teaching

Down the Memory Lane: Math in K-12 Science Classes

Zinemin has a great post on understanding physics (and math) in high school.

I started writing a comment, then it got so long-winded that I decided (for once) to not hog other people’s comment threads with my verbosity, but to put it all in a post. Here’s what the comment would have been (Zinemin is a physicist, so some of the verbiage is more physicist-friendly than entirely general).

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I grew up and went to grade school and college in Europe, so my experience as a student is quite different from what I see that my kids and students experiencing.

I think I started falling in love with math sometime in primary school (we had grades 1-8 as primary school, then grades 9-12 as secondary/high school). I had a wonderful math teacher in grades 5-8 and I think that made a ton of difference. (By the way, all teaches in grades 1-4 were what would here be education majors, but to teach grades 5 and onward the teachers had to have a bachelor’s degree in the subject they were teaching.) My primary school math teacher made everything clear and I remember looking forward to practicing at home from the books of problems (we didn’t have homework in most subjects past grade 5, just collections of problems from which to work at home); I remember doing problems in algebra and proving congruence of triangles. I think this confidence that I gained in grades 5-8 never left me when it comes to math.

I started having physics as a separate subject in 6th grade. I remember one of the most appealing aspects was the fact that I got to use my beloved algebra; we did the basic mechanics stuff — motion with constant velocity or constant acceleration; ballistic motion. We must have done the concepts of force and energy, because  I remember making my dad teach me some basic trigonometry during the summer after grade 6th because I wanted to do inclined-plane problems. The physics lab was beautiful, I still remember these posters with the basic SI units, derived SI units, common prefixes. The physics teacher was excellent.

In high school I had a great math teacher throughout, and a great physics teacher in grades 11 and 12. My physics teacher in grades 9 and 10 sucked, when we covered thermodynamics and much of electromagnetism, and I still feel like I don’t know them very well. This is of course ridiculous, since thereafter I won awards in all sorts of physics competitions, I went on  to major in theoretical physics and get a PhD in a related discipline. Still, there is a faint visceral insecurity about those particular classical physics topics stemming from this wobbly initial exposure, even though I use thermodynamics and electrodynamics all the time in research and teaching.

I started loving chemistry in high school, because I had several excellent teachers who showed us what the underlying laws were and why. I even went to chemistry high school competitions (I could titer with the best of them).  During high school, I developed a deep distaste for biology because all that my two high school biology teachers ever made me do is cram and regurgitate their lectures back to them; I still occasionally have nightmares about answering questions about the nervous systems of nematodes. I never particularly cared about the nature/outdoors (the kid of the concrete jungle and all that), so all the botany stuff was lost on me. I really enjoyed what falls under basic cell biology (e.g. what different organelle do, the role of RNA). At one point, in perhaps sophomore year, we were learning about neural synapses, and based on what she taught, it seemed to me like I could think of synapses as little capacitors that can get charged of discharged; I don’t remember the details other than that I came up with this simple circuit-level model of how information travels through a network of neurons based on how I understood what she had taught and based on what I knew of electrical circuits; the teacher was very rude and dismissive, she said something about not being interested in my silly ideas and to take the stuff to the physics teacher, and that she wanted me to learn the material exactly as she had lectured. So yeah. I don’t like biology because my fee-fees were hurt. Even though intellectually I recognize the importance and difficulty of problems in biomedical sciences, something deep inside me cringes and shrivels whenever someone proposes a collaborative project that veers anywhere towards bio.

These early exposures seem to have a pronounced effect on how much confidence we gain, and confidence appears critical for later achievement. But I digress…

My Eldest is like an education experiment for me and my husband, because the system is very different from what we are used to and we have no idea what comes next. Where I went to school, the system was challenging and very good for smart kids, while average and below-average kids were left to just get bad grades or flunk and generally never do well. The US does a much better job catering to the average future citizen, presumably because the above-average ones are expected to find a way to excel anyway; they sometimes do, but they rarely do if they are poor.  (nicoleandmaggie write a lot about challenges in getting access to education for gifted kids).

