TITLE: That's a Shame
AUTHOR: Eugene Wallingford
DATE: December 30, 2020 3:38 PM
DESC:
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BODY:
In the middle of
an old post
about computing an "impossible" integral, John Cook says:
In the artificial world of the calculus classroom, everything
works out nicely. And this is a shame.
When I was a student, I probably took comfort in the fact that
everything was supposed to work out nicely on the homework we
did. There *was* a solution; I just had to find the pattern,
or the key that turned the lock. I suspect that I was a good
student largely because I was good at finding the patterns,
the keys.
It wasn't until I got to grad school that things really changed,
and even then course work was typically organized pretty neatly.
Research in the lab was very different, of course, and that's
where my old skills no longer served me so well.
In university programs in computer science, where many people
first learn how to develop software, things tend to work out
nicely. That is a shame, too. But it's a tough problem to
solve.
In most courses, in particular introductory courses, we create
assignments with that have "closed form" solutions, because we
want students to practice a specific skill or learn a particular
concept. Having a fixed target can be useful in achieving the
desired outcomes, especially if we want to help students build
confidence in their abilities.
It's important, though, that we eventually take off the training
wheels and expose students to messier problems. That's where
they have an opportunity to build other important skills they
need for solving problems outside the classroom, which aren't
designed by a benevolent instructor to have follow a pattern.
As Cook says, neat problems can create a false impression that
every problem has a simple solution.
Students who go on to use calculus for anything more than
artificial homework problems may incorrectly assume they've
done something wrong when they encounter an integral in the
wild.
CS students need experience writing programs that solve messy
problems. In more advanced courses, my colleagues and I all
try to extend students' ability to solve less neatly-designed
problems, with mixed results.
It's possible to design a coherent curriculum that exposes students
to an increasingly messy set of problems, but I don't think many
universities do this. One big problem is that doing so requires
coordination across many courses, each of which has its own
specific content outcomes. There's never enough time, it seems,
to teach everything about, say, AI or databases, in the fifteen
weeks available. It's easier to be sure that we cover another
concept than it is to be sure students take a reliable step
along the path from being able to solve elementary problems to
being able to solve to the problems they'll find in the wild.
I face this set of competing forces every semester and do my best
to strike a balance. It's never easy.
Courses that involve large systems projects are one place where
students in my program have a chance to work on a real problem:
writing a compiler, an embedded real-time system, or an AI-based
system. These courses have closed form solutions of sorts, but
the scale and complexity of the problems require students to do
more than just apply formulas or find simple patterns.
Many students thrive in these settings. "Finally," they say,
"this is a problem worth working on." These students will be
fine when they graduate. Other students struggle when they have
to do battle for the first time with an unruly language grammar
or a set of fussy physical sensors. One of my challenges in my
project course is to help this group of students move further
along the path from "student doing homework" to "professional
solving problems".
That would be a lot easier to do if we more reliably helped
students take small steps along that path in their preceding
courses. But that, as I've said, is difficult.
This post describes a problem in curriculum design without
offering any solutions. I will think more about how I try to
balance the forces between neat and messy in my courses, and
then share some concrete ideas. If you have any approaches that
have worked for you, or suggestions based on your experiences as
a student, please
email me
or send me a message
on Twitter.
I'd love to learn how to do this better.
I've written a number of posts over the years that circle around
this problem in curriculum and instruction. Here are three:
I'm re-reading these to see if past me has any ideas for present-day
me. Perhaps you will find them interesting, too.
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