Andrew Hacker on the Supposed Superfluousness of Algebra

An Op-Ed titled ‘Is Algebra necessary’ is bound to provoke reaction. So, here I am, reacting to Andrew Hacker’s anti-algebra screed (New York Times, July 29th, 2012). It is a strange argument, one unsure of what it is attacking–mandatory math education, elementary algebra, higher algebra?–and one founded on an extremely dubious premise: that the way to carry out educational reform is to cherry pick your way through a curriculum, questioning the ‘utility’ of a particular component in case there are no jobs that require an exact application of its material. Hacker makes things worse by leaning on statistics that cry out for alternative explanations and pedagogical reform, rather than the ‘lets drop the subject students seem to have difficulty with’ approach that he favors. If American students are struggling with algebra, it might be time to inquire into how it is taught, to show students how abstraction and symbolic representation are key to understanding a modern world underwritten by science and technology. Dropping algebra seems like a profoundly misguided overreaction.

The ‘surrender in the face of poor test scores’ approach results in a series of bizarre statements of which the following are merely representative samples:

It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.

Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever used it in diagnosing or treating their patients. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice.

I have news for Hacker. There is little evidence that being able to leads to ‘more credible political opinions or social analysis’ either. Furthermore, if job skills  are examined as superficially as Hacker does in his examples then it becomes all too easy to dismiss large parts of one’s educational background as being irrelevant. Hacker would be alarmed, I presume, to find out that even though modern physicists hardly ever roll balls down inclined planes, freshman physicists are still required to spend a semester solving problems that are full of problems that stress just that. Hacker dismisses the argument for a general education in mathematics with the alarmingly glib ‘It’s true that mathematics requires mental exertion’ without stopping to inquire what that ‘mental exertion’ might consist of and what it might engender in turn. This is hardly an attitude toward pedagogical reform that breeds confidence.

It is a consequence of Hacker’s argument that the only students who should receive an education in algebra are those preparing for careers that require them to apply algebraic techniques and concepts in their jobs. Everyone else can be spared its ‘difficulties, ‘ like the above-mentioned abstraction and symbolic representation. How would an extension of this argument work in, say, fields like history or literature? A relentless whittling down of the curriculum would result, leaving us with a list of subjects read off the Help Wanted Ads section.

This is an impoverished, grimly utilitarian, and ultimately soulless view of education.

The Copyright Police Catch Up With ‘Hung Up’

Well, I’ve finally run afoul of the copyright police. More precisely, two videos I had uploaded to YouTube–some six years ago–have been taken down. Last night, as I searched for them repeatedly, I wondered what might have happened to them. This morning, as I thought about their content, I realized why they might have got the copyright chop: they both featured the video for Madonna’s ‘Hung Up.’

Back in 2006, I moved to my current location in Brooklyn, Ditmas Park, from Fort Greene. Our move was onerous, as most moves are, but some its pain was eased a bit by inviting over my good friend and Decoding Liberation co-author, Scott Dexter, for a  beer-infused packing session. As the night wore on, and as my possessions miraculously found their way into the boxes scattered all over my apartment, we took ever-longer breaks for food and liquid sustenance. Finally, worn down by the tedium of packing, we called it a day (or night), and took refuge in VJ’ing YouTube videos. Among them: Madonna’s ‘Hung Up,’ which features ample footage of that lady’s dancing prowess.

As Scott watched the video, inspiration struck: why not provide a little musical accompaniment? The instrument he picked–yes, he just happened to be carrying it around–was the Vietnamese lip lute, the Đàn môi. We played the video several times as Scott played the Đàn môi, picking up the beat, strumming brilliantly against his lips. If I may say so myself, it was a virtuoso performance, adding a quirky twang to ‘Hung Up’s pop and dance sensibility. At one point, I turned on my digital camera and shot some video of Scott playing, panning around the room to show the packed boxes, my desktop computer playing ‘Hung Up,’ and finally, on myself. Later, my wife shot some video with similar footage. Yes, it was all pretty juvenile, but that’s how most home videos go.

