Teaching Fractions

Monday, September 30th, 2013

Many students cruise along just fine in math — until they hit fractions:

National tests show nearly half of eighth-graders aren’t able to put three fractions in order by size.


Knowing how to place fractions on a number line in third grade is a better predictor of kids’ fourth-grade fraction skills than calculation ability, working memory or the ability to pay attention, according to a recent study of 357 children headed by Nancy Jordan, an education professor at the University of Delaware, Newark’s Center for Improving Learning of Fractions. The effect continues at least through fifth grade, based on recent research, Dr. Jordan says.


A child’s knowledge of fractions in fifth grade predicts performance in high-school math classes, even after controlling for IQ, reading achievement, working memory, family income and education, and knowledge of whole numbers, according to a 2012 study led by Bob Siegler, a professor of cognitive psychology at Carnegie Mellon University.


“If you don’t understand fractions, it’s literally impossible for you to understand algebra, geometry, physics, statistics, chemistry,” Dr. Siegler says. “It closes a lot of doors for children.”

The Science of Trips and Falls

Monday, September 30th, 2013

Shirley S. Wang reports on the science of trips and falls:

The body has three main systems that help us stay balanced. The visual system takes in information from the outside world and transmits it to the brain. The proprioceptive system, which incorporates sensory systems throughout the body, tells us how the body’s parts are oriented relative to each other. And the vestibular system, located in the inner ear, focuses primarily on how the head is moving. Generally, if at least two of these systems are impaired, people tend to have trouble with balance.

As people age, the vestibular system becomes less sensitive. Instead, individuals tend to rely more on their vision, which is relatively slow compared with the vestibular system. As a result, older people don’t process information as quickly to correct for missteps, Dr. Cullen says.


After a fall, older people often say they tripped or slipped. Researchers at Simon Fraser University, in Burnaby, British Columbia, wanted to observe what really happens. The team outfitted a long-term-care facility with video cameras and recorded residents going about their daily lives. They recorded 227 falls from 130 individuals over about three years. Tripping caused just 1 out of 5 of the incidents. The biggest reason for falling—accounting for 41% of the total—was due to incorrect weight shifting, like leaning over too far, says Stephen Robinovitch, a professor in the biomedical physiology and kinesiology and engineering science departments. Other, less frequent reasons for falling included loss of support with an external object, like a walker, or bumping into something.

Spring Has Sprung

Sunday, September 29th, 2013

This Tragedy comic reminds me of the giant-hornet situation in China — even if it’s more of a late-summer phenomenon:

Tragedy 398 Spring Has Sprung

Giant-Hornet Attacks

Sunday, September 29th, 2013

Dozens have died and hundreds have been injured in giant-hornet attacks in central China:

The hornet attacks are a recurring problem in the area from May to as late as November. According to Ankang police, 36 people died in the city and 715 were injured by the creatures between 2002 and 2005. But Zhou said the issue had been particularly severe this year, possibly because of weather changes.


The culprit appears to be the Asian giant hornet or Vespa mandarinia, which grows up to 5cm long with a 6mm sting, although the area is also home to the smaller Asian hornet, Vespa velutina nigrithorax.

Yeah, the Asian giant hornet is pretty terrifying:

The stinger of the Asian giant hornet is about 6 mm in length, and injects an especially potent venom that contains, like many bee and wasp venoms, a cytolytic peptide (specifically, a mastoparan) that can damage tissue by stimulating phospholipase action, in addition to its own intrinsic phospholipase. Masato Ono, an entomologist at Tamagawa University near Tokyo, described the sensation as feeling “like a hot nail being driven into my leg”.

An allergic human stung by the giant hornet may die from an allergic reaction to the venom, but the venom contains a neurotoxin called mandaratoxin (MDTX), a single-chain polypeptide with a molecular weight of approximately 20,000 u, which can be lethal even to people who are not allergic if the dose is sufficient. Each year in Japan, the human death toll caused by Asian giant hornet stings is around 30-40. Advice in China is that people stung more than 10 times need medical help, and emergency treatment for more than 30 stings. The stings can cause renal failure.

