Category Archives: Mathematics

Math

Why Americans suck at it:

American institutions charged with training teachers in new approaches to math have proved largely unable to do it. At most education schools, the professors with the research budgets and deanships have little interest in the science of teaching. Indeed, when Lampert attended Harvard’s Graduate School of Education in the 1970s, she could find only one listing in the entire course catalog that used the word “teaching” in its title. (Today only 19 out of 231 courses include it.) Methods courses, meanwhile, are usually taught by the lowest ranks of professors — chronically underpaid, overworked and, ultimately, ineffective.

Without the right training, most teachers do not understand math well enough to teach it the way Lampert does. “Remember,” Lampert says, “American teachers are only a subset of Americans.” As graduates of American schools, they are no more likely to display numeracy than the rest of us. “I’m just not a math person,” Lampert says her education students would say with an apologetic shrug.

Consequently, the most powerful influence on teachers is the one most beyond our control. The sociologist Dan Lortie calls the phenomenon the apprenticeship of observation. Teachers learn to teach primarily by recalling their memories of having been taught, an average of 13,000 hours of instruction over a typical childhood. The apprenticeship of observation exacerbates what the education scholar Suzanne Wilson calls education reform’s double bind. The very people who embody the problem — teachers — are also the ones charged with solving it.

…Left to their own devices, teachers are once again trying to incorporate new ideas into old scripts, often botching them in the process. One especially nonsensical result stems from the Common Core’s suggestion that students not just find answers but also “illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.” The idea of utilizing arrays of dots makes sense in the hands of a skilled teacher, who can use them to help a student understand how multiplication actually works. For example, a teacher trying to explain multiplication might ask a student to first draw three rows of dots with two dots in each row and then imagine what the picture would look like with three or four or five dots in each row. Guiding the student through the exercise, the teacher could help her see that each march up the times table (3×2, 3×3, 3×4) just means adding another dot per row. But if a teacher doesn’t use the dots to illustrate bigger ideas, they become just another meaningless exercise. Instead of memorizing familiar steps, students now practice even stranger rituals, like drawing dots only to count them or breaking simple addition problems into complicated forms (62+26, for example, must become 60+2+20+6) without understanding why. This can make for even poorer math students. “In the hands of unprepared teachers,” Lampert says, “alternative algorithms are worse than just teaching them standard algorithms.”

No wonder parents and some mathematicians denigrate the reforms as “fuzzy math.” In the warped way untrained teachers interpret them, they are fuzzy.

It’s a long, but interesting, and depressing article.

I should note that I was one of the kids who suffered from the “New Math” in the sixties, but I had a great algebra teacher in junior high (I forget her name, but she was a black woman), and good ones in high school as well. We actually learned calculus and analytic geometry from Mr. Troyer.

[Update a while later]

The more I think about this, the more furious I get that we have these worthless schools of “education” that don’t even teach teachers to teach.

Complexity

Frustration with the leftist fools who don’t understand the knowledge problem:

Mr. Bouie insists that he is not simply trying to make an excuse for the president’s revealed incompetence in sundry matters, but of course that is precisely what he and other apologists for the administration are doing. If they were really interested in complexity as such, then they would bring it up on the front end of the policy debate, rather than on the back end.

I’ve seen this happen so many times that every other policy debate looks to me like an ancient rerun of Three’s Company: Do you think there’ll be a comic misunderstanding in this episode, too? It unfolds like this: Politicians on the Barack Obama model promise that they will muster their native intelligence and empirical evidence to bring order to, e.g., the health-care industry, through the judicious application of regulation. People like me tell them that the effects of such regulation are almost certainly going to be other than what was intended, because such markets are too complex to be understandable, predictable, or steerable, even in principle. Even if every bureaucrat who touches health care or the labor market has the brain of an Einstein and the soul of a St. Thomas Becket, it will not turn out the way it is intended. And then, when it doesn’t turn out as intended, Jamelle Bouie et al. protest that the toldya-so chorus “betrays an ignorance of the size and complexity of the federal bureaucracy.”

