Today on the front page of the dailycal is an article discussing the hardships student parents wil face as a result of UC budget cuts. The people interviewed in the article seem to think we should be moved by the unfairness of reducing the child care subsidy provided to graduate student parents and support the Graduate Assembly’s resolution to exempt child care from the proposed budget cuts. While I can empathize with any graduate student who faces tough choices because of our low wages (particularly at UC Berkeley) the universities subsidy of child care is blatantly discriminatory against people with other lifestyle choices and should be totally abolished not saved. I mean we surely wouldn’t tolerate a program that offered straight couples who wanted to have their own apartment (rather than rooms in a shared house) a subsidized low rent apartment but denied gay couples the same benefit so why do we tolerate a program that discriminates on this lifestyle choice?

My fiance and I will never have children but this hardly means that graduate school imposes no hardships on us. She is a graduate student at Harvard and I am finishing up at UC Berkeley and just as the low salary of graduate students makes it difficult to raise a child it also makes it tough to afford flights across the country. Yet does the university offer me a subsidy to visit my fiance the way it does to graduate student parents? No! Worse, this term UC Berkeley gave me a MWF teaching assignment (instead of the Tuesday one I requested) that made it impossible to visit my fiance over the weekends. But long distance relationships don’t get any consideration by the university while graduate students with children get automatic first dibs on teaching slots that are convenient for their child care arrangements. Moreover, the department is expected to bend over for graduate students with children if they need a particular day free while it’s just tough luck for me if I want to visit my fiance but can’t find anyone to substitute.

In light of this blatant unfairness does the article offer us any particular justification as to why we should subsidize those students who make the choice to have children? No, we are merely given a string of observations about how difficult it is to raise a child as a graduate student.

“If you have an infant, it’s $20,000 a year just in child care fees,” Keeley-Saldana said. “(The cost) really prohibits students from seeking their higher education degrees.”
…
With a new baby on the way, Cruz said the heightened costs would be “impossible” for he and his wife to meet.¹
…
Senior Dana Parsons, 32, said campus child care services are essential for student parents such as herself.
….
“Had it not been for subsidized care on campus, I would not have been able to attend school full-time,” she wrote in an e-mail.
…
“There is no good solution,” she said. “I’m not saying that I don’t think it’s fair for Early Childhood to be spared from cuts, but I’m hoping that they really do value the children on campus.”

First of all let’s make this absolutely clear. Failing to subsidize child care doesn’t force anyone to stay at home, leave graduate school or otherwise deny them the benefits of higher education. The lack of subsidized child care merely forces people to choose between the benefits of using their resources to have a family or attend school. This is no different from the fact that without subsidies or special considerations Sharon and I must choose between graduate school and getting to see each other more than rarely during the school year. It’s blatantly unfair to offer monetary subsidies and preferences to one lifestyle choice without the slightest official consideration for the other.

Of course sometimes radically unfair policies can be justified if they offer sufficient benefit for the society at large. However, in order to overcome the presumption against unfair policies such as this one would need compelling evidence that this was really the most cost-effective way to increase the number of US graduates in math/science or the equivalent. Since women make up a majority of graduate students even finding that subsidized child care did more to retain women than men wouldn’t justify the program.² Even restricting such subsidies only to the fields where women were underrepresented and granting the bizarre idea that numerical underrepresentation is ipso facto unfair³ one would need to establish that this kind of subsidy was particularly effective (more so than just giving women extra pay) to justify discriminating against those women who didn’t plan to have children.

I’m not going to even go into how this policy implicitly discriminates against those who have a more difficult time having children (the infertile, gays and lesbians). However, I will note that offering these benefits only to parents and not to those of use with other lifestyle preferences goes directly against the valid feminist justifications for legally required maternity leave and other bars against the implicit discrimination against women smuggled in via career punishment for maternity. However, unlike the lauditory goal of stopping corporations from imposing unfairly excessive penalties for one lifestyle choice (partially because of female stereotypes) we have a situation where the university is unfairly benefiting one lifestyle choice over another.

Of course I realize that few people are likely to be convinced by a logical argument in this situation. Most people want to have children themselves so, as is common with discrimination, it seems right and proper to them that people like themselves should receive a benefit. Moreover, the people who benefit from this program are easy to see while the small cost that all graduate students pay as a result is diffuse. So if you aren’t yet convinced just ask yourself this. How would you feel if things were reversed? Suppose I got subsidized air fare to go visit my fiance and got first pick of teaching assignments so my schedule would allow these visits but graduate student parents received no official consideration at all. If you find that disturbing tell me what’s different about this situation.