The Girlfriend-Boyfriend Culture

Sunday, September 29th, 2013

Bruce Charlton discusses the girlfriend-boyfriend culture:

Growing up in the late sixties to seventies, the impression I got about the purpose of life was that you ought, at all times — from the age of about 10, to “have a girlfriend” — and that what life was mainly about (the kind of life I saw on TV, movies, read in books).

Thus life ought to be focused around 1. having a girlfriend and 2. doing fun things.

The idea was (implicitly) to have quite a few but not too many girlfriends, perhaps one a year? to demonstrate that you were “serious” about “relationships” — and one at a time to demonstrate that you were honest and capable of being faithful.

That was the baseline for everything else — such as education, work or hobbies — and indeed, education, work and hobbies themselves were implicitly aimed at greater long-term success at girlfriends and fun.

I remember, aged 17, attending a (compulsory) talk by a Church of Scotland minister who — in response to questions — said that sex should be only within marriage. As a basis for life, I found this idea bizarre and crazy — and in fact life-denying; because I had absorbed the prevalent culture that the extra-marital boyfriend-girlfriend framework was simply the main thing about life: after all, it was the subject of almost all the TV, movies and books I had ever seen, including many of the best ones and the ones which most made me want to emulate the characters.

There seemed to be no point in marriage, and especially not in having children — because these were “irrevocable” decisions; and a responsible person would not put themselves into a position of being “tied” by “permanent” situations — the ideal was that when the situation changed, then life should change. That seemed obvious.

Jimmy Fallon, the Roots & the cast of Sesame Street play the “Sesame Street” theme on classroom instruments

Saturday, September 28th, 2013

Jimmy Fallon, the Roots & the cast of Sesame Street play the “Sesame Street” theme on classroom instruments:

Camera Traps

Saturday, September 28th, 2013

Linda Kerley of the Zoological Society of London and Jonathan Slaght of the Wildlife Conservation Society have been using camera traps for six years to monitor Amur tigers in the Lazovskii State Nature Reserve in Primorye in the southern Russian Far East. They recently caught a different predator at work:

“I saw the deer carcass first as I approached the trap on a routine check to switch out memory cards and change batteries, but something felt wrong about it. There were no large carnivore tracks in the snow, and it looked like the deer had been running and then just stopped and died.” said lead author Kerley, who runs the camera trap project. “It was only after we got back to camp that I checked the images from the camera and pieced everything together. I couldn’t believe what I was seeing.”

Golden Eagle vs. Deer

“The scientific literature is full of references to golden eagle attacks on different animals from around the world, from things as small as rabbits — their regular prey — to coyote and deer, and even one record in 2004 of an eagle taking a brown bear cub.”

Pointless Counter Pointless

Friday, September 27th, 2013

Colbert celebrates the return of CNN’s Crossfire by moderating his own Pointless Counter Pointless:

10 Things You Probably Didn’t Know About Star Wars: Return of the Jedi

Friday, September 27th, 2013

The most shocking factoid from 10 Things You Probably Didn’t Know About Star Wars: Return of the Jedi isn’t even on the list:

Also, Lucas really thought David Lynch was going to direct Jedi — Lynch was Lucas’ first choice, and Lucas was shocked when Lynch turned it down.

This is after Lynch made Eraser Head and The Elephant Man. He turned down Jedi, of course, and made Dune instead.

If you thought the Ewoks ruined Jedi

Visualizing The Wheel of Time

Friday, September 27th, 2013

I haven’t read the late Robert Jordan’s epic fantasy series, the Wheel of Time, but I’ve heard that it drags along in the middle books, which is what this quick visualization demonstrates:

Wheel of Time Ratings - Amazon

It’s more complicated than that though, as the additional data from GoodReads demonstrates:

Wheel of Time Ratings - Amazon vs. GoodReads

On Amazon, where leaving a review is an ordeal, there are far more reviews for the lowest-scoring books:

This suggests that the really low scores are actually a result of frustrated readers motivated to express their concerns, rather than a reflection of relative enjoyability or quality per-se.