In connection with Zinemin’s post, I am witnessing my Eldest in the US pre-college education system and it is appalling how little connection is made between math and any of the sciences. Eldest is a freshman in high school, and they have integrated science (won’t have physics separately till junior or senior year, and even so only as an elective). This year, so far he’s had a unit of physics here and there, but they do not use math at all. You should have seen how they covered light that we observe from different stars, and inferences about star temperature or distance from color and brightness; it made my skin crawl. The math needed for the Stefan-Boltzmann law or Wien’s displacement law is really not that hard, a high school student could understand the power emitted per unit area of what’s essentially a generalization of the heater on the stove goes as temperature to the fourth, or why the intensity decreases as inverse distance squared from a source (such as a lightbulb; or a star). But it was all very qualitative, completely hand-wavy, with vague concepts such as perceived brightness and actual brightness (no definition of either and no textbook; based on the problems assigned, I managed to decipher the two to be, respectively, the intensity of light here on Earth (power per unit area) and total power emitted from the entire surface of the star; the fact that one is called perceived brightness and one actual brightness and they don’t even have the same units makes me want to break something. Once I deciphered what was meant, I was able to help my son with the work, but you should have seen his resistance. He is very good at math and can definitely do the manipulations needed for the calculations (it was a problem with three stars and their perceived/actual brightnesses and sizes and distances from Earth, so very simple algebra was all that was needed). Eldest just didn’t understand why I would want to inflict this math on him when the science teacher didn’t do it, it wasn’t necessary, and everything could just be handwaved. This is the only physics unit I saw him have this year; he might have had more, he just didn’t need help (he has excellent grades overall). But from what he mentioned  in passing, most of the integrated science focuses on biology, a little chemistry, some geology and some astronomy, but nothing with even with a little math.

When I try to show my kid what I do for research, he zones out within 20 seconds because it is boring, and cannot understand why I would want to work on the stuff I work on because boooooring. This attitude appears common and continues into college. My undergraduate students still seem to think that they can be taught things in our physical science discipline without using math, as if math were some cruel curiosity that has no real use or connection to the concepts. It pains me when I hear this. Math is the language of nature and the fact that we can speak it is nothing short of miraculous.

Musings on Teaching

What makes a good teacher? I am sure that people who work in education have precise metrics for what effective teaching means.

I am not an education scholar, but I do teach, so doing it well is important to me (and to most of the readership, I am sure). I am at a research university, which means that teaching is an important aspect, but also one that is secondary to research. It is not faculty who unilaterally decide to focus on research. The prestige and grant funding that come from research are what drives this emphasis, which is enthusiastically endorsed by university administration.

In my view, there are roughly three important facets of traditional teaching. The performance art of teaching, the 1-1 or small-group interactions with students (discussions, office hours, emails), and the course materials (including exams).

The performance art of teaching: being “good in the classroom,” being charming and engaging. Being able to convey your knowledge clearly and effectively. At research universities, some of the best in-class teachers-performers are indeed the well-funded and successful researchers. This should come as no surprise, as the ability to explain and engage are as important when impressing panel reviewers as they are when trying to animate sleepy undergrads in a required freshman course. Being an interesting lecturer correlates strongly with good teaching evaluations: students highly value being engaged. This aspect of teaching is also one that comes much more easily to some faculty than others; for those who are naturally charismatic presenters, it doesn’t take much time or effort to mesmerize the crowd.

The second part are 1-on-1 or small-group interactions. The flipped classroom strives to eliminate the lecture in favor of small-group interactions that follow out-of-class viewing of videos. In a traditional classroom, these may be office hours or a discussion section. Few-people interactions are very beneficial to student learning, but many students don’t take advantage of them. Holding frequent office hours, for instance, where only 1-2 students show up, requires a lot of professorial time, but likely has a very small effect on teaching evaluations, even though it helps a lot to those who show up. Also, spending a lot of time on email is one of those things that everyone expects, so you will likely be penalized in evaluations if you don’t do it, but won’t be praised if you do. Gotta love the thankless effort.

