Archive for Boundary Value Problems

Teaching those who want to learn

Posted in Biographical, Education, mathematics, Maynooth with tags , , , on April 21, 2023 by telescoper

Yesterday afternoon I ran the last formal Computational Physics laboratory of the term. As is often the case with these sessions, the students were given a Python task to work through, with assistance available from myself and a demonstrator (and indeed other students). We have 25 students registered on this module, who are split into two groups, so about a dozen students were in yesterday’s session. That’s a comfortable number to make sure everyone can get some help.

This is the sixth year I’ve done this module, and I decided a long time ago that the best way to ensure that students learn the necessary skills is to give them things to do and let them work things out for themselves (with help where necessary). A couple of years ago, on my module feedback questionnaire, a student wrote an intended criticism along the lines of – “It’s like he expects us to learn to code by doing it ourselves, rather than him teaching us”. That is, of course, exactly what I intended, though we do give plenty of help during the labs.

Just as the best way to learn a foreign language is by speaking it, the best way to learn coding is by writing programs. Some of the students on this module have done any before, so for them the early stages of the module are rather straightforward. At least half the class, however, haven’t done any programming, so for them it’s a fairly steep learning curve.

Anyway, it being the last formal session of term this week’s task was a rather challenging one, involving the solution of a boundary value problem via the shooting method. It’s a good exercise because it brings together methods for solving ordinary differential equations with root-finding, as well as requiring some thought as to the general construction of a code that combines these two.

As expected, given the difference in background of the students, some finished this in good time, but others went more slowly. Some very excellent things happened, though, which made me very happy with the the whole experience.

One was that instead of leaving as soon as they had finished, a few of the students who had completed the task early stayed behind to help their friends. I encourage this, but it doesn’t always happen as much as yesterday. It’s called teamwork, and it’s essential not only in physics but also in everyday life.

The lab session was supposed to finish at 4pm, but not all students were done by then. Another excellent thing though was they didn’t just quit when they had run out of time. I stayed well past 4pm to help those who were determined to finish. In one case it was just a ‘0’ that should have been a ‘1’ in the index of an array that stopped it working. I don’t know why it took me so long to spot this, but we got there in the end.

One student, however, had another class at 4pm so left, only to return at five to continue. The student finally left, having completed the exercise, at about 6.45. The persistence shown by the students in refusing to be defeated was truly admirable. This harks back to a piece of advice I gave some time ago:

If you really want to develop as a physicist, don’t just solve a lot of easy problems; challenge yourself by tackling difficult ones too. Don’t be afraid to get “stuck” or make a mistake, as those are both necessary parts of the learning process. Above all, develop the confidence in your ability to take on a problem and back yourself to solve it and don’t be deterred if the answer doesn’t come quickly!

You may say that if it took some students much longer than the allocated time to finish then the problem was too difficult. That may be the case, but do you ever really learn if you’re not stretched? There is a place for straightforward formulaic tasks in higher education, but there’s much more to a university education than doing things like that.

Obviously the lab took up much more of my time as I had originally planned – more than double, in fact – but I went home pleased with a good day’s work. As I’ve said on this blog many times before, there are few things more rewarding than teaching students who want to learn.