Red Nails

Friday, September 27th, 2013

Tim Callahan and Mordicai Knode look back at Appendix N of the original Dungeon Masters Guide — Gygax’s list of inspirational and educational reading — in their Advanced Readings in Dungeons & Dragons series on Tor.com, and start by looking at Robert E. Howard‘s novella, Red Nails:

The two elements that really strike home here in terms of inspiration are the populated dungeon as its own character of rivalry and strife, and black magic. The city as one massive labyrinth is great, as is the characterization of its architecture & embellishment — gleaming corridors of jade set with luminescent jewels, friezes of Babylonianesque or Aztecish builders — but it is the logic of the city that shines brightest to me. “Why don’t the people leave?” There are dragons in the forest. “What do the people eat?” They have fruit that grows just off the air. “Where do all these monsters come from?” There are crypts of forgotten wizard-kings. There is a meaningful cohesion to the place; Howard manages to stitch dinosaurs, radioactive skulls, Hatfields and McCoys, and ageless princesses into something cogent.

Naturally the commentary turns to the “problematic” handling of race and gender. I am shocked to find such outdated views amongst antediluvian barbarians.

Cookie Monster on The Colbert Report

Thursday, September 26th, 2013

Cookie Monster appeared on The Colbert Report back on June 19, 2008:

Jihad vs the Shopping Mall

Thursday, September 26th, 2013

Gary Brecher (The War Nerd) isn’t talking about the recent Nairobi attack in his recent piece on Jihad Vs The Shopping Mall:

American exceptionalism is always just American provincialism, no matter how benevolent it seems. Not everyone is like us, and a lot of people are actively trying not to become like us. Jihadis are, roughly speaking, the armed wing of that group.

The truth about the clash of civilizations you hear people discussing is that it’s all the other way: The Mall is invading Islam, the Mall is taking over. There isn’t any Sharia Law in North Carolina, but there damn well are US-style malls in even the most conservative Islamic countries.

In Najran, in the most remote corner of Saudi Arabia, a state so afraid of Western contamination that it doesn’t even issue tourist visas, there is a mall. And, when I lived there, you could watch — literally watch — the conflict between Sharia Law and Mall culture, five times a day.

The mall was anchored by a huge market, HyperPanda, complete with its own cheery green and red logo. HyperPanda sold everything from camel meat to iPods. It was pretty much the only place in town where you could walk around without attracting the attention of the police, risking your life at a pedestrian crossing, or dying of heatstroke.

It was such a huge relief to come out of that sun and into the wide, cool, tinted-glass mall. The sun hurts in Najran, and the landscape has no color but army khaki, burnt sienna, ochre — all the least-favorite crayons in the box. You go in the mall and the logos of all the high-end retailers of Europe and Asia wink at you, and there are even chairs and benches for the tired grandmother to slump in while the kids try their skate-shoes on the marble floors. No one is contesting the space with you, for once. The sweat dries, you feel more benevolent as you relax, no longer fighting other drivers for the right to continue living. You’re almost anonymous, a very rare thing in places like Najran.

Naturally, the whole town comes to the mall whenever it can. And naturally, the state, or the local culture — Saudi Arabia doesn’t attempt to separate those concepts — did its best to hold the alien element of the mall at bay. The most dramatic demonstration of this containment effort came at prayer time. HyperPanda covered the whole back part of the second floor of the mall. It was wide open — the front wall was 25 meters wide, with nothing but a few pillars to stop you from coming right on in.

But that changed when the mall’s own muzzein, located in a small kiosk under the escalator, announced prayer time. Saudi muzzeins are not shy; in fact, Muslims from other countries always grumble about the unmusical way they scream through the mic. That’s because they’re not trying to be musical, especially in a city of suspect orthodoxy like Shia Najran. They’re trying to be loud and clear.

The dawn prayer, Fajr, wasn’t a problem; HyperPanda didn’t open that early. But the noon (Zuhr), afternoon (Asr) and sunset (Maghrib) prayers were. By Saudi law all commercial establishments must close during prayers. That was easy enough for shops on the old-style local model: They shoo’d the last customers out and pulled a metal grate across the door before the Mutaween could come around and arrest them for harboring customers in prayer time.

With a new-model mall hub like HyperPanda, the closing for prayer was something much more dramatic, more on the lines of a castle preparing for a siege. The first calls come over the public address system 15 minutes before the next prayer time. Shoppers stop wandering around in a happy daze and start actually looking for stuff. Older sisters round up the little kids. Everybody pushes toward the checkouts, and ridiculously long lines form. Everyone is anxious, because prayer time lasts 40 minutes and nobody wants to be stuck in a shut-down mall that long.