We ended up with two short clips of Scott on the Đàn môi playing along with ‘Hung Up’.  They were pleasant mementos of time spent with a good friend; we decided to put them up on YouTube to share them with friends. Yes, there was some goofy mugging for the camera; there was a musician showing me how skilled he was; there was a little bit of Madonna. A bit of a lark, as it were.  I sent the links to a few folks, and in the years that followed would show the videos off once in a while. I don’t think they were viewed more than a hundred times in all.

Technically, I suppose they were ‘derivative works‘ of ‘Hung Up,’ and as such, my use was an infringement. (I’m not sure I’d have a fair-use defense.) But it still all seems a little silly: we were being Madonna fans, and the videos showcase Scott’s performance more than anything else. Now, they are gone. The world of entertainment isn’t exactly poorer as a result of these two amateur efforts disappearing from YouTube, but the pettiness of it all is a little depressing

Final Exams, Testing Regimes, Contd.

Daniel Kaufman left a very interesting comment in response to my post on final exams; it captures a great deal of what is wrong with testing regimes in general. I’d like to offer some brief responses to it.

First, testing regimes lay excessive emphasis on memorization and rote recall, which has a questionable connection with what might be termed the ‘application of knowledge’:

There is absolutely no value whatsoever for memorizing anything in philosophy. If you are a surgeon and forget where the spleen is, while you’ve got someone opened up on the table, the consequences will be dire. There is no comparable consequence to forgetting something in philosophy. You simply look it up. In philosophy, understanding is everything. So, at a minimum, there is no reason that tests should not be open-book, open-notes, as mine are.

Or consider another subject: computer science, where students are often asked to write code fragments, correct errors in programs, trace out program flow with output etc. The typical programmer in his workplace is not asked to perform these tasks in anything remotely resembling the environment of a final exam. The closest he will come to this is in an interview for a job. For which, see Dan’s point below about ‘the next set of institutions’ and reader JP’s comment  on the post on final exams.

The entire regime of testing, in subjects like philosophy, suffers from a lack of obvious raison d’etre. Students who really care about learning will learn, regardless of testing, and those who aren’t interested in learning will not be “forced to learn” by a test.

And what, precisely, is the connection between ‘testing in time-controlled environments that emphasizes recall of memorized material’ and ‘learning’? I, for one, have no idea.

2a. The idea is supposed to be that testing allows one to quantify *how much* the person understands in the given subject. The problem is, it is not at all obvious that understanding can be measured in a quantitative way in the humanities.

I suspect this might even be the case in the supposedly ‘more exact’ disciplines.

2c. Consequently, it seems the only real reason for testing in subjects like these is so that students can have grades, which then makes it possible for the *next* set of institutions that they will confront, can select them or reject them.

Indeed; the existence of testing regimes is dependent on a host of institutions that need a quick and dirty method of assessing candidates for a variety of tasks. Accurate, perspicuous assessment of the relevant skills in many of these domains remains an inexact, difficult science. Why not take refuge in the faux objectivity of the test score?

3. I would much prefer that grades be based on oral examination and in-class participation, but with the teaching loads that many of us have to carry, with no grading-help, this is simply not possible. So we are stuck with this.

In recent years, I have steadily increased the percentage of my class grades that is earned by participating in class discussions. My rationale has been that participating in a class discussion in philosophy is a great chance for a student to ‘talk their way through’ an assigned reading, to discuss an argument’s weaknesses and strengths, and to ‘think aloud.’

Finally, as to the deeper ethos reflected here, we are quite unfortunate to live in a culture that seems to have absorbed two unfortunate principles: (1) Work is the most valuable thing a person does in his/her life; (2) That things are only really valuable if they hurt. Both ideas, of course, are a legacy of Christianity—both Protestant and Catholic—and contradict both the pre-Christian, largely Greek lionization of Leisure and Contemplation (a la Aristotle), and the Hebraic view that pleasure is a gift from God and should never be rejected (which is why there is no Ascetic tradition in Judaism).

This needs little comment, except to note these ‘unfortunate principles’ have had a deeply pernicious effect on our political life, hijacking too much discourse with a an impoverished vision of the human condition and the ‘good life.’

