The fallacy of teaching by derivation

A large chunk of my research time this week was spent trying to teach myself a couple of relevant background concepts.  Whenever I find myself in this situation, the first thing that happens is that I feel really dense.  I’m an Nth-year PhD student, how could I not understand that topic?  The second thing that happens is that I get frustrated about the way the subject is presented in most references.

Without giving away too much about my field of study, let me just say that it can involve a lot of math.  But, for the most part, the math is applied: it’s used to describe real things that exist and happen.

The topics I was looking up this week were almost universally presented in texts and notes in this fashion:

  1. Brief introduction to topic.  We’re talking 2 or 3 sentences.
  2. Extensive, step-by-step derivation of the key equation(s) used to describe the phenomenon.  Usually these equations are named after people.
  3. [optional] Another handful of sentences explaining the results from part 2.

And, ta-da!  You know the math, so now you know the concept!

Except… my brain doesn’t work that way.  It doesn’t easily convert gammas and rhos and plus signs to a mental picture of real physical things.

It’s not that I’m bad at math.  I’m good at math, in fact.  Very good.  I don’t mean to brag or nuthin’, but my partial differential equations professor in college asked me for my notes at the end of the semester.  It can be time-consuming to work through derivations, but I can absolutely do it.

And it’s not that the math isn’t important.  Mathematics is a critical tool for describing, interpreting, and predicting the world.  If you’re in a highly applied field, like, say, architectural engineering, being able to do the math correctly could make the difference between a building staying up or collapsing on the people inside of it.

But knowing the math is not the same thing as knowing the concept.  Teaching the former does not automatically confer upon your students an understanding of the latter.

My brain isn’t the only one that struggles to convert equations to conceptual understanding.  During my time as a PhD student, I’ve been a teaching assistant (read: lab instructor, grader, substitute teacher, and cell-phone patroller) for a number of introductory classes.  Some of those classes were geared toward students hoping to major in the subject, while others were designed for folks trying to check a box on their list of Gen Ed requirements.

It turns out that there are exactly two differences between these groups of students.

One, the majors are significantly more motivated than the non-majors, on average.

And two, the majors are better at math.

You know what wasn’t a difference?  Their conceptual understanding.  The majors could rearrange equations and calculate numerical answers like nobody’s business, but they made the same basic errors as the Gen Ed students when asked to explain how things work.  All that math we were showing them didn’t help them build a better mental framework of the fundamentals.

So why do we do this?  Why is “teaching by derivation” the default in science and engineering?

Is it that there’s a subset of people whose brains do readily make the connection between math and concepts, and those are the people who go on to be STEM professors?

Is it that (and I suspect this is most likely) that our professors are just presenting the material the same way they were taught?

Or is it that (and I really do wonder if this might be a little true, too) that they don’t fully grasp the underlying concepts themselves?

Whatever the case, if you are teaching science or engineering, or putting together lecture notes, or writing a textbook, I beg of you: please, please, please explain the concepts before you go through all of the derivations.  If the derivations reveal new concepts, explain those too!  Use words!  Use pictures!  Be different!

Your students will thank you.

Ouch ouch ouch ouch ouch and useless advice

Having my first experience with a clogged milk duct this week.  Ow.  The achy soreness seems to have subsided, but the spot where the blockage was still stings like a &^%!*&#^% at times.

Of course, I did a Google search for tips on how to treat it.  One of the first hits was this page from La Leche League, which helpfully begins its advice with,

Your best move is to take your baby to bed and stay there for as long as possible.




BWAHAHAHAHAHAHAHA!  (That’s the sound of maniacal laughter, in case you can’t tell.)

Leaving aside any commitments that I myself might have that might preclude me from hanging out in bed all day, Little Boy would not stand for this.  He would lie still next to me in bed for exactly 30 seconds before gleefully wiggling away to play.  Maybe, if it were nap time, I could convince him to doze off nursing for a bit.

To be fair, there’s nothing strictly wrong with this advice.  It probably will help, if you can do it.  It’s just so… unrealistic.

The pocket problem

Yesterday, I came across “How to Use a Simple Pocket Notebook to Change Your Life.”  Click-attracting title hyperbole aside, it’s a very appealing idea.  My life is built on paper notes, partially because I don’t have a smartphone and partially because of my innate attraction to physical handwriting.  I also have a very visual memory, such that I can picture the page of a research notebook that contains a desired piece of information, and even remember approximately where that page is in the book.

However, I don’t always keep a notebook on me.  My research notebooks and my day planner live mostly in my backpack, my “miscellaneous” school notebook stays in my office, and my doodle sketchbook and my random-household-stuff-but-mostly-packing-lists notebook migrate around the house.  Plus there are all the sticky notes with lists of songs I want to buy, and a collection of electronic notes on my laptop, iPad, and iPod from the times when I wanted to make sure I didn’t lose an idea.

A little pocket notebook — especially one with very few rules for use, so that the perfectionist in me wouldn’t get caught up in worrying what to put in there — would be nice.  There’s just one little problem…


Or rather, the lack thereof.

Women’s clothing sucks when it comes to pockets.  On a good day, my pants have enough pocket space for some lip balm and my office keys (because I’m not going to take my purse with me every time I leave my office).  On a bad day, I’m wearing a pocket-less dress or a skirt or stupid jeans with fake pockets and end up awkwardly carrying my keys around in my hand and hoping I don’t forget them in the bathroom again.

