Before I talk about group work in a math class, I would like to reassure you, dear Unfogged commenter, that I would not have compelled you to work in a group, if you were in my class. I would have read your pained expression and invited anyone who preferred to work alone to do so.

So, creating well-functioning groups in a math class is very tricky. The biggest problem, in my opinion, is that when a group contains students with a wide range of abilities, the slower students do not have a chance to ponder a problem and try to brainstorm, and build their skills of working through problems, and have their own insight, because they're just hanging on, trying to keep up with the faster students. (So it actually serves me very well to peel you off into your own group of one, dear reader.)

I hit upon a system that worked pretty well in Real Analysis this semester, which was to ask students to self-sort according to how closely they wanted me to hover. There were roughly three categories of independence. The students who elected to have me hover most closely were the students who are most clueless in the class.

The part that I think is interesting is how the self-sorting went between the intermediate-supervision and the highly independent groups. The highly independent group was mostly fast thinkers who throw a hundred wildly wrong ideas up on the board, race through them, arguing like mad, and do develop a pretty good understanding of the material on their own, although sometimes I come over and say, "Guys. You are 100 miles off course. I love this exploration, but in the interest of time, let me steer you back over here." The middle group was mostly slower, methodical thinkers, who tend to stare at the board for longer and write much less on the board, but when they put something up, it is usually a correct step. They're more likely to just get writer's block, so to speak, where they are all just standing quietly and finally admit that none of them know what to do. Usually they don't need an answer so much as for me to point their attention: "So remind me what you all were thinking about when you wrote this inequality over here?" Both groups tend to solve problems in equal lengths of time.

I can very much relate to both spaghetti-on-the-wall and methodical concentration. They're both useful skills and they complement each other, and they feel very different when you're in the zone of each one. Spaghetti thinking can lead you to believe you understand something when you really don't, whereas if you can write your answer methodically, you can trust your thinking. Methodical thinking can leave you feeling stuck when you need a lateral jump. The goal should be to be able to switch back and forth, as needed for a problem.

Spaghetti thinking came naturally to me, and I had to be trained in methodical thinking as a teenager and adult. I don't know how universal that part is.

This probably has a name in the psychological or economic literature, but one thing I haven't seen discussed is that we weight the risk of dangers that are endemic differently from that of dangers that we think will pass, even if the danger itself doesn't change.

A somewhat deadly virus that will hang around for a year? Hunker down, take extreme measures to keep yourself, your family, and your community safe.

Two years? Oof, keep it up, but everyone is going to cut some corners to find joy and human connection, and we understand.

Forever? For the foreseeable? This is when I think it makes sense to stop tolerating all but the least disruptive countermeasures and throw ourselves on the mercy of fate. And this where I am with Omicron. I've been very careful throughout the pandemic, but if we're not going to be able to wait this out, then I'm going to go back to indoor pools and museums and restaurants. At some point, I expect I'll give up the N95 for a more comfortable mask, too.

It's hard to say what's "normal" for a human life, given the ways we've lived across the centuries, but I'm pretty sure that not gathering together, or having a medical-grade mask on whenever we do gather, isn't it. Unfortunately, this position is too damn close to unimaginably stupid position of the American right, but I'm not sure what to do about that, except get your boosters, do a home test if you're symptomatic, and don't be a moron.

Teofilo writes: Barbados is now a republic. It's a perfect opportunity to give them South Carolina.

Heebie's take: Is South Carolina the state with most for us to gain if it were given away? Or were you just being politely deferential about Texas?

So it says in the article that Barbados declared independence 55 years ago to the day, and just now was successful, but it doesn't say why now. Is this something that was waiting on Barbados to bite the bullet and cut the last tie? Or is this something that the Queen finally relented on allowing some ceremonial cutting of symbolism?

So this article claims that D-K is probably not real. The explanation isn't quite spelled out well enough for me, though. Here are the explanations:

1. A computer randomly generating data for self-assessment and test results produces results that look just like D-K. (For some reason, the graph demonstrating this is written in XKCD font?)

2.

In Dr. Nuhfer's own papers, which used both computer-generated data and results from actual people undergoing a science literacy test, his team disproved the claim that most people that are unskilled are unaware of it ("a small number are: we saw about 5-6% that fit that in our data") and instead showed that both experts and novices underestimate and overestimate their skills with the same frequency. "It's just that experts do that over a narrower range," he wrote to me.

To me, this is really confusing. My confusion hinges on the explanation of DK, which isn't what I thought DK was. I thought DK meant that experts are more accurate at assessing their own ability than laypeople are. But according to the link, DK actually cares about whether you're overestimating or underestimating your ability:

If I am terrible at English grammar and am told to answer a quiz testing my knowledge of English grammar, this bias in my thinking would lead me, according to the theory, to believe I would get a higher score than I actually would. And if I excel at English grammar, the effect dictates I would be likely to slightly underestimate how well I would do.

So then, the hot take at the link is just confirming what I thought DK meant all along? That it's about accuracy, and who cares whether your ballpark estimate is slightly too high or too low?

FWIW, the computer generated XKCD-style graph replicated the paper's meaning of DK, I guess.

