Thoughts from March Meeting
I had a great time at the APS March Meeting. Since I’m attempting to blog anonymously, I’m not going to get into the specifics of which talks I found most interesting/relevant to my research, but there are a few more general things I want to talk about over the next couple days. I’ll discuss some more fun things in the future, but for now, a somewhat grumpy bit about mentoring graduate students.
One of the moments during the meeting which really stuck with me was when a professor got up to give a contributed talk and explained why he was standing there, rather than his doctoral student (whose name was listed in the program). He said something like, “My student was going to give this talk originally, but I decided it was too important not to present myself, so I pushed him away. [chuckle] I hope he isn’t too mad at me.” (The use of the verb “pushed” I remember clearly.) After a brief pause, there was some (I think nervous) laughter from the audience, then he plunged into the rest of his talk.
For what it’s worth, though the talk did cover a reasonably important development, they weren’t the only group talking about it or the first ones to have demonstrated it, and their results weren’t particularly breathtaking as far as I could tell. What I think happened was that a more well-known group was reporting similar results, and when this professor saw the abstracts scheduled, he wanted to seem just as cool as them. But I’m willing to grant for the sake of a thought experiment that the results are actually unique and important. Also, for clarity’s sake: plenty of people give talks for other people at March Meeting. Sometimes people are sick or unexpectedly busy and unable to make it, and someone else in their group covers for them. It’s no big thing. So that part’s not my issue.
I may just be lucky — no, I know I’m lucky — to have an exceptionally nice advisor… but doesn’t this professor’s behavior seem really out of line? I know he’s the one in charge, and (in some cases) the one working day and night in order to win the favor of his tenure committee, but I don’t see any reason for stepping in in this case other than sheer arrogance and credit-greediness. He could have given his own talk; it is okay for multiple talks to come from the same group. (Though he would have had to come up with something at least slightly different to talk about.) The first and, if you want, last slide in the talk can have the professor’s name on it. Really big, if you like. With a picture, so everyone can recognize and find him later if they want, for congratulations or questions. He can make sure to be in the audience. It’s not considered really out-of-line for PIs to jump in during the Q&A period after a talk with more thorough answers than their students give, or offers to discuss issues after the session, so he could have made himself visible to other conference attendees that way too.
I can imagine a professor trying to do important things and get credit for them in order to impress his or her superiors (to get tenure, to get a promotion, to get some other special responsibility assigned to them, etc.). What I can’t imagine is that the tenure committee, or department head, or whoever, cares who is standing in the front of this breakout room in the Pittsburgh conference center to give this 10-minute talk. It doesn’t change whose name is listed in the official record! And presumably all that matters to the tenure committee (or whomever) is that important work was done under the supervision and guidance of this professor. Training brilliant and successful graduate students probably also matters to them, a little bit, yeah? So, having your grad student give this important talk at March Meeting on behalf of your lab is presumably just as good as you giving it yourself, if not better, in terms of your own career advancement.
For the student, on the other hand, being recognized at the conference is potentially a lot more important. Networking is significantly harder when you’re one of the small fish, and a great way to meet people is for them to approach you and ask you questions after your talk. That student is probably going to want a postdoc position someday, probably in the not-so-distant future! It’s not crazy to imagine that he’d end up making contacts in other groups that could lead to eventual postdocs or even permanent jobs.
In talking about this with others, I heard the suggestion that the student might have been terrible at the talk during practices beforehand, and the professor could have been stepping in to save face for his group. In that case, though, I think there’s no reason to explain it this way in front of the audience. (Maybe it’s the explanation you give your student if it’s the last minute and you just can’t convince him he’s unprepared.) You say something like, “My student wasn’t able to present this talk today, so I’m taking his place.” Something that makes it sound like he could have been sick, though you might leave it ambiguous if you’re really averse to little white lies.