I’ve always sorta suspected that explaining mathematics to students in very concrete ways wasn’t really a shortcut but it was like being offered a magic lamp with a genie who will grant your wishes. You know something about it is too good to be true even if you don’t really know what it is. Anyway apparently now there is some evidence that my intuitions are correct.

Of course I don’t think this means one should never use analogies to concrete situations or that math must be presented as uninterpreted formal manipulation. Nor is it really true that I didn’t know why I found the teaching of math in a super concrete fashion troubling. Ultimately math is the use of abstraction to solve problems. The power of things like group theory, analysis, recursion theory or even calculus is the result of abstracting the relevant features from the motivating examples. This is just as true for the subjects we try and teach our students as it is for the subjects we study ourselves. For example, in order for students to understand (not merely memorize) how to take the derivative of an integral using the chain rule and fundamental theorem of calculus requires the students have abstracted away from the idea of functions as rules they can right down in terms of powers,ratios, trigonometric functions and exponentials and can accept a define integral they can’t compute as just another function.

Ultimately, interpreted correctly I don’t think this study really says anything that shouldn’t have already been obvious. It doesn’t say that concrete examples can’t help students grasp the abstract concepts being presented (they can) it just tells us that there is no shortcut to mathematical understanding. If you want students to actually understand math that means teaching them to understand the concepts abstractly and if you take the easy way out and encourage your students to understand mathematics in a particular concrete fashion instead of offering the concrete examples/analogies and encouraging them to move beyond it their understanding will suffer.

As a side note the entire discussion around this study is a perfect illustration of the fundamental confusion at the heart of mathematical education today. Framing the study as showing that concrete teaching methods fail because they aren’t as effective in teaching students to solve other concrete problems seems totally backwards to me. Frankly in the modern world being able to compute when too trains will pass or find the symbolic integral of sin(x) isn’t an important skill for most people. Go ask anyone over 40 who doesn’t work in a technical field to solve a system of two linear equations, integrate a function, or even multiply fractions and they aren’t likely to be able to do it. If the particular skills we pass on in math class were so important to everyone how has our civilization manage to flourish up till now? It might be sad, you might not like it but the strategies of asking a technical friend, using a calculator, or just not dealing with mathematical problems work pretty damn well for most people. On the other hand the ability to abstract away particular features of a class of examples is a skill virtually all professionals require.

Ideally we would stop blindly teaching the traditionally expected skill set and ask what we mean to accomplish. If we want to give people practical skills to use in their life we need to take a look at some empirical data about what if any mathematical education translates to practical benefit. You might think that everyone should be able to calculate with percents and fractions but if most people simply use the calculator on their cell phone then we have to consider the possibility that we’d be better off helping them practice computing in that way. Certainly some people need to learn how to do things like multiply fractions, compute integrals and so forth but that isn’t everyone. On the other hand if the reason to teach mathematics is to impart quantitative reasoning and the ability to reason abstractly then why the hell is most of our mathematical education blind computation?

In the chronicle of higher education yesterday there was a short snippet about academics taking performance enhancing drugs and if you have a nice proxy server you can read the longer article or the commentary in nature (you can also find the Volokh Conspiracy article that brought it to my attention). Now I was quite pleased with the reasonable approach taken in the Nature article. In particular I thought the following paragraph hit things right on the head.

Rather than individuals purchasing substances over the Internet, we believe it would be better to ensure supervised access to safe and effective cognitive-enhancing drugs, particularly given potentially dangerous drug–drug interactions. Such regulation must be evidence-based and a product of active dialogue between scientists, doctors, ethicists, policy-makers and, importantly, the general public. This may necessitate a new form of regulation because the remits of the existing health and drug agencies are for the regulation of medicines for treatment, not for enhancement.

If a new class of compounds (so far most ‘cognitive enhancers’ are effectively less euphoric versions of amphetamines) really is developed that appeals primarily to educated wealthy people rather than being associated with lower socioeconomic classes such a change in our regulatory outlook might actually occur. True, I’m skeptical that more than a modest cognitive enhancement effect is possible from drugs (they can’t fundamentally rewire the brain) but accepting the careful use of drugs as enhancements has the potential for massive increases in utility. While I doubt drugs are ever going to make us all geniuses there is no reason to believe that future pharmaceutical research can’t produce mood enhancing drugs with only mild side effects. The benefits to depressed people alone of not stupidly insisting that depression is always a disease (rather than an unfortunate extreme end of a distribution) and researching medications that might make everyone a bit happier would be huge¹. More broadly I’m sure that everyone has noticed that some people tend to be more happy and energetic than others (and studies have suggested these people are more productive as well). The benefits to society of a compound that could shift everyone’s baseline amount of happiness up to where it naturally lies for these bright happy people would be greater than any other change since the industrial revolution.