But there’s a weird camaraderie too, as if prayer time were a part of the local weather, a sudden shower we’re all trying to shelter from.


HyperPanda’s most direct affront to the culture is that it provides an attractive nuisance, in insurance terms, to the adolescent population. Malls draw teens in Najran just like they do in Minnesota. But the Mutaween have taken a, shall we say, proactive stance toward that fact in Najran.

The Mutaween (“Society for the Promotion of Virtue and the Suppression of Vice”) has hundreds of men, and even a few women, working in Najran. Some wear the big beards and special headdress, but others are in disguise. And what these undercover morality police do, mostly, is patrol HyperPanda to see if boys are talking to girls, or looking at girls, or throwing girls little folded-up slips of paper with their cell phone numbers. That last one is perhaps the greatest threat to morality in town, and HyperPanda is the scene of most such crimes. The Mutaween mount multi-cop surveillance routines, with some disguised as Malays or Filipinos, to detect any instances of heterosexual contact at the mall.

The culture, the law, are very clear. No pre-marital fooling around, and that includes flirting at HyperPanda. Mall rules are very clear too: It’s an obvious place for boys and girls to check each other out. When mall meets culture, hijinks ensue — and murders sometimes follow, with the male relatives of the girl who’s been compromised at HyperPanda hunting down and killing the boy who accosted her.

Ten years ago, the mall didn’t exist. Cell phones, the other contributor to the delinquency of minors in Najran, have only been around for 20 years, like the internet that gives girls notions of romance, thanks to the South Korean soap operas they all watch.

Everything is tilting toward the mall, away from the old rules, and the resistance is always futile, and worse yet, ridiculous. Every day one piece of this resistance breaks away.

Simulating Social Evolution

Thursday, September 26th, 2013

Intensive agriculture is necessary for a complex society — which relies on costly bureaucracies, organized religion, and constraints on the ruling elites to promote the common good — but not sufficient. Complex societies only evolve when they compete against each other, and the losers disappear.

This is the thesis of Peter Turchin’s recent PNAS paper, which Catherine Crawley explains:

Simulated within a realistic landscape of the Afro-Eurasian landmass during 1,500 BC to 1,500 AD, the mathematical model was tested against the historical record. During the time period, horse-related military innovations, such as chariots and cavalry, dominated warfare within Afro-Eurasia. Geography also mattered, as nomads living in the Eurasian Steppe influenced nearby agrarian societies, thereby spreading intense forms of offensive warfare out from the steppe belt. On the other hand, rugged terrain inhibited offensive warfare.

The study focuses on the interaction of ecology and geography as well as the spread of military innovations and predicts that selection for ultra-social institutions that allow for cooperation in huge groups of genetically unrelated individuals and prevent large-scale complex states from splitting apart, is greater where warfare is more intense.

While existing theories on why there is so much variation in the ability of different human populations to construct viable states are usually formulated verbally, by contrast, the authors’ work leads to sharply defined quantitative predictions, which can be tested empirically.

The model-predicted spread of large-scale societies was very similar to the observed one; the model was able to explain two-thirds of the variation in determining the rise of large-scale societies.

Complex Society Evolution Simulation

There were several recurrent questions that came up in conversations with reporters:

Why does a question such as this need a computer model to answer?

Although our theory is relatively simple, it’s too complex to reason through using verbal arguments. There are important nonlinear feedback loops that can be captured only mathematically. Furthermore, the heart of our approach is getting detailed, quantitative predictions that can be compared to a large dataset on historical evolution of states in Afroeurasia. This can be done only with a quantitative, dynamical model.

Does this model tell us anything new, or is it a way to confirm what we already know?

The model results in new knowledge. Before we went through this exercise we did not know whether competition between societies, taking the form of warfare, was really an important driver in the evolution of large complex societies. Now we know that it is the main factor, with the presence of agriculture as a necessary condition, and various environmental effects (e.g., rugged terrain) also playing a role. Undoubtedly, cultural peculiarities are also important, although they were not included in the model. But since the model predicts 65 percent of variance in the data, such other factors must be of lesser importance than those included. At best, they provide the remaining 35 percent of the explanation. Our main result, that patterns of warfare are the most important factor explaining the rise and spread of large states is quite novel, and it will not be immediately accepted by most anthropologists and historians (although I expect that political scientists will be more sympathetic). Our results are likely to generate much controversy, which is why we plan to continue with this research program to address various criticisms that people will be bringing forth.