3. It occurs to me that the first quote in 2 could be implying something entirely different - an artefact of how we give tests. In other words, you get an A if you're in a very narrow 10 point range out of 100, and you fail if you're in a large 60 point range out of 100. Therefore if experts have a narrower range, they're not necessarily more accurate in a meaningful sense, because no one actually uses the 100 point scale linearly.

(It would be easy to just test D-K in an area entirely unrelated to giving tests that are scored on a 100 point A-F, though.)

4. Regression to the mean - this link says it's not just regression to the mean:

It's not just Dr. Nuhfer and his Numeracy papers. Other academic critics have pointed the finger, for example, at regression to the mean.

But as Patrick McKnight points out, regression to the mean occurs when the same measure is taken over time and we track its evolution. If I take my temperature every morning and one day spike a fever, that same measure will (hopefully) go down the next day and return to its mean value as my fever abates. That's regression to the mean. But in the context of the Dunning-Kruger effect, nothing is measured over time, and self-assessment and performance are different measures entirely, so regression to the mean should not apply.

I thought regression to the mean meant that outliers usually have many contributing factors, and so if you take another measurement, it's likely that not all the factors line up quite the same way. I could see it working like this: the bottom quintile and the top quintile are composed of two types of students: students who would get the same score if you tested them every day for a week, and students who had an unusual day, so they underperformed/overperformed according to whether they're at the bottom or top quintile. Whereas if you're in the middle quintile, you have three types of students: students who performed as expected, students who overperformed, and students who underperformed. So if you average the predictions of the middle quintile students, their errors average out to being fairly accurate. If you average the predictions of the bottom quintile, the students who underperformed have overestimated their performance and pulled the average prediction up. Likewise, if you average the predictions of the top quintile, the students who overperformed will have underestimated their performance, and pull the average prediction down.

I draw no conclusion.

(via firefox pocket)

Minivet writes: Jesus Christ:

In the past six years, the European Union, weary of the financial and political costs of receiving migrants from sub-Saharan Africa, has created a shadow immigration system that stops them before they reach Europe. It has equipped and trained the Libyan Coast Guard, a quasi-military organization linked to militias in the country, to patrol the Mediterranean, sabotaging humanitarian rescue operations and capturing migrants. The migrants are then detained indefinitely in a network of profit-making prisons run by the militias. In September of this year, around six thousand migrants were being held, many of them in Al Mabani. ... "The E.U. did something they carefully considered and planned for many years," Salah Marghani, Libya's Minister of Justice from 2012 to 2014, told me. "Create a hellhole in Libya, with the idea of deterring people from heading to Europe."

Perhaps the most valuable help comes from the E.U.'s border agency, Frontex, founded in 2004, partly to guard Europe's border with Russia. In 2015, Frontex began spearheading what it called a "systematic effort to capture" migrants crossing the sea. Today, it has a budget of more than half a billion euros and its own uniformed service, which it can deploy in operations beyond the E.U.'s borders... A spokesperson for Frontex told me that the agency "has never engaged in any direct cooperation with Libyan authorities." But an investigation by a coalition of European news organizations, including Lighthouse Reports, Der Spiegel, Libération, and A.R.D., documented twenty instances in which, after Frontex surveilled migrants, their boats were intercepted by the [Libyan] Coast Guard. The investigation also found evidence that Frontex sometimes sends the locations of the migrant boats directly to the Coast Guard.

Heebie: oh god, that article is awful. (I mean the situation is awful.)

This is intended to be our system for checking in on imaginary friends, so that we know whether or not to be concerned if you go offline for a while. There is no way it could function as that sentence implies, but it's still nice to have a thread.

Episode Kobe six.

LW writes: House arrest for unwelcome candidates.

Home threats, dead animals and exterior vandalism.

Step 1 is threats alone. A DOJ memo and hopefully subsequent action is an ok start at addressing those, but I am afraid that this is a trajectory worth understanding. Thinking about places that are worse now goes against exceptionalism, one more way it's hard to talk to the other America.

Heebie's take: The first link is wild:

Zudikey Rodríguez , candidate of the PRI-PAN-PRD coalition for mayor of Valle de Bravo , in the State of Mexico, was deprived of her liberty by hitmen of the Michoacan Family on Tuesday, May 18, 2021, just a few days before that the midterm elections will be held.

Rodríguez had come within two points of Morena's candidate , Michelle Núñez . Unknown people tore her from a political rally and transferred her to Tejupilco.

In a gap, aboard a truck, one of the top leaders of the Familia Michoacana was waiting for her.

...In the days that followed, Zudikey's propaganda was removed from poles, screens and public spaces: it was clear that organized crime had directly intervened in the political development of the municipality.

I gather she is an Olympic runner turned reality show contestant turned politician. I'm guessing the fact that she is well-known and well-liked protected her a bit, and that's why she wasn't outright killed? It seems easier to kill someone than place them under house arrest. Although maybe if you're not worried about consequences whatsoever, you sometimes decide not to kill people anyway?

The second link is happening nationwide, I think: rightwing extremists have been mobilized to direct their anger and violence at school board members in the name of stopping mandatory masks and CRT. I'm at such a loss.