However, in the chronicle article we find a much less enlightened view from one interviewee.

The notion raises hackles in some parts of academe. “It smells to me a lot like taking steroids for physical prowess,” said Barbara Prudhomme White, an associate professor of occupational therapy at the University of New Hampshire, who has studied the abuse of Ritalin by college students. Revelations about the use of performance-enhancing drugs in professional baseball have stirred public interest recently, and she sees parallels between athletes and assistant professors. “You’re expected to publish and teach, and the stakes are high. So young professors have to work their tails off to get that golden nugget of tenure.”

Now I’ve always thought it was kinda silly to keep performance enhancing drugs out of sports² but there at least it’s merely a game and fairness is a principle concern. In academics, however, we are supposedly actually producing something of worth. We don’t try and tell academics they can’t spend more time on their work because other people have children to take care of or family obligations. It’s not about being a fair competition but about maximizing academic output. True, perhaps one might reasonably worry that these performance enhancing drugs don’t genuinely lead to more performance in the long run, i.e., they are a way of gaming the system, but short of that I see no reason why they shouldn’t be allowed.

Also I found it amusing the way everyone seemed to assume that it was unacceptable for students to take these sorts of drugs during exams yet no one tries to stop people with ADD from taking ritalin or amphetamine during exams and often even give them extra time. Of course ADD is a real issue but it falls on a continuum and the same drugs that help concentration with ADD have been shown to boost everyone’s scores on the SAT.

So I finally got my application in for the NSF postdoc and got some needed sleep. So instead of working on my math like I should be now I went and downloaded the new Radiohead CD, “Rainbows.” Now I don’t actually like Radiohead that much so I didn’t pay anything at all¹ and that’s a perfect example of the inefficiency of the current copyright system. I’m likely to get some positive utility out of this (satisfying a hoarding instinct if nothing else) and this utility is a pure loss on a normal copyright system. However, it’s pretty annoying to hear all the people on the media and in forums act as if the fact that people are paying Radiohead for their CD shows that this is a plausible alternative model.

Even paying $0 for real honest reasons (worth less to me than transaction cost of using a credit card) even I was inclined to feel a little bit guilty and no doubt this is what causes people who actually like Radiohead to chip in a reasonable amount. But one feels guilt primarily because you feel that Radiohead is somehow stepping out on a limb by trusting users to set their own price. If this was ever to become a common practice that pressure would disappear. More critically is that the very people like me this system benefits will cause it to break.

People have strong intuitions of fairness and if you ever tried to distribute music more generally with this sort of system people would start feeling like suckers when they pay twice what their friend did for the music. Ultimately there will be an inevitable slow creep to the bottom as people check with their friends and see that their only paying $6 so that’s not cheating if I do that or come up with other reasons why it’s okay not to pay a bit less. I mean hasn’t everyone someone justifying their use of P2P by saying they would buy music if only the studies didn’t produce such crap? The same process of self-justification would start to happen with self-priced products as well. Besides, who is going to decide to buy 5 CDs worth of music they only sorta like for their car trip because they only have $15 to spend and they value the CDs they really like more than that?

No, I’m afraid solving the inefficiencies of the copyright system will require a fundamental change to the system of IP for creative content. Some means of truly collective purchase is required and the best system that I can think of at this point is to put works in the public domain after 3 years or so with a taxpayer funded system that compensates content producers based on numbers of tracked downloads from some central online repository. Maybe some clever person can figure out something better but as IP fills a bigger and bigger role in our lives the unacceptable inefficiencies of the current market become less and less bearable so sooner or latter something will change.

Rumsfeld’s plan to become a fellow at Stanford’s Hoover Institution has become the focus of protest. Now I think that Rumsfeld fucked up Iraq pretty badly and is thereby responsible for thousands if not millions (remember the Iraqis) of deaths. Given his popularity, especially among the left, it is no surprise that some liberals would protest this appointment. Some people would protest the fact that he was getting any job more prestigious than janitor. However, for Stanford professors to demand he not be given this appointment is an unacceptable attempt to tear down academic freedom and turn academic appointments into popularity contests.

First of all let’s make it clear that the protesters really are trying to subject academic appointments to a political test. Sure, they might raise a smoke screen about Rumsfeld not having authored many (any?) academic papers but if this was really the pivotal concern they would be demanding universities end the general practice of hiring ex-politicians as fellows. No one has given any plausible reason to believe that Rumsfeld would not have at least as much to offer the campus community in terms of real world experience in government and inside knowledge of his eventful years in government as other politicians who are offered these kinds of appointments. In other words it is as clear as day that those protesting this appointment of Rumsfeld are demanding that an otherwise valuable addition to the campus community be passed over for his political views¹.