Finally, there are the course materials. In my opinion, good course materials (I include exams in this category, as a good exam is not just a test but an education opportunity) are critical for student learning and require considerable time to create. These days, many people teach with PPT slides. It works for some, perhaps many people, so kudos to the readers for whom it does. I appreciate that PPTs take a ton of time to make, so the effort is not lost on me. But I have always hated PPT lectures as a student, as they made me fall asleep. The teachers who worked with PPTs alone generally didn’t move from the lectern, which further made everything more static and my narcoleptic self would just doze off. Good homework assignments and projects (and their equivalents in the humanities), which  really bring key concepts into focus and enforce what was done in class, are hard to develop. In my view, this is exactly the most important part of learning for the students, because they don’t really retain anything until they try to apply what they think they grasped in lecture to actual concrete problems. That’s where they see they didn’t get all they thought they got. However, copious or difficult materials that really lead to learning are not necessarily widely appreciated by students, especially not in the short term, i.e. not on the time scales relevant for student evaluations.

Some of the best lecturers I have had didn’t end up teaching me much in the long run. The lectures were breezy and fun, but the breeze and fun came at the cost of rigor and substance. On the other hand, some of the people that I learned the most from were pretty boring in the classroom, but the materials that we had to go through really did it for me and made me learn. Of course, it is quite possible and perhaps not even rare to have a teacher who is both charismatic in the classroom and a master project/homework creator. My absolutely best teacher ever was the author of a beloved textbook classic, magnificent in the classroom (not what you would call charismatic, but still strangely captivating), and giving the best, most interesting exams I have ever had in my life — they profoundly affected how I design my exams these days. I remember loving his courses and looking forward to his brain-teasing tests; most of the graduate student populace dreaded them as tricky.

Sometimes people say that great teaching doesn’t require a lot of time. I would say that great lecturing probably doesn’t require a lot of time. I am the first to say that I can work an undergraduate classroom quite effectively with very minimal preparation. While a traditional lecture with an enticing teacher is where interest might be sparked, learning doesn’t happen until the students themselves do the work.

My best teacher ever said that 20% of the students will do well no matter how poorly you teach, 20% will do poorly no matter how well you teach, and there is the middle 60% where your teaching can make a difference, so they are the ones we should be teaching to. Based on my experience, a good teacher inspires a student to want to put in the work and learn; a great teacher organizes the course and makes the materials such that even the students who are not inspired end up learning the essentials, in spite of themselves.

Research University, Now With Words

I am at a major public research university. Sure, this is a university and teaching is important, for some definitions of important; anyone who says that research does not beat teaching to a pulp is a liar.

Bringing in extramural funding is the most important metric in most STEM fields. It translates into overhead dollars for the university. It also generally translates into high-profile work, for money means you are doing work that is “hot” and also money can pay for a lot of smart students and postdocs who actually do the work in many fields (with the exception of math and some fields like theoretical physics and computer science). The most highly paid and most coveted members of the faculty are those who do flashy, news-worthy, high-profile work. [Between research productivity and  funds raised is an implication (–>) rather than equivalence (<–>), i.e. money is a necessary but not a sufficient condition for high productivity or flashy papers; there is such a thing as having too much money to efficiently handle. But I digress.]

We are professors, yes, but our peers and our administration care about research almost exclusively. So, where do teaching and service come to play?

Teaching has to be good. If it is bad, you will not get tenure. It has to be decent. But, anything better than decent, unless it is at the level of prestigious national teaching awards, is not rewarded. Being better than a decent teacher is all on you, and feel free to do it if it makes you feel good. But, if you are doing a better-than-passable job, people may (as I know from experience) ask what it is that you are not doing instead when you are wasting time on this silly teaching business. Not all colleagues are like that; in fact I have several in the department who really value and do an excellent job of teaching while also having some political gravitas. However, for the most part, spending considerable time on teaching is looked down upon by the most-research-productive colleagues, who sometimes consider teaching a nuisance that should be minimized or avoided to the extent possible.