Why rant about this, Z? you are probably asking. This one guy was a jerk. Big deal. Well, I’ve read and heard other people’s accounts of working with nightmarish advisors, so I know he’s not the only jerk out there. Also, if I saw one guy like this in during the small slice of the conference I attended (12 out of 14 sessions, minus a few talks here and there that became part of my lunch breaks), there are probably a few more. Each session has about 40 rooms of simultaneous talks. If we assume I saw a reasonable sampling of personalities at the conference, that predicts more than a handful of other professors out there like this one (not to mention a few more who think his behavior is okay but didn’t happen to act like him this time).
I just wanted to put it out there on the tubes that I think this sort of behavior on the part of a professor is inappropriately selfish and not at all constructive. I’m very interested in hearing the opinions of others out there in academic-blogger-land, on how frequent this sort of thing is and whether it’s as bad as it seems to me. (Those links are to people I thought of off the top of my head who’d probably have something to say on this, but this question goes out to everyone.) Tell me: am I very sheltered, or right to be outraged?
Math instincts
This article from the New York Times is somewhat old, but it’s still interesting. Research about how humans (and other animals) understand numbers, in a kind of primitive mathematics, can give us insight on how to teach math to young children.
One research team has found that how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses. Other scientists have shown that preschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific. Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.
Try this Flash game to evaluate your own number sense.
Are you here for advice?
We get a significant amount of traffic for searches like
- do you have to be good at math to understand sciences
- bad at math but a good engineer
- smart people who are bad at math
- why do i always do bad at math
- can you be successful if youre bad at maths
because of a few of our old posts on innumeracy and attitudes about it. It seems like people are looking for advice and answers, and our posts don’t really provide them, so I thought I’d give it a shot today.
It appears that many of you Googlers (or Yahooers, or what-have-you) want to know whether it’s possible to be a good engineer or scientist while being bad at math. My short answer is: probably not. My longer answer begins with a question back to you: what do you mean by math? For most things I’d consider engineering or science, you need to have a good handle on geometry, high school algebra, trigonometry, statistics, and calculus. If you’ve taken classes with those names and failed them, a career in the sciences is probably not for you.
I assume most people who would ask this type of question are already in school to become a scientist or engineer, though, and are having second thoughts. Don’t worry, university classes are supposed to be harder than high school, and it’s normal to struggle a bit in the transition. Maybe you’re taking your first math class that includes serious proofs as part of the curriculum. If you’re good at calculations but struggle with proofs, there’s no problem with a career in engineering and plenty of available paths to take in the sciences. You probably won’t end up a string theorist, but we’ll still love you. (I suppose I should also ask, what do you mean by science? If you consider anything ending in -ology to be science, you have a wider range of options, including some that use almost no math.)
Then there are those of you asking why you are bad at math. I don’t know. I would obviously need some more information. Maybe you’re not taking notes or paying attention. I tutored some kids during high school that were failing math for that exact reason. Once I suggested that they bring their notebooks to class and, you know, write things down once in a while, their grades shot right up. Maybe you have a terrible teacher. That’s far from impossible, based on my experience. It’s also a possibility that you just don’t naturally think in the way that math requires you to think. It’s good to try to think that way — don’t write off math from the very start — but if you find that over and over again you just can’t seem to get the hang of it, perhaps math is not for you. That doesn’t mean you’re bad, and it also doesn’t mean that math is bad. Find something to do that you enjoy and excel at, and please, continue to respect people who are good at math — the same way that I respect people who are good oboists, or good swimmers.
It’s certainly possible to be successful and bad at math and/or science. (Just look at Congress!) I would also say that it’s possible to be smart without being good at math, though I’m a little more hesitant. What you mean by “smart” and what you mean by “good at math” plays a big role. I don’t think it’s possible to be smart without being capable of logical analysis. You can be smart without knowing that “integral” is a noun as well as an adjective. There are plenty of brilliant lawyers and insightful columnists and effective managers who never got the hang of l’Hôpital’s rule, and I’d still consider them smart. (I think Gardner’s theory of multiple intelligences doesn’t have much merit as science, but it does offer some insight into what we mean when we talk about being smart. There’s more than one way to do it.)
Any more advice for our search engine visitors? Feel free to leave it in the comments.