Indeed this isn’t too far from what is being said in the petition against Rumsfeld’s appointment. A petition the New York Times says is being signed by many professors.

We view the appointment as fundamentally incompatible with the ethical values of truthfulness, tolerance, disinterested enquiry, respect for national and international laws and care for the opinions, property and lives of others to which Stanford is inalienably committed

Whoa. This is fucking nuts. Are they saying that Stanford should refuse to hire professors who argue against respecting national laws? What about academics who argue that government lie more or that the values of tolerance are overstated? Even if you actually believe that these sorts of views should disqualify one for a fellowship it’s merely a political belief that Rumsfeld is particularly at odds with these values. A good case could be made that Rumsfeld is more truthful than many of his equivalents and cares more for the property and lives of others than the protesters. He may have made a stupid mistake in invading Iraq but at least he seems to be concerned about the fate of the Iraqi people unlike many of the anti-war protesters who don’t seem to have even stopped to seriously consider what is in their interest. Ultimately what you believe about how good a defense secretary Donald Rumsfeld was is irrelevant. Rumsfeld is not advocating any anti-scientific or beyond the pale view like intelligent design or white supremacy and however strongly you might disagree with his politics or choices as defense secretary these aren’t good reasons to oppose his fellowship.

So several professors have called into the kqed show about this topic while I’ve been writing this and justified their opposition to the appointment by claiming that Donald Rumsfeld’s involvement with Abu Gharab make him a human rights violator and a violator of international law. Presumably the argument is that it would be reasounable to deny Hitler or Stalin appointments no matter what their academic credentials and it is thus reasonable to deny Donald Rumsfeld an appointment on the same grounds. This is pure sophistry to justify acting on their strong emotional reaction to Rumsfeld.

Not only is there insufficient evidence that Rumsfeld was more than negligent or cultivated an approving attitude of harsh terrorism to deny him a job even if he had personally tortured prisoners for information this still wouldn’t justify denying him the appointment. The view that it is reasonable to torture people for information when you believe it will stop more suffering than it causes is hardly beyond the academic pale and if you believe that we’ve made Iraq worse than it was in Saddam you are tacitly agreeing that sometimes human rights violations are a net positive (when they hold sectarian violence in check). The international law point is pure bullshit since there is more clear cut reason to believe Clinton violated international law with his (laudable) intervention in Bosnia than Rumsfeld did and if people really believed in this justification they would be getting out treaties and citing chapter and verse instead of using them to stand in for their vague emotional feelings on the issue.

Ultimately I’m skeptical of the idea that any views or prior actions justify denying academic appointments² but even if some views or actions are beyond the pale the mere fact that Bush was reelected just four years ago with Rumsfeld by his side is enough to show that Rumsfeld doesn’t fall into this category. You can try to play clever word games to reclassify just the people you really really don’t like fall outside the protection of academic freedom but if academic freedom is going to be worth anything it needs to offer a robust protection of divergent views and there is no robust distinction that can be drawn between Rumsfeld and other similar appointments. Ironically Rumsfeld is just going to come give some talks at Stanford, his days of causing harm are over, but the professors protesting his appointment are attacking important academic values. Does that mean that by their standard it would be fair to oppose hiring them?

I’ve been critical of the UAW grad student union at UC Berkeley for some time. While I’m generally skeptical of the (direct)¹ benefits of unions I think there is a plausible argument for graduate student unions as well as unions in potentially hazardous working environments, professions with particularly low liquidity or those employing illegal workers². In potentially hazardous professions unions serve an important social good by mitigating the harm of many people’s irrational tendency to underestimate risks in familiar situations. Left up only to the free market I suspect that people’s desire for the immediate reward of high pay would often encourage them to accept jobs where the risk of serious injury outweighed the reward of increased pay. This is obviously not the case for grad students but there is a similar problem of hidden risk. In particular graduate study is only a worthwhile payoff if one truly receives a diploma meaning that every year spent in graduate school is effectively a deposit of resources into the university that goes uncompensated should you not graduate. Just as people’s irrational failure to take into account future risk of death can justify the otherwise inefficient mechanism of union bargaining so too can their irrational failure to take into account the risk of either not graduating or receiving poor recommendations if they don’t do excessive lab work for their mentor justify grad student unions. Somewhat counter-intuitively I take the primary benefit of unions at this stage in US history to be their role in restricting employee choice. That is by preventing employees from agreeing to certain arrangements (yes I’ll work this dangerous job for more cash or I’ll do 80 hours a week in lab for a good recommendation) they prevent employers from providing incentives that prey on human irrationality.