And they never even consider the question: If the federal bureaucracy is so vast and complex that its behavior cannot be adequately managed, how is it that the phenomena that the bureaucracies are tasked with managing—orders of magnitude more complex than the bureaucracies themselves—are supposed to be manageable? To consider the question with any intellectual rigor is to accept real, meaningful, epistemic limits on what government can do.

Can’t have that. It doesn’t allow them to run other peoples’ lives.

Scientists And Philosophers

Why they need to talk to each other:

Most of climate science is in ‘shut up and calculate’ mode. This is a very dangerous place to be given the substantial uncertainties, ignorance and areas of disagreement, not to mention the problems/failures of climate models. Climate science needs reflection on the fundamental assumptions, re-interpretations, and deeper thinking. How to reason about the complex climate system, and its uncertainties, is not at all straightforward. And then of course there are the ethical issues, including understanding how the climate debate has gone so badly wrong.

Yes.

Ocean Heat

Where is it?

I have previously written about the fact that the heat in the ocean isn’t there. A Facebook commentator produced some excellent graphs based on the ARGO data which showed NO heat accumulation at any level in the world’s oceans. This lack of warming contradicts completely (Anthropogenic Global Warming) AGW theory as put forward by such AGW stalwarts as Trenberth and England. It also has Hansen scrambling for weird and whacky explanations.

So it is plain in the ARGO era that the oceans are not warming and this contradicts AGW.

Denier.

The Missing Light

It’s a mystery:

As one participating scientist points out, to miss the mark by so much means what we understand about the universe is fundamentally wrong. The universe continues to be exciting, a little scary, but mostly—a mystery.

And yet some have the hubris to tell us they can predict the temperature of the planet and level of the seas decades from now.

Heidegger

Since we were discussing philosophy the other day, Lileks has some thoughts:

The article concerns the anti-Semitism of Heidegger, and how the publication of recent texts the philosopher intended to be the capstone of his output reveals that he didn’t have the easy, lazy cultural anti-Semitism of the era, but really, really thought hard on how the Jews were putting the stick to the decent noble Volk. Not just any kind of Jews, though: worldwide jewry! It’s the richest kind.

..Anything that starts out with “Russia and America are the same” is the product of a mind so high in the clouds it cannot tell the different between red and black ants. But while Russia did indeed have “unrestricted organization of the average man,” an inevitable consequence of the state’s politicization of the entire society, you could say Germany under Hitler had a smattering as well. Or a gerschmatturung, to use Heidegger’s word. Just kidding; he doesn’t. But the article is full of German words intended to set off a Concept, as though expressing a concept in a train-wreck of consonants makes it important. I suppose the point is to be accurate, use the terms the author uses so there can be no misunderstanding. But for my part that would require anything close to comprehension, and I cannot grasp a lot of what Heidegger is talking about, perhaps because there seems to be no point in understanding what he’s saying.

Philosophy isn’t useless, but some philosophers are. Or worse than.

Climate Change

…and hot air:

In other words mitigation to slow or halt GHG emissions will be costly today with little payout over the next 100, if not 1000, years, making it unlikely that large mitigation projects have a positive net present value. And for these results to occur, the United States would have to be joined by the rest of the industrialized nations as well as the developing ones, something that is not going to happen.

Given that mitigation has gained little policy traction, many climate scientists seem to be paying more attention to adaptation. Indeed, the subtitle of the IPCC’s 2014 report is Impacts, Adaptation, and Vulnerability. In contract to earlier IPCC reports, the press release in April mentioned mitigation only once and adaptation 12 times. According to Chris Field, chairman of one of the IPCC working groups, “The really big breakthrough in this report is the new idea of thinking about managing climate change.”

What a concept.

[Noon update]

Math is math: “(100,000′s of Jobs + Billions of Taxpayer $’s) x 85 years = 0.018° C.”