New SAT policy
I read in the New York Times that the College Board has changed its policy on score reporting for the SAT. Rather than having all scores automatically sent to colleges they’re applying to, students can select only the score or scores they want the colleges to know about. The goal, according to the article and the policy statement, is to help students relax about standardized testing and be confident that they can give colleges a good first impression. In reality, all it does is give students more incentive to retake tests over and over… though I’m not sure how big a change that is from the status quo. At any rate, college admissions committees are overall not pleased.
The SAT currently has three sections, taken on the same date: critical reading, mathematics, and writing. (Critical reading and writing were split from the old verbal section.) Each section gets scored separately from 200 to 800 and a total score is calculated. With the new “Score Choice” policy, students can choose which date’s scores to send, but they can’t pick their best subscores from multiple testing dates. Surprisingly (to me), this is one of the complaints that colleges have. Many schools apparently only care about your best reading score, your best math score, and your best writing score, and they pull those scores from your full report then disregard everything else (even if it’s all 200s). Colleges won’t be able to extract information if students choose to send only the test results with the highest total score, and in some cases that could actually harm their chances of admission.
That’s a pretty charitable policy, and I didn’t realize it was as widespread as it seems to be. The other common practice is to consider only the test with the highest composite score, no matter how many test dates are reported, which — I also didn’t realize — is done by most colleges. (The US Naval Academy is the only school I can find that takes the average of tests taken. Thanks, Congressman Connie Mack!) [EDIT 1/5: Commenters tell me that this information is no longer accurate. My apologies. If anyone knows of a school that really does average scores on multiple tests, please let me know.] For schools who truly consider only the highest composite score, the Score Choice policy doesn’t seem to make any difference at all. There are some minor complications coming from schools that say they require all scores but will only look at the best one — but if they only look at the best one, what does it matter?
The reason it matters, of course, is that many schools aren’t only looking at the best composite score. Sure, they’re using that number to fill in the “Total SAT Score” blank on the summary sheet, which helps the student to a degree. They’re also looking at how many times the student had to take the SAT in order to achieve that score. The fact is, that information is relevant.
I could tell you I made a free throw with my eyes closed, but that doesn’t make me as good as Michael Jordan. It’s important to know the additional information that it would take me ten thousand tries to make it once, purely by chance. An NBA recruiter doesn’t just want to hear about the best shot you ever made; he wants to know about your entire history as a player, because that’s a better predictor of your future success. College is very similar. If you had to take the SAT every time it was offered from sophomore year right up to the college application deadlines (along with, probably, plenty of tutoring and additional practice), in order to get a score you felt comfortable submitting, it would be a lot less impressive than if you were able to get that good score on the first try.
I don’t think the SAT is a perfect test, but I think there are useful things that admissions committees can glean from a student’s SAT performance. (I’ve explained this in some comments here already.) Given that, it seems like an incorrect decision to limit the amount of information colleges get. We shouldn’t forget that the College Board makes a ton of money off SAT registration fees, and stands to make more if students retake the test in larger numbers. They’re not being purely charitable and thinking only of students’ test anxiety here. However, as long as students rather than colleges are the paying customers of the College Board, the College Board policies are going to shift according to student demand, not in the best interest of education in general.
College endowments
Senator Grassley recently held hearings into how colleges use their endowments. There’s some understandable interest here. Universities frequently control large amounts of money, with a handful of them controlling huge assets. (Harvard, the richest by far, has over $34 billion.) With college costs rising faster than inflation, some in government have thought about ways to force colleges to put this money to work faster to help out with their expenses and reduce tuition. I really think this debate, though, has missed a few points.
First of all, and I think this is the most important point, the money has to be used on education/research eventually. Most of the money in endowments is tied to specific uses. It’s for scholarships, or the salary for a named professorship or something. Even what isn’t specifically targeted is going to end up being used by an educational institution. The real complaint here is just that colleges are saving more than they should — overvaluing education in the future as compared to the present.
I’m inclined to think they are not. Recognize first of all that, to a great extent, any lack of them funding education out of their endowments right now will be replaced with funding from people paying tuition, as long as tuition doesn’t get so high as to dissuade people from going to college. Now, I believe it’s clearly the responsibility of government to provide enough financial aid that everyone can attend college (assuming they put in the effort in high school to make themselves qualified). This is what’s annoying congressmen, since they don’t want to make room in the budget for it, and of course that’s understandable.