I recognize the benefit the UC grad student union provides for many grad students in this fashion (thankfully not truly necessary in math) and since I think TA’s here aren’t paid nearly enough I remained in the union despite a certain skepticism of it’s political policies and role in restricting differential grad student pay for different departments. However today I finally sent in an email asking to be removed from the rolls when I saw the most recent bargaining update they released. I provide the full text after the break but the section that really drove me to ask to be taken off the roles was the following:

CHILDCARE: the administration rejected our proposal to subsidize employee childcare costs though they recognized the need for a childcare program. One university spokesperson accurately characterized our proposal as “a subsidy program to enhance an [employee’s] ability to matriculate, be gainfully employed and contribute to the mission of the university.” The next day, another university representative, in rejecting our proposal, said, “The University believes that there are sufficient child care resources provided to most of the individuals that you represent, and those programs are both effective and cost effective . They provide services at a reasonable cost, recognizing the financial needs of the students.” This remark displayed an arrogant disregard for the realities of life for teaching assistants, readers, and tutors with children, who more often than not face lengthy waitlists and programs that absorb at least half of their monthly wages.

I have every reason to believe that grad student pay is a zero sum game. Every dollar the UC spends to increase child care resources is one less dollar that can be used for other sorts of graduate student support. Thus by taking the position they have the union is basically advocating for a transfer of money from my pocket to the pockets of people with families.

Now I don’t have anything against grad students who choose to raise families and I sympathize with the fact that it is very difficult to raise a child on a graduate student’s salary. However, it’s also fucking difficult to try and afford frequent plane flights across the country to maintain a long distance relationship. I’m sure it’s equally difficult to try and visit sick relatives, help with the family business or any other major life choice that requires money. Now I could see an argument that certain sorts of life choices tend to produce more utility so we should subsidize those at the expense of people who would use their money to go skiing in Vale. Yet on such a theory it should be relationships, which have a much stronger correlation with happiness than children, that should be supported and I have no doubt the number of grad students at Berkeley in long distance relationships is of the same order of magnitude as those who have children.

Now someone is undoubtedly going to say something about women running out of time to have children but I would argue that relationships, not reproduction, is the truly time sensitive concern. Very few women in grad school are anywhere near menopause and upon graduation they can still choose to reproduce but once out of grad school your ability to meet worthwhile new people plummets. Sure you could argue that once out of grad school it is very difficult for a woman to have a child without taking damage to her career but it is misleading³ to suggest this is a gender equity issue and uncompelling compared with the unconditional increased difficulty of meeting a significant other outside of school. Now I certainly agree that academia unnecessarily penalizes people with competing interests such as child care while they are young but if anything academia needlessly penalizes relationships with other academics more than it does reproduction. In other words every valid concern about fairness or individual utility that favors subsidizing childcare also favors subsidizing my plane flights to Boston as well as many other life choices.

What then about the argument that affordable childcare is needed for the child’s wellbeing? This might be a compelling argument if we were talking about a group besides grad students but while expensive child care might burden the grad student it is unlikely to cause the child to be neglected or otherwise suffer. Given the various studies suggesting that the difference merely adequate and excellent parenting makes in quantitative measures of a child’s future success is quite small this argument just doesn’t hold water for grad students. Grad students are the one group we can count on to delay having a child or rearrange their lives to make sure the kid isn’t neglected.

What then about the final argument that we need to encourage more grad student types to reproduce. I think this is the only plausible case to be made but I no longer think it is compelling. The idea that we need to encourage smart people to reproduce as some kind of selective breeding program seems to make a subtle mistake about the way natural selection works. In the long run evolution will either manage to put together the little tweaks that make grad students smart with a strong desire to reproduce or it will find a better unrelated path toward intelligence. As far as the near future I don’t see subsidies for grad student families making huge differences in the electorate but I do see social benefits accruing from discouraging academic women to reproduce. Certainly anyone who believes in the role model theory for affirmative action should think that the more we can do to discourage women from opting out of academia for children the better. In fact anyone who believes that women are somehow triked or brainwashed into taking more than their fair share of childrearing should oppose this sort of reproductive support on the grounds that it reduces the unfairness and works to eliminate the stereotypes that caused the problem.