The Distraction of Distraction

I’ve written on distraction on this blog before (several times: detailing my ‘Net distraction; comparing the distraction attendant when trying to write with a pen as opposed to a word processor or blog editor; describing the effect of changing locales of work on distraction and of persistent online activity on the ‘offline’ world; noting how constraint might be essential to creativity.) This would indicate distraction is often on my mind, that I’m distracted enough by distraction to write about it–again and again. I’d like to think writing on distraction might be curative, that describing my strategies for dealing with it, appraising and evaluating them, might enable me to, as it were, ‘see through them’ to understand what goes wrong. Perhaps writing on distraction will also enable some reckoning with the internal monologues that lead to the breakdown of my ever-weakening resolve to not be distracted; perhaps coming to grips with its phenomenology–the release of tension experienced by responding to a distracting stimulus, the breakdown of my inner resolve to not look away, to not procrastinate–all might help. (It is impossible to write about distraction without writing about anxiety so that little demon will presumably make an appearance.)

At the outset, I should say I find my distraction incapacitating to the extent that–without exaggeration–I can say I am terrified and made unhappy by it. I am prone to thinking I am the most distracted person in the world. (I pen these words in the hope someone will make the effort to try to convince me I’m not so, for  misery needs company.) I experience distraction as a fraying at the edges, a coming apart at the seams, a sundering of the center–whichever description you want to use, it’s all that in my feverish imaginings and experiencing of it.

Since my primary mode of distraction is ‘Net distraction, I’d like to offer another description it. I sometimes use ‘screeching’ or ‘scratching’ in trying to describe the activity in the inside of my cranium that makes me want to stand up and run away–and check mail or reload a page–from reading or writing. All too quickly, when working on a computer, I need ‘release’ and the act of moving the mouse so that something else appears on my screen promises relief. A change of screens, that’s all it is. And ironically, I can never take in whatever it is that I switch to. My mind is too blank at that moment, still perhaps processing residual irritation. Then, seething with rapidly accumulating anxiety about my still-on-the-burner work, I switch back. A little later, the ‘scratching’ begins again. I jump in response. Repeat ad nauseam.

The resultant composite sensation resembles nothing as much as it does a kind of emptiness, a vacuity. Nothing has been taken in, nothing emitted. I feel merely depleted. This depletion calls out for replenishment, and thus, strategies for ‘holding down’ the restless wanderer as well. Nothing has worked yet, and by that I mean no strategy–internet fasts for instance–has shown itself to be sustainable. Perhaps the most successful behavioral modification is architectural as in physical distancing, like that present in my trips to the gym, where for a brief, intense set of moments, I can immerse myself and concentrate on physical effort. In those moments, there is genuine relief, not the empty kind experienced when switching tabs. Then, all too soon, the workout ends, I towel off and head home, already, bizarrely, anticipating the moment when I will sit back down at the scene of my perdition.

Note: In subsequent posts I hope to describe my experiences with the strategies I have tried for dealing with distraction.

RIP Sally Ride

Like many other schoolboys in the 1980s, transfixed by the awesome sight of the space shuttle lifting off from the Kennedy Space Center, by the legend of the moon landings, and by the culturally enforced vision of the astronaut as our era’s most intrepid pioneer, I had a thing for those that went into space. Needless to say, I wanted to be like the men, those dashing, crew-cut, sunglasses-wearing types, piloting jets and shuttles. But that didn’t mean that women astronauts couldn’t make me admire them, especially if their credentials for spaceflight included degrees in physics like Sally Ride‘s did. I was a physics nerd too–one inordinately proud of explaining to anyone that cared to listen what pions had to do with the relationship between a proton and a neutron–and found the idea of civilian scientists and not just military pilots heading into space incredibly inspiring. If I ever dreamed being an astronaut, it was as a Mission Specialist and not as a Pilot  Commander that I imagined myself; I didn’t think I would join the military. And I also dreamed about a career as an astrophysicist, so a physicist-astronaut seemed wonderfully cool.