What are “large complex societies”?

In the simplest terms, societies counting a million of individuals or more. Such societies are invariably organized as states, have many complex institutions that are designed to prevent them from breaking up, extensive division of labor, complex internal organization, and so on. So they are ‘complex’ in many different ways

Why do you call these societies “anonymous”?

For most of our evolutionary history humans lived in small-scale societies — numbering just hundreds of people. These human groups were integrated by face-to-face interactions. In other words, everybody knew everybody else. Then there was a transition to large-scale societies, starting 10,000 years ago. In large societies of today each of us knows only a tiny proportion of people — the huge majority is strangers. In this sense our societies are anonymous. We interact all the time with people who are not personally known to us (think of taking a subway in New York City, or shopping in a supermarket).

How did you go about developing this model? How did you decide which data inputs to include?

Our model was guided by a general theoretical framework — cultural multilevel selection (CMLS). This theory predicts that competition between societies is the main driver of evolution of complex societies. Thus, emphasis on warfare. But then we needed to ‘operationalize’ such quantities as ‘warfare intensity’. What does it mean? It turned out that for the period of history we focused on, 1500 BC–1500 AD, we could capitalize on the spread of warhorse-related technologies as a proxy for intense warfare. The importance of rugged terrain was also suggested by the CMLS theory. It is easier to defend mountainous areas.

And it is clear that agriculture is a necessary condition for the rise of complex societies. That was already well known. However, our model shows that just the spread of agriculture does a not-so-great job explaining where and when large-scale societies arise. It’s a necessary, but far from sufficient condition. Warfare patterns do the bulk of explanation — that’s what allowed such a remarkably good match between model results and data.

Why do you think intense warfare and the spread of war technology turned out to be so important in deciding which large states would form?

That comes out from the CMLS theory, as I explained earlier. To evolve to a large size, societies need special institutions that are needed for holding them together; preventing them for splitting along the seams. But such institutions have large internal costs and, without constant competition from other societies, they collapse. Only constant competition between societies ensures that ultrasocial norms and institutions will persist and spread. So it really was war that made the state.

Were you at all surprised by these results?

I was certainly surprised by how well the model predicted the data. Even with first-guess parameters, the ones I tried during the early phase of the work, the model output looked very much like data. Quantitatively the model explained >50% of variance. Moderate adjustments of just 4 parameters increased prediction to 65%. This is much better than anyone, including myself, had thought can be done with historical data. Even though history is very complex, it turns out that simple models can capture very well many of its patterns.

What are the limitations of this sort of approach? Are there any nuances or particular cultures’ idiosyncrasies that affect their expansion and can’t be incorporated into mathematical models?

Of course, differences in culture, environmental factors, and thousands of other variables not included in the model all have effect. If you look carefully at Figure 1, you will see that there are lots of differences in detail between data and the model. That’s as it should be. A simple general model should not be able to capture actual history in all its glorious complexity. Both general processes and cultural idiosyncrasies play a role. But most historians and the lay public don’t realize that general processes can be very powerful in shaping history. Our model proves that they are wrong.

Sick From Freedom

Thursday, September 26th, 2013

For many slaves, liberation was a death sentence:

At least one quarter of the four million former slaves got sick or died between 1862 and 1870, Professor Downs writes, including at least 60,000 (the actual number is probably two or three times higher, he argues) who perished in a smallpox epidemic that began in Washington and spread through the South as former slaves traveled in search of work — an epidemic that Professor Downs says he is the first to reconstruct as a national event.

Historians of the Civil War have long acknowledged that two-thirds of all military casualties came from disease rather than heroic battle. But they have been more reluctant to dwell on the high number of newly emancipated slaves that fell prey to disease, dismissing earlier accounts as propaganda generated by racist 19th-century doctors and early-20th-century scholars bent on arguing that blacks were biologically inferior and unsuited to full political rights.

Instead, historians who came of age during the civil rights movement emphasized ways in which the former slaves asserted their agency, playing as important a role in their own liberation as Lincoln or the Union army.

Indeed, southern slave-holders did predict this outcome.