Ultimately I was uncertain about my support for the UAW grad student union in the first place and this message finally convinced me that my membership was doing more harm than good. The university doesn’t even want to go back to the days where biology grad students could be made to work 80 hours a week but my support for the union signals my acceptance of fucked up feel good policies like prioritizing families over the childless and silly demands for equality between the summer session and the school year⁴. Since the union isn’t going to disappear all my continued membership does is help convince the union and the university these stupid policies are what the grad students want. Besides I just feel dirty being affiliated with a organization that not only makes such unjustified policy demands but also alleges “bad faith” on the part of the university for simply believing that the union’s positions aren’t correct.blah⁵

(more…)

In addition to the cost I usually find closed source text editors and similar utilities to be lacking in features and insufficently extensible. Textmate for OS X, however, is a glaring exception. It is well worth the cost and I’m constantly surprised by the many useful bundles and customizations available (for instance convienient remote editing with Cyber Duck or easy blog posting using the MetaWeblog API). So when Texmaker started slowing down on large complex files¹ I resolved to switch over to using textmate to write up my mathematics in LaTeX.

However, textmate’s prompt syntax highlight combined with the depreciated use of ‘$$’ to start displaymath mode was really annoying. Each time I would start to add inline mathematics by typing ‘$’ textmate would automatically provide the closing ‘$’ leaving me a line like this:

every $g \fungeq f$ that is ‘close’ to $f$ can compute $$

Of course textmate now interprets the remainder of my file as part of a displaymath block started by the ‘$$’ consequently changing the syntax highlighting. Since writing up theorems involves lots of inline mathematics this quickly became very annoying.

Anyway in case anyone else runs into the same problem let me share the quick fix I used. Go into your bundle editor and in the Latex bundle edit the language TeX. Find the following section

name = 'string.other.math.block.tex';
   begin = ‘\$\$’;
   end = ‘\$\$;

and change it to:

name = 'string.other.math.block.tex';
   begin = ‘\[';
   end = '\]‘;

Of course this is something of a dirty hack since it disables the correct syntax highlighting for the ‘$$’ abbreviation. But since that is depreciated you always use ‘[' and ']‘ right?

If anyone knows the ‘right’ way to do this I’d love to hear.

To avoid confusion let me emphasize that I think it is pretty much mandatory for GSIs to make themselves available during the time leading up to the final to answer student questions and otherwise explain the material to students who ask. But the more I think about it the more it seems like offering a true review session, the sort of thing where you prepare specific problems for the students and have a spiel prepared for them is actually harmful (posting a list of practice problems to the web for all the students to try is a different matter and something I approve of).

Before we can even get a grip on this question we need to be clear about the goals of a class like this. Given that these students are fairly unlikely to ever use this material outside of this class three reasonable goals spring to mind.

1. Actually create real understanding in the students
2. Actually teach the students the skills of calculus.
3. Prepare the students for the second half of the year if this is the first semester.
4. Train the students to think quantitatively/formally (in a very weak sense)
5. Function as a hurdle passage of which indicates a certain level of work ethic, intelligence and ability to learn

No matter what we take the goal of the course to be we have two possibilities to face. Either review sessions are genuienly effective at improving student performance on the final or they are not. If offering genuine review sessions (as opposed to say office hours) doesn’t offer a substantial benefit over holding office hours then holding them is either a waste of time or some kind of dastardly trick played on the students (who are all clearly lead to believe the aim of the review session is to help them study) and in either case ought to be discouraged not celebrated . On the other hand if offering genuine review is substantially effective at raising exam scores we have to ask what makes these few hours have such a big impact.

From my experience I would conclude that what makes a review session effective at raising exam scores isn’t that it conveys more understanding than office hours, just the opposite in fact, but because it helps the students get the low hanging fruit. In particular it’s been my experience that the primary advantages review sessions have over office hours consists of helping the students avoid stupid errors like forgetting the +C in an integral, bootstrapping off the Ta’s implicit understanding of what sort of problems the professor is likely to ask, and seeing all the types of problems laid out at once letting the students build up a lookup table letting them infer what type of problem they are being asked using textual hints rather than real understanding. In short, to the extent review sessions are effective it isn’t because they make significant contributions to understanding.

Yet even if you think that having a real review session as opposed to just office hours has some benefit surely this is offset by the harm it does undermining the value of the test as an assessment. For starters since review sessions are offered outside normal class periods it is likely that some students will be unable to attend, or find it significantly more difficult to do so. With office hours the same TA will often have a range of options while with real review sessions there is often implicit (if not explicit) pressure not to attend another Ta’s review session and frequently only one or two Ta’s will offer full scale review sessions while the rest will offer something between office hours and review sessions.

