve as many needy communities as possible in the rural Himalaya, he would be expanding the organization by training new generations of staff and volunteers to do the same work that he does, and he would be hiring fundraising and publicity experts to spread the word and apply much-needed political pressure.

But that’s not his goal. His goal is the same as all of us. To find our way home.

It’s hard to blog about great books

It bugs me that I still have not written up blog posts about some of the very best books I’ve read. In fact, my very first blog post was an unfulfilled promise to follow up with interesting thoughts on Zen and the Art of Motorcycle Maintenance. There was too much to say, and not enough time to say it.

I think it’s true in general that the best books are difficult to summarize. Whereas I can easily summarize in a blog post the important ideas of a merely decent book, the really great books are concise and nuanced and reward a full and careful reading. What can I say in a blog post to do it justice?

So perhaps I will start creating placeholder blog posts, which simply tell you that a book is so worth reading, I’m at a loss to even describe it.

Pure Heart

In college, I took a Congolese dance course taught by two elders from the Congo. One of the things they discussed with us was how the African borders drawn by European colonial powers essentially disregard the traditional nationalities and ethnic groups in Africa. For example, the cultural region of the Congo overlaps several modern African states.

I asked one of these wise men what seemed like an obvious question. Why were the borders not re-drawn after those countries gained independence?

He squinted at me and said, “What is your name?”

I answered hesitantly, “Robin…?”

He looked at me piercingly. “Robin, you have pure heart.”

“Um, thanks, I think?”

He went on to explain that power, once held, is not easily taken away. These countries had gained independence, but re-drawing borders would mean giving up power by losing land or even whole countries. The new independent rulers were no better than the colonial powers in this regard.

For some reason, this interaction has stuck with me. I don’t want to be totally naive. But I do want to be a little naive. To view the world with a “beginner’s mind” and approach tough problems with the optimism that people are capable of doing the right thing.

School gridlock

“Schools are government-run and their employees are unionized; how do you expect to get anything to change?”

-Evan Miller

Agents of change

“Children are phenomenal agents of change.”

-Jaime Lerner (former mayor of Curitiba, Brazil; via Scientific American)

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.

 

Concerns

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?