When Ride’s selection for STS-7 was announced, I took notice.  It didn’t matter she was a woman. Physics just made everyone that studied it cool, and besides, she was an astronaut. What was not to like? I studied shuttle flights closely in those days, diligently making trips to the American Library in New Delhi to watch videotapes of reports on each mission; STS-7’s details–its satellite deployments, for instance–received a great deal of wide-eyed attention from me. (It helped that the mission was led by the dashing Bob Crippen.)  Later, I saw Ride on television handing interviewers with aplomb and grace. I do not remember if any of them asked those sexist questions that were so often directed at her but it is entirely possible that I might have heard and seen a few and not realized just how offensive that line of questioning was. I do remember Carl Sagan being paired up with her for a television interview, and on being asked if he was envious of astronauts like Ride, saying he didn’t consider ‘puttering around in low earth orbit to be space travel.’ In the neighboring television window, Ride just smiled, refusing to fall for the bait. She seemed graceful, smart, and tough, a winning combination at all times.

One thing I didn’t know about Sally Ride then was that she was a lesbian. I wonder what I would have thought then as a seventeen-year-old schoolboy, one relatively unsophisticated in his understanding of human sexuality and its diverse forms of expression. My guess is that while I might have had some puerile curiosity about her sexual orientation and would have jumped at the opportunity to crack a crude joke or two in juvenile company, I think that in the end, the combination of astrophysics and manned space flight would have trumped it all. It still does.

RIP Sally.

Why Not A Syrian Mandelian Midwife, Mr. Friedman?

An acute application of gynaecology to international relations, conjuring up visions of revolutionaries being led gently through birthing procedures is on display–again and again, and quite possibly, again–in Tom Friedman’s latest column in the New York Times. Apparently, the Middle East–especially Syria– is pregnant with possibility, fertile with newly planted seeds of political change. It needs midwives by the truckload. ‘ Well-armed’ ones preferably. Pistol-packin’ mamas’ aides, taking revolution from conception to birth–and presumably on to postpartum depression as well if the comparison with the US in Iraq is to hold water. (All the while, unassisted by doulas, but ready to hand off to obstetricians at a moment’s notice?)

First, the necessity of a midwife in extracting nations embedded in English philosophers (the mind boggles at the imagery conjured up here):

[F]or me, the lesson of Iraq is quite simple: You can’t go from Saddam to Switzerland without getting stuck in Hobbes — a war of all against all — unless you have a well-armed external midwife, whom everyone on the ground both fears and trusts to manage the transition. In Iraq, that was America. The kind of low-cost, remote-control, U.S./NATO midwifery that ousted Qaddafi and gave birth to a new Libya is not likely to be repeated in Syria. Syria is harder. Syria is Iraq.

Second, the explanatory power of the fearsome midwife (like those of yore, that struck fear into the hearts of busybody mother-in-laws and hospital staff everywhere):

The only reason Iraq has any chance for a decent outcome today is because America was on the ground with tens of thousands of troops to act as that well-armed midwife, reasonably trusted and certainly feared by all sides, to manage Iraq’s transition to more consensual politics.

Third, the absence of a suitably ‘armed and external’ midwife induces reticence and modesty into punditry:

I know columnists are supposed to pound the table and declaim what is necessary. But when you believe that what is necessary, an outside midwife for Syria, is impossible, you need to say so.

Fourth, the low probability of the presence of the aforesaid midwife should result in the maturation of nascent revolutionaries:

Since it is highly unlikely that an armed, feared and trusted midwife will dare enter the fray in Syria, the rebels on the ground there will have to do it themselves.

Lastly, the absence of midwives and Middle-Eastern Madibas  has inflammatory potential:

Without an external midwife or a Syrian Mandela, the fires of conflict could burn for a long time. I hope I am surprised.

I think the primary occasion for surprise is already upon us: Why does Mr. Friedman not seize the opportunity presented to him by his last sentence and run with it? There is a midwife, a country, Syria, and a name, ‘Mandela.’ Endless recombinatory possibilities present themselves. In the spirit of charity,  and because Mr. Friedman will surely revisit the smoldering Middle East again, I hereby gift one of these to Mr. Friedman for artful deployment in one of his future columns, :

What Syria Needs is a Mandelian Midwife