Review sessions surely reduce the effectiveness of the exam in estimating work ethic or ability to learn independently as compared to office hours. To the extent that these math courses are simply hurdles to make sure that the students are smart and disciplined enough any kind of hand holding (as opposed to offering office hours for those who want to make use of it) is counterproductive. As many people don’t attend review sections because they judge it a poor trade off (need to study for other finals more) any ability review sessions have to improve grades without increasing understanding or future ability to apply the material undermines the ability of the exam to measure these attributes. Also more generally it seems like the more test taking strategies that students learn to use on the exam, e.g., learning to use textual clues to the type of problem, the worse the test will be at judging either actual understanding or ability to apply these skills in any context but this particular course.

In short it seems to me that the benefits of actual review sessions are quite small compared to those from office hours even though they may be quite effective at raising exam scores. On the other hand the harm done by review sessions to any reasonable conception of what course grades are supposed to track seems significant. Yet despite this holding actual review sessions seems to be uncritically regarded as a good thing for a TA to do and I’ve never heard of a professor banning them. At the very least professors should require that any TA who makes a review sheet available post it on the web to make it easily available by those without friends who attended the review section.

I’m well aware that most review sessions are offered with the best of intentions but that is my real complaint. During my 5 years of teaching I’ve seen a lot of strong attitudes about how teaching should be done and a whole host of other background assumptions about what makes for good teaching but virtually never heard any serious ground up analysis of what we are trying to achieve. At the very least it seems perfectly plausible that review sessions are actively harmful yet this sort of consideration doesn’t ever seem to come up. Perhaps doing so is too depressing and we need to pretend we aren’t inflicting totally useless material on students who won’t ever use it while making them hate math along the way but it seems we could be a lot more useful if we actually thought through what we were trying to do rather than taking for granted how we should teach and then trying to justify it.

For instance I think just having to draw a line between when it is acceptable to muck with grades to motivate students (allowing not turning in HW/low attendance to impact grades) and when it is not (seripticiously giving girls a 5% bonus in the class if we discovered this improved both sexes motivation) would be a huge improvement over the current situation.

So I’m listening to ‘Work with Marty Nemko’ on KALW (91.7) and he just accused college professors who are good at research but not temperamentally suited to good teaching of being immoral for taking jobs at universities. This is an utterly ridiculous claim. As the vast majority of research jobs are exactly such university jobs this implies that we would be better off with happy calculus students than our cutting edge research.

Still he definitely has a point when he says that research and teaching are very different skill sets. The question is whether it makes sense to ask (as he does) for separate tracks for teaching and research. My personal interest is clearly to encourage such a division. We would still have to employee researchers in some fashion and if we freed them from the annoyance of teaching that would be great.

However, I think this notion comes from an overly narrow notion of what good teaching constitutes. There is good teaching like we might want in high school which grabs the average student’s interest and helps them learn some simple set of skills that will help them in the real world. There is also teaching which has the potential to create a productive engineer, scientist or other highly skilled profession. The problem is (most) of the people with the skill set to do the first sort of teaching are utterly incapable of doing the second sort of teaching.

For instance look at what happens to people who are genuienly gifted or interested in math/science in high school. They are repeatedly frustrated and turned off by teachers who, while quite good at teaching to the average student, don’t understand enough of the subject to answer the interesting questions. While this conflict could be reduced by finding teachers who are skilled in both research and marketing their subject to the average student even in this magical world of perfect teachers there would be tension between the two goals. Good teaching for the casual learner is about taking the subject and transforming it via metaphor to something they already understand. Good teaching for the aspiring researcher is about teaching the student to think in a different way.

A perfect example is the epsilon-delta definition of the derivative. If one is teaching casual students insisting on a symbolic understand of this definition is about the worst thing one can do, instead one wants to give vague pictorial understanding. On the other hand for the aspiring mathematician the goal is to banish, or at least explain, the vague pictorial understanding in terms of the formal definition.

The problem of teaching in universities is partially illusory and partially a result of an unclear division between research universities and glorified versions of DeVry.

The apparent but non-existent problem of teaching arises when students who are pre-law or pre-med are (effectively) required to take calculus courses. It then appears that they are being poorly taught because they have no intention of becoming researchers in mathematics but are taught by professors selected for their ability to research and teach real understanding not practical calculus skills. The reason this is only a matter of appearance is that learning calculus really has nothing to do with why they are being made to take the course.

Frequently courses like calculus are required for no other reason that to weed out students who aren’t going to be able to hack it. For this purpose all that matters is the uniformity of teaching in the class. While their are obviously a few outliers (the profs who try to make them learn it all rigorously) for the most part the different teachers are equivalent and that’s all that matters. To some extent what these students are learning is how to take classes and study material they aren’t excited about and don’t have a teacher who makes it interesting or seem relevant to their lives. If these students had the sort of super teachers you see in ‘Stand and Deliver’ it would defeat the whole purpose of these weeder classes.