The real problem here, though, is that the vast majority of endowment money is held by only a small handful of schools. Maybe Harvard, Princeton, Yale, Stanford, and MIT can make college free for everyone for a little while by spending down their endowments (or at least, not growing them fast enough to keep up with inflation), but that only affects a tiny minority of college students in the US, and those schools already offer enough financial aid that students from poor families pay very little if anything. Most students go places that don’t have much in the way of endowments, and Congress is still going to have to offer enough financial aid to keep those places affordable.
However, these big endowments do constitute a form of national savings for the US. The American savings rate is low (or negative, really) and could use every bit of help it can get, and a half-trillion dollars in savings isn’t something we should be trying to get rid of. Also, more importantly, it helps to lock in the leading status of US universities. The world’s most elite universities are near-universally in the US (the main exceptions being Cambridge and Oxford). This is largely a consequence of economics. The schools with the ability to bring in the top people will always be the best. The US isn’t going to stay the world’s biggest economy forever, and the gap is definitely going to shrink fast. Building up huge endowments in our top universities essentially locks in their top position, guaranteeing that they’ll be able to fight and stay at the top even as the overall position of the United States deteriorates.
The government should try to avoid forcing private actors to spend their money. I’m not a libertarian, and regulation of nonprofits is something I could live with when clearly necessary. Here, though, I don’t think it is. Harvard is still raising lots of money, so clearly their donors don’t have a problem with the way the endowment is being used. At a time when the United States is failing in general to invest in the kind of long-term society-building things that keep a country at the top of its game, private charities that devote resources to planning for the very long term should be helped, not hurt.
Updates in scientific literacy
Several stories have been floating about lately, all generally on the topic of popular understanding of science. Here are the highlights.
A court has ruled that the University of California was well within its rights to deny admission to students they found unqualified as a result of their having attended Christian schools. The schools in question taught many classes that were extremely Bible-centric, to the exclusion of nearly all other content, making it impossible to meet the UC admissions requirements with their courses misleadingly called “biology” or “history.” I found this personally interesting in light of my earlier comments on how far it’s appropriate to extend religious tolerance. Even though it has upset some religious people, the courts have ruled that it’s okay to assess religious descriptions of the world and find them academically lacking.
Speaking of lack of academic background, I was happy for once to read USA Today, which reported that 76% of Americans believe that improving science education should be a priority issue for presidential candidates. In keeping with this, about 26% say that they themselves have an adequate understanding of science, but more ridiculously “44% couldn’t identify a single scientist, living or dead, whom they’d consider a role model for the nation’s young people.” My reaction is similar to Doug Natelson’s: Or dead? Really? We couldn’t name, oh I don’t know, Einstein? Perhaps he is not hip enough for the youth. (Check out Doug’s post for some more details on presidential candidates and their support for science research funding, as well.)
The USA Today article discussed science literacy in the context of voting ability. If Americans aren’t sufficiently “science-savvy,” how can we make the right choices about science issues? It’s not just about budgeting for research, it’s also about healthcare availability, education, stem cells, abortion… and it’s about every issue that invokes statistics. A bit more math than science, yes, but if we were more educated about science we’d be better at identifying large enough sample sizes and acknowledging deviations from the mean. That applies to almost every issue on which there is public debate involving presentation of evidence.
I certainly agree that science education should be a bigger priority than it currently is, and my opinions were only reinforced by this report on end of life care, which stated that 57% of the American public believes that “God’s intervention could save a family member if physicians declared treatment would be futile.” Almost 20% of medical professionals share this belief. While I don’t believe in miracles myself, I of course can’t offer positive falsification of their existence. What we should all be able to agree on, though, is that if all medical signs point to imminent or already-real death, a miracle recovery is not coming this time. There are many other interesting outcomes in the study, such as differing opinions about persistent vegetative state and how long it is acceptable to demand continuing treatment of a dying loved one. Orac of Respectful Insolence wrote a very thoughtful and thorough treatment of all this, cautioning against becoming too preoccupied with the religion aspect. I agree wholeheartedly with his bottom line:
Indeed, the focus on religion takes away the focus from the real issue: improving public understanding of scientific medicine and what it can and cannot accomplish. Lots of patients have unrealistic beliefs about health care based on all sorts of things, be they religion, faith in pseudoscientific quackery, or just fears based on misinformation that is rife in the media (i.e., the claim by antivaccinationists that vaccines cause autism). … Persuading families and patients that what evidence-based medicine recommends is the best for their injured or ill loved ones requires a far gentler touch.