ValueTeaching

For example, when I told a colleague that I give 3 midterms, hour-long and in-class, over the standard 2 longer evening exams (more frequent exams are less nerve-wrecking for the students because their grade does not hinge on any one exam so much, and it’s also less daunting for me to grade so I do it faster and they get the results sooner), the colleague told me that I must have too much time on my hands; he, who apparently must be the yardstick by which all workload is to be measured, has only one midterm (this is way too few for undergrads, in my opinion). So it’s not “you do this, I do that,” it’s an explicit statement that me doing something that I feel benefits the students is indicative of an unforgivable professional deficiency (not being busy enough). The same colleague told me “That’s loser talk” a few years ago when I complained that a grant was unjustly slaughtered in review (likely by this guy); needless to say, I am not discussing grants with that colleague again.

People who run very large groups and raise a lot of money generally have very hectic travel schedules and are overall very busy. I know from what students tell me that it translates into many cancelled and rescheduled classes, which is probably not a big deal for graduate students, but it is for undergrads, whose days are usually packed to bursting with classes, labs, project group meetings, and often part-time work. The extremely busy colleagues would often love to have the absolute minimal teaching load, and perhaps they should, for everyone’s benefit.

What about service? There are some important service assignments, and I understand and endorse that they have to be done. Many of them have to be done by faculty (e.g. serving on PhD dissertation committees, or tenure and promotion committees). My beef with service is threefold. First, there are people who really do the fewest and the lightest assignments; they tend to be either among the very high performers or, unsurprisingly, among the very poor performers (deadwood) who have mentally checked out. My second beef is that there are many committees that are pointless because what is needed is money, but the money is not forthcoming; while meeting to brainstorm and bloviate may appease whomever because it seems like something is happening, nothing really is, so the whole thing is a time-wasting charade. Third, service doesn’t do anything for an individual’s career unless it is a formal administrative position (e.g. you serve as department chair), and even so the gains appear… dubious.

The most aggravating part of life at an R1 university is that, during the semester, teaching and service can easily eat up your entire work week. I have several student papers to edit, I haven’t been able to get to them in way longer than I would like. We are dealing with a completely nuts situation, in which much of the core university mission work (teaching, service) takes up so much time that, if you are at all conscientious, your research — the only part that can potentially advance your career — suffers terribly; if you don’t want to neglect your research (or your career in general), you shaft the core mission or your personal life, usually both.

I don’t think faculty are at fault here. People do what is expected of them, and smart people read expectations very well.

Wrong, Wronger, Wrongest (Adventures in Grading)

In science, a potential answer to a problem is either right or wrong. But when it comes to teaching and learning, and especially grading student exams, there is wrong and then there is WROOONG.

Here’s an example. Let’s say you need to compute a certain distance that has to do with the behavior of electrons in a nanostructure.

Correct answer: 160 nm

Incorrect answers:

Wrong: 300 nm (wrong, but within the order of magnitude)

More wrong: 1.6 μm  or 1.6 nm (wrong order of magnitude, but still meaningful, within the scales of nanostructures)

Nonsensically wrong: 1.6 m (height of an adult woman) or 1.6 fm (size of an atomic nucleus; fm=10^(-15) m). While it may seem that mistaking the 160-nm length for a macroscopic height of a woman is more silly and thus more wrong than the nuclear size, the latter is actually “wronger” because it is 8 orders of magnitude off (versus 7 orders of magnitude for the former).

Two things that we don’t teach our students enough, that we perhaps don’t insist enough on, are minding units and building intuition about orders of magnitude. They are amazing, priceless tools for sanity checking.

Question from Reader: Dishonesty in Fellowship Application

Reader Sameir had a question:

“… I just found out that a student has copied my NSF proposal for his GRFP * and got awarded the fellowship. What should I do? On one side I think it is only a student and I should let it go, on the other hand this level of dishonesty is unacceptable.”

Ouch.

Sameir, is it your grad student or an undergrad working with you and currently applying to grad school (presumably to go elsewhere)? Could you tell us a little bit about how the student got the proposal, and how you found out about him/her using the proposal for the fellowship? (I am just  asking for completeness.)

Blogosphere, what say you? What is the proper course of action for Sameir? Should the student be penalized and, if yes, how? Should NSF be notified?