I think there is a good argument that we shouldn’t have these sorts of fake requirements that exist for no other reason than to be hard. I definitely think many breadth requirements exist for no other reason than show and should be revised either to demand real understanding or clearly be nontechnical survey classes. Unfortunately all too often the continued warnings about our lack of math/science skill are answered by useless requirements for students to solve calculus problems without understanding that they will never use. However, it isn’t justified to criticize university profs for not teaching well when there isn’t actually any content the students are really supposed to learn.

The second issue is more of a real problem. Unfortunately universities no longer only educate the intellectual/academic class they serve as general training for the job market. Partially this is just the effect I mentioned above, university graduation is just a proxy for work ethic, smarts and knowing the right social behaviors. To this extent it doesn’t matter how good the teaching is as long as it is relatively uniform, and it is nearly impossible to achieve uniformly excellent teachers. However, there is also a sizable fraction of students who are using university to receive practical training in applied careers.

These are the students who need to learn to work in a lab to be a DNA/forensic technician but don’t need a deep understanding of the chemistry. Or they are elementary/HS teachers who need to learn how to present the material but can’t be expected to really understand it. Or they are electronic technicians who need to be able to solder or maybe use mathematica to solve some fixed set of equations but once again need no deep understanding. The problem here is that these students would be best served by going to a school/program that focused on doing technical training but the low status of these programs guarantees such a degree is evidence of poor ability.

To deal with this problem the distinction between research universities and other schools needs to be made much more clear, not only to the professors but the students as well. You shouldn’t have schools like University of Illinois at Chicago which hires serious mathematicians for their department even though their undergraduate student base is pretty clearly on the technical end. I get the feeling that this is much more similar to what happens in the UK where students are tracked far earlier but I’ll wait for Adam to chime in on this.

Unfortunately I’m not sure such a change would be possible of even desirable. It may not be possible because we put greater status on real academic understanding and some people who can’t hack that are always going to want to go to the half-assed research schools. It may not be desirable because I suspect the net effect of such a distinction would be to shift nearly all the monetary support to the research schools.

So in the story of the student who shot his principal to death is making its rounds in the news. Now obviously shooting your principal is not only wrong but just plain stupid. However, at least in this situation why it happened is extremely understandable.

Apparently Erik Hainstock, the shooter, was the victim of frequent harassment (people rubbing up against him calling him fag etc..). He complained about this treatment to the teachers and authorities who appear to have done nothing, or next to nothing. Yet despite failing to enforce discipline on a serious matter of harassment the same people made sure to enforce the rules and give him an in class suspension when he was caught with tobacco. Someone in this situation really is totally fucked and without options. Of course it’s just highschool and it will pass but we all know that it doesn’t feel like that in highschool.

The negligent inability of teachers to deal with situations like this is perfectly illustrated in the comment that his teacher Nowak made to the news, “He wasn’t picked on. He was the one who would have picked on people.” Of course his friend when interviewed was aware that Erik was picked on a lot as well as admitting that he did a fair bit of harrassing himself. But this is exactly the psychological profile one expects from someone who is harrassed. Basic competancy for school teachers, especially special ed teachers, should include knowing that the common reaction to being picked on is to make yourself feel better by going and picking on others.

Disgustingly Erik threw a stapler at his teacher just two weeks before, obviously indicating something was wrong, and apparently they just put him back into the same class. Not doing cruel idiotic things like this should be basic training for teachers and basic policy in our schools.

Though not right it is emminently understandable why someone, especially someone who had been put in special ed would fell something like this was their only option. Hell if I hadn’t been crazy smart and come from a family where college was assumed or slightly more vengefull I could see myself having done this sort of thing.

What really disgusts me about these situations is the failure of most people to see the strong mitigating circumstances in situations like this. I mean imagine it was a woman being sexually harrassed about her weight (jokes about big sexy or something) and her supivisors did nothing to fix it while disciplining her for minor issues. Not only would the company be sued people would be horrified at their immoral behavior and ultimately changes would be made to fix it. Certainly no one would be pointing out that she sometimes gossiped about women being fat so she couldn’t be the victim. Or imagine he really was gay, the fact like many gay guys he mocked some people for being really flaming wouldn’t be seen as a reasonable response to his harassment.

This is also why I have big qualms about special protections for certain sorts of harassment (sexual harassment, sexual orientation harrasment). Ultimately harassment is harassment and it all hurts for the same reasons. It doesn’t hurt any more because you are a member of a group who is commonly victimized. Yet unfortunatly it sometimes seems like these special harassment protections soak up the sympathy and the willingness to fix the problem. If something can be shoehorned into one of these salient categories great if not then people don’t care so much.