I was somewhat irritated that the original article didn’t mention this issue at all, and that the one attempt to raise it in the comments received only joking responses.  I don’t have a ready-made solution, either.  Someday I might actually buy a smartphone and want to carry that with me, but it’s not clear how.

Readers who wear women’s clothing, how do you circumvent the lack of pockets?

I get my best ideas at bedtime

It’s rather annoying, actually.

On an average evening, I have a bit of time after dinner, when Little Boy is in bed and tomorrow’s lunches have been made and baby bottles washed.  But I’m tired.  My brain is tired.  It doesn’t want to write, or read interesting things to get ideas.  It wants me to veg on the couch and read mindless Facebook shares and watch TV.  Which is totally understandable after a long day of parenting and research and more research and more parenting.

However, when I start getting ready for bed – taking a shower, brushing my teeth – my brain wakes back up again.  Suddenly, it’s composing my next three blog posts.  And not just a hey, you should write about that sometime; there are whole sentences and paragraphs just running around in my head.

If I were back in college, unencumbered by normal work hours or the needs of a tiny human, I might choose to run with it.  Sit down at my computer for an hour and let the words flow.  But I’m not a college kid any more, I’m a mom who has to get up in the morning and needs a lot of sleep to function, so I have to go to bed.

Fortunately, the free-flowing sentences don’t usually prevent me from falling asleep.  In fact, they’re can be somewhat meditative.  Unfortunately, some of them are lost by the time I wake up in the morning.  I should start keeping a little notebook and pen by my bed to jot down some key points, but unless I take the time to write down everything, something’s going to be forgotten.

When do you find your best ideas brewing?

Rage against the IT

A now-defunct, grad-student-written help page for printing in my department began with the sentence, “Printing doesn’t really work at [this department].”  It went on to describe some options that might, if one were lucky, produce pieces of paper with ink, and where those pieces of paper might be found in the building.

When I first arrived, I was assigned a “new” desktop computer.  This computer, like those of my fellow students, refused to speak to any of the printers in the building.  After a good deal of pestering, I convinced one of our IT guys to provide me with a program that would allow computer-printer communication (I have no idea why this program was not given to everyone by default).  This program had to be re-run every time my machine was restarted, and it would only allow printing directly from the command line, never from within an application.

Several years later, I installed a new operating system on my computer (because it was faster and less hair-pullingly frustrating that waiting for the IT guys to fix what was wrong with the old one).  This included setting up printing myself.  For a brief and glorious period, I was able to print from any application.

Then my officemates and I were booted out to a portable trailer.  For exactly three days, I was still able to send documents to the fancy printers in the main building as well as to an old black-and-white printer that had been set up for us in the trailer.

When I returned from maternity leave, the trailer printer was not broken, but it was no longer talking to my computer.  The other printers’ network had been subtly changed, for reasons the IT guys chose not to share.  After some fiddling with settings, I could still print from any program, but I had to hike outside to pick it up.  This set-up probably encouraged me to save paper.

Recently, the most-used printer was “helpfully” upgraded to a newer model.  Not only can I no longer print to that machine, but I apparently can no longer print to ANY printer on the network.  If I can’t figure this out or find another student who can help me, I might have to break my current rule of IT avoidance.

“Printing doesn’t really work,” indeed.

“Because it’s good for you”

I’ve always been a big fan of the comic strip Calvin and Hobbes.  So much so that at one point in my childhood, my parents decided that my brother and I needed to read something else for a while, and they put all the Calvin and Hobbes collections on top of a high bookshelf in their room.  That didn’t last long.  Anyway, in the strip, Calvin’s dad is always telling him that he needs to take out the trash (or shovel the driveway, or go camping with the family, or basically anything Calvin doesn’t want to do) because “it builds character.”

I was reminded of Calvin’s dad this week when the grad students in my department received an email from the enthusiastic new faculty member in charge of Journal Club.  Evidently I’m not the only grad student who has been staying away: just three students were in attendance this week, and that is apparently an unacceptably low number.

In addition to singing the praises of the talks that we all chose to miss, the email finished by telling us that we should come to Journal Club because it,

will help you learn how to be successful as a postdoc.

This irritated me.  (In a roll-your-eyes kind of way; I’m not upset about it and I certainly don’t feel guilty about my lack of attendance.)

For one, it’s extremely condescending, albeit unintentionally.  With the possible exception of the first-years, the grad students aren’t avoiding Journal Club because we don’t know what it’s about, or because we haven’t realized that speaking and listening and presenting are valuable skills for us to have.  We’re not attending Journal Club because we’ve tried it, been unimpressed, and have decided that there are far more productive ways to use our time.

So it doesn’t actually solve the issue.  Productive ways to increase attendance might include making Journal Club more interactive, spending more time on topics of interest to students, and encouraging speakers to start preparing their presentations sooner than the night before.  Or perhaps trimming down all of the other seminar-like events students are also expected to attend.

Finally, it illustrates the deeply-ingrained assumption that there could not possibly be any other reason to get a PhD other than to prepare for a career in academia.  Is it really that inconceivable that you wouldn’t want to follow that track?

To be fair, if my time in grad school is any indication, learning how to sit through boring talks without falling asleep is a valuable skill for a career in academia.  Perhaps that’s what she meant.