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* GRFP: NSF Graduate Research Fellowship Program

Editorial and Professorial Nuggets

—  I am an associate editor of a specialized disciplinary journal. I try my best to include junior researchers (postdocs, young profs or nonacademic scientists, even some senior graduate students) as reviewers when I know they do good work based on what I have heard or seen them present at conferences. It turns out, a surprisingly high number of people cannot write a review to save their life. Some of them are junior, so they have the excuse of inexperience, but some should really know better.

I get these cryptic two-line reports with a recommendation to reject. WTF? That is not a report. I cannot send that on to authors, it gives me a basis for nothing. Especially if you are going to reject, you better give clear reasons for doing so.  Even if the paper is crap, it usually (although not always) presents a considerable amount of work by the authors. If the paper sucks, tell them precisely why it sucks and how much it sucks, so they would know whether to try and fix it or that there is no hope and they should drop it.

How does one learn to write referee reports? Well, when it comes to my students, I send them samples of my reports to look at (ranging from minor revisions to rejections). But, one first and foremost learns from the reports received of one’s own papers. Which is why I wonder, especially for senior folks, how unobservant and unable to generalize they are,  that they cannot figure out what is to be done based on their own experiences with being on the receiving end of reports.  These are all skills necessary for doing science, how is it possible not to apply them when learning how to write reports?

— There are career editors and then there are editors who are practicing scientists. Either way, the longest part of the review-and-publication process should be the actual peer review. It should not be the time taken by the editorial office staff to check the formatting; it should similarly not be the time the editor takes to make a decision and transmit the referee comments to the authors after the peer review has been completed. I have found myself dreading submission to certain journals, because I know a paper in a certain field will go to a certain editor, and the editor has a habit of just sitting on the paper for days or weeks on end, both when it comes to making referrals and when it comes to making a decision (the time they take doesn’t seem to correlate at all with how hand-wringing the decision-making process might be; hearing about “major revisions” appears to take just as much time as receiving “publish as is”.

For editors who are practicing scientists, why do people take on this role if they are not committed to doing a good job? I know, becoming an editor in a good journal is an honor, but it’s also a job, and an important one. And part of doing it well also means doing it fast. I know some great associate editors who handle dozens of new papers per week very efficiently. But then there are others. And I wish someone gave them a kick in the pants so they’d finally get going.

Yes, I am very impatient. But you can bet that I am very efficient as associate editor.

— In professorial news, once again, the biggest problem of my undergrads is that they don’t know the math that they should know. They don’t have the facility with basic calculus, let alone analytic geometry. While some fairly complicated concepts can be hand-waved down to the levels of calculus or geometry, it’s of little use because these concepts, which should have been internalized long ago, appear only vaguely familiar to students as opposed to being tools wielded with confidence. Part of it, at my university, is the ever-shrinking list of required math courses so students could all get as many free electives as possible (?!); that’s because students feeling warm and fuzzy upon having customized their studies to the point of senselessness  beats actually getting a solid education in the major. The worst thing is the students’ attitude that this insistence on calculating stuff, on — gasp! — using math, is somehow unnecessary and is in the way of actual real knowledge. They want to make it go away and get to the good stuff. They cannot. I am all for pictures and analogies and building one’s intuition. I draw in class more than I write equations. But this is fairly high-level stuff, and the intuition has to be already honed by both math and experience with other similar problems. Students cannot expect everything worth knowing as a senior in a physical science discipline to just be qualitative or requiring no more than arithmetic and high-school algebra. I am really tired of having to apologize for what is really not particularly high-level math that they should be proficient in anyway.

People Who Are Soooooooo Much Busier Than You

A colleague once told me this great Chinese proverb:

“Time is like water in a sponge; if you try really hard, you can always squeeze out some more.”

So very true. People will always find the time for the things they want to do, end of story. If you can’t find the time for something, that just means you don’t actually want to do it. At least, I am like that and I assume others are as well; after all, it wouldn’t be a proverb for nothing.

In professional communication, saying “I’m too busy” is often a perfectly fine euphemism for “I don’t really want to do this thing right now (or possibly ever), sorry.” After all, a lot of academic work is work for free (refereeing papers, partaking on conference program committees) or for absolutely minimal compensation (e.g. serving on NSF panels, proposal review), and just because I ask for something doesn’t mean that you have to care enough to try to find the time.