Carnival of Education #185
It’s carnival time again. My post on reasons for learning math has been featured in the Carnival of Education. This carnival has plenty of interesting stuff, especially if you teach. There are a couple more general audience articles as well, including this cool post adding a bit of reality to the classic teacher-inspires-troubled-youth genre of movies.
Why we learn math
There are lots of students who aren’t interested in math, and lots of math teachers who want to motivate them to actually put effort into the subject. Most of this struggle seems to revolve around how useful math is, with kids saying (or at least perceived to be saying) something like “I’ll never need this” and teachers trying to convince them that math is everywhere.
For a variety of reasons, I’ve never been happy about this way of looking at why one learns math. Most importantly, I think, teachers are bound to fail at convincing students of the usefulness of math, even with the most applicable of topics. Part of the reason is that the subjects that apply the math are always taught after the math itself. Physics, economics, and so forth make the need for quadratic equations very clear, but you would never teach someone physics unless they had first mastered quadratic equations. This means that the math a student is currently learning is never being used in their other classes as they learn it. Some students see stuff they learned years before now being used routinely, and they learn to trust that the things they’re being taught now will turn out equally useful in years to come. That’s a healthy attitude, but even with an explicit explanation of the situation, many students will not adopt it.
It’s also worth mentioning that there are in fact topics taught in high school (especially in a school with a strong math curriculum) that aren’t likely to be used in the future by many of the students. Calculus is helpful in a variety of occupations, but far from all. Geometry, barring the straightforward basics, is only helpful in unusual circumstances. Imaginary numbers are unlikely to come up too frequently. A teacher is therefore bound to fail at showing the usefulness of these things directly.
I also think, though, that judging math by its usefulness is missing the point. Why do math teachers need to prove that their material will be vital for daily life in order to make it worth learning? Poetry would never be able to pass that test, nor would history or art. You don’t “use” Shakespeare very frequently. Of course, that’s obviously not the point. We fully recognize that sonnets aren’t “useful,” but we still learn them. We think it makes your life better to have the wider, deeper view of the world that comes with having studied art and literature. We think they’re part of being an educated person. We think that by studying them you build fundamental skills of critical thinking, imagination, and interpersonal relationships that are important, even if the actual material you’re learning is not. These things are all true about math as well, but people don’t think of math that way. They think of it as a prerequisite for other (important) things.
Math should be taught as something you learn because it’s interesting and enlightening. It should of course be mentioned that it’s also useful, but that should never be seen as the only reason why it’s being taught. To do this, it would help to change the math curriculum a bit. Anyone who’s ever taken proof-based math in college knows that mathematicians don’t spend their days doing the stuff that’s taught in high school. Engineers solve a lot more equations than mathematicians do. Mathematicians deal with abstract topics, proving new facts. This kind of open-ended, puzzle-like problem is a lot more fun to do, and a much better way to show students what math is really like, than the computational topics that take up the current standard curriculum.
If math can be taught as something that’s interesting, rather than as something that’s useful, it changes the way students look at it. It becomes the kind of thing that one would expect some people to really, deeply like. It can be fun and exciting. If it’s being done because it helps design bridges, it’s a chore. The application is cool sometimes, but the thing you’re learning never is. Math as useful calculation will never be appreciated by anyone who can’t see themselves going into science, engineering, or accounting, but math as clever puzzles that help us understand the wonder of pure reason can be something people really want to learn.
More on innumeracy
Given all the comments on my post about people who readily admit to being bad at math, as well as the discussion occurring on various other blogs, I figured it was time to respond to some of what’s been said.