But when you are too busy to look at a paper on which you are a coauthor, to which you contributed infinitesimally yet don’t have the courtesy to take self off the author list?
That’s just being a pub-blocking douche. Know that I hate your guts for it. Either $hit or get off the can — comment promptly or say it’s fine to go as is.

I hate the people who go around bolstering about how busy they are and who generally busy themselves with the business of out-busying everyone. For some, it’s a way to show that they are superior and more in demand than you. Maybe for some it’s a way to hide the fact that they are not actually all that busy. And I am sure for many that means they don’t have their priorities straight and/or are inefficient; working with them drives me bonkers.

There is a guy I know from graduate school who has for years now been going progressively more and more on my fuckin’ nerves about his busyness.
A few weeks ago he sent me an email devoted entirely to how unbelievably busy he was; it was a full paragraph, multiple-sentences long,
but without a single punctuation mark. Apparently, when you get to be really truly busy, punctuation has to go. Before you think he had some unusual crunch at work, he didn’t. The email content was the same as ever. He works for a company, as do many other people, but he works from home, has no kids, and is part of a dual career couple; when he’s not whining about how much busier than everyone else on Earth he is, he takes long vacations in exotic places. So waaaaah, waaaah, cry me a fuckin’ river.

When I was in grad school, my PhD advisor had a big group. He and a few other faculty had an administrative assistant, C, who was the most efficient and organized person I had ever met in my life: Whatever any of the students or faculty needed, she did impeccably, never needed to be asked twice, and she never actually looked busy. In contrast, the department chair’s secretary was ironically one of the worst assistants in the department (so said everyone), and was constantly dying under the piles of paperwork; you routinely had to ask her twice or three times to get anything done, and things were often wrong. This was a perfect example of busyness being anti-correlated with doing anything useful.

I have some collaborators who are very difficult when it comes to scheduling anything, nominally willing, but each meeting requires me to endlessly wait to hear back from them and people exchanging numerous emails. If I say what everyone is thinking “You know, you don’t actually want to schedule this, why don’t I do it without you as I see fit, and you do whatever it is that you prefer doing,” then I am too impatient, too emotional, and generally not academic-politics-savvy. Some friends are like that too; it takes many weeks so schedule a dinner. WTF? Why is it such a big deal? Just pick a night and come over, why does it have to be so complicated? Or should I again assume you don’t actually want to do this, ever?

The thing is, the proverb above definitely works for me. When something is important, I will make the time. I have a small number of very high, ironclad priorities, and I will make time for them at the expense of a whole bunch of other $hit, probably more so now than before tenure. I have colleagues who have some sort of priority-insensitive pipeline; things just get into the pipeline and then get tended to when they get tended to. Nope, not here. Submitting grant applications is an intermittent but very important and time-sensitive priority, it bumps everything else. Not so time sensitive, but no less important, is editing papers to submit sooner rather than later; it bumps a whole bunch of other stuff down or off the pipeline. Seeing my students when they need to talk to me is a very high priority. In general, anything that’s instrumental to the careers of junior people whom I support is a high priority [e.g. promptly writing letters of recommendation for my trainees; promptly responding with my availability (or lack thereof) when someone else’s student needs to schedule PhD defense]. During the semester, teaching is a very high priority (emails, homework assignment and solutions postings, exam grading).

Also, I don’t procrastinate with the stupid $hit that is key to getting the important things done and off the table, like returning proof corrections. It drives me crazy when people sit on them for a week — just read through the damn thing and send it in! In general, our job offers plenty of busy work that is necessary to complete in order for the harder, intellectually demanding work to get done. A good example is doing the proposal boilerplate (biosketch, budget and budget justification, data management statement, equipment description, etc.); I kinda enjoy working on the boilerplate, as it’s like foreplay before getting to the hard stuff  (see what I did there?).

The tl;dr version of this post is — I kind of hate you if you constantly complain that you are busy. I think you are either not busy but lying, seeking to get the upper hand/admiration, or just don’t have the guts to tell me that you don’t want to do what I asked. In the off chance it’s none of the three, you need to get shit together and get your priorities straight and get organized. Especially if other people’s education and careers depend on you.

Busy