There were some people who expressed skepticism of the phenomenon I was complaining about. These comments (both here and elsewhere) were things like “I always talk about how bad I am at writing” or “I’m an English major, but I know plenty of science.” I have no doubt at all that the incidents cited in the comments really did happen, and they do go against the trend I talked about, but I think they are the exception rather than the rule.
Putting aside for a moment the question of how much knowledge someone should have about any particular field, I want to give some clear support for my assertion that math/science people do know more about the humanities than humanities people know about math and science. I should first be clear about what I’m counting as what. By “humanities” I mean not only literature and fine arts, but also history, social sciences and languages. While there are some arguable cases (economics comes to mind), I think it’s pretty clear that that stuff clearly goes on the humanities side of the divide. When I refer to “sciences,” I mean technical fields in general, including both theoretical and applied math, computer science, engineering, and applications like medicine.
It’s obviously impossible to compare levels of understanding in two different fields. How much calculus do you need in order to equal the amount of knowledge that encompassed by fluency in a foreign language? It doesn’t make any sense to compare these things directly. Still, I believe that we can make the general claim that some incredibly basic, simple science is considered “equivalent” to much more advanced levels of humanities knowledge. Z commented to this effect, using Jeopardy! questions as a proxy. Something a little more quantitative (ha, ha) would of course be preferable.
The best metric I could come up with was simply to look at how much effort was being put into learning material on the other side of the divide, rather than how much material was actually being learned. I decided to look up core curricula at some of the country’s most prestigious universities. These curricula seem as good a proxy as any for what the intellectual class feels a well-educated person should know. The humanities part of the core requirement generally determines how much time a science student has to spend on humanities, while the reverse is true of the science part of the requirement. Of course, many on both sides choose to learn much more than is required, but I think the requirements are a good proxy of what is considered necessary in order to consider yourself well-educated. I tried to vary the colleges I looked at. I chose two schools with a technical focus (MIT and Caltech), three general top universities (Harvard, Princeton, and Yale), and two of the top liberal arts schools (Swarthmore and Williams). Results below: Read more
Being bad at math
If you work or study in a technical field — particularly if you’re in math itself — you get used to a particular type of reaction when you tell someone what you do. It’s far from universal, but frequently the response is something like, “I was never very good at math” or “Math just wasn’t my thing.” You learn to get used to it, but really, I’m sick of it.
It’s not that it’s not true. Probably these people really are bad at math. Probably it was always their worst subject. I’m just tired of no one feeling bad about it. These kinds of sentiments are very common, but imagine how weird it would be if you replaced “math” with “English” or “reading.” Do you think authors, when they tell people they write for a living, ever get told “I was just never very good with words” or “I’m just not a reading person”? They obviously don’t, because it’s not acceptable to be lacking in reading skills. Some people are, but they would never go around saying so, and they usually work very hard to get better. Somehow it’s become dishonorable to admit English is a bad subject for you, but perfectly fine to say the same for math.
It’s really sad that in a technical age, where more and more people are engineers, scientists and computer programmers, we don’t have this deep societal appreciation for math and science. The same thing that makes people freely admit their math skills also affects college curricula. Look at the required curricula at most liberal arts colleges, which proudly proclaim the value of the “well-rounded” education that they give. There are very few math/science/computer/engineering classes, and extremely few math classes in particular. What requirements there are can always be filled by worthless classes. Then look at the curricula for technical, math/science-focused schools. They always have a substantial humanities requirement, and a totally unscientific survey of people I know has found that there tend to be few joke courses to fill those requirements, and that most students don’t take them. Which schools really give the most well-rounded education?
In this day and age, there is no excuse for brushing off math. It’s tough if you’re bad at it, especially since faking competency is a lot harder in math than in the humanities. Nevertheless, brushing it off and not caring is not an acceptable defense mechanism. There’s a part of me that really wants, next time I hear someone say “I was always bad at math” to respond with “Well, I guess you’re just stupid.” It’s obviously not the correct response, but at least it’d move the average in the right direction.
Update: some follow-up comments here.
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