Fresh Wallaby Juice

I gave my students their first big exam on Monday. Finishing up grading it tonight, so this is both a reflection and procrastination…

The exam itself was 5 pages. For an hour-long exam. Was I insane? Yes, I’d test-driven it the day before and finished up in about 25 minutes… but I’ve got a PhD in this stuff and I knew exactly what I was thinking. In the future, keep it shorter.

The first part of the exam was very straight-forward: Define 8 terms, straight out of the textbook. There were a couple that gave them trouble, such as dynamic range. Yes, they had trouble defining dynamic range. That’s one of those “core concepts” in instrumental; one of the criteria by which different instruments are evaluated. (It’s the range of concentration over which an instrument gives a linear response, between the limit of detection and the limit of linearity.)

We’d been over this in class. It’s in the textbook. Only two out of the 10 students got even half credit.

Another question dealt with propagation of error – comparing the uncertainty that we calculate (estimate, really) for using pipettes in lab. The equation to use was on the exam – not identified as such, but as long as they had some idea of what they were doing with that, they should be able to pick out the formula. The question said, “use propagation of error”.

Again, the question told them how to do the problem. ALL they had to do was pick out the formula and plug in the numbers.

Not one of them got it right.

Was it my wording? Was it their background? I’ve known/suspected that most of them have fairly limited backgrounds in analytical to begin with. Perhaps I should not have asked them about that.

And yet… this class (this subject) is all about working precisely and intelligently to achieve the best, most accurate, most precise, results possible. Understanding how uncertainty accumulates is (IMHO) a core part of that.

I dropped the question, the grades were bad enough from the rest…

Was it that they didn’t understand what I was asking? After those first “definition” questions, most of the problems were given some kind of context. They were measuring traces of zinc in copper ore, or testing fluorescence instruments. Did they have trouble picking out the useful information? Did they have trouble understanding the question I was really asking?

(Some of my students have asked for extra practice problems in calculating parts-per-million concentration units – I learned that in high school, certainly by the time I’d had the first analytical class. Are they ready for this class at all? If they’re not, how can I get them ready?)

We spent an hour in class talking about spectral resolution of different instruments. We saw in class what narrow lines look like seen through too-wide slits. The textbook also covers this in detail. I asked them to sketch what two closely-spaced emission lines would look like through a monochromator without enough resolution (actually two different slits to choose from, one 0.2 nm that was just barely adequate and one 0.7 nm that wasn’t).

One of the better students gave me a very nice graph showing a narrow line at the position of each emission line. One had a height labeled 0.2, the other’s height was labeled 0.7. Another drew two broad peaks and labeled one “excitation” and one “emission”.

Is that a case of not understanding the problem? or not knowing the answer?

I really want to know which. In either case I consider that I’ve done poorly – in one case, for getting too clever on the test so that they wasted their time instead of showing me what they do know; in the other case, I failed to present this essential content in ways that they could understand and retain in useful ways.

First thing to do, I think, is to talk about this pretty frankly with them when we go over the test in class tomorrow. They’ll be worried about their grades; I’m more worried about how we’re collectively doing in picking apart the material in ways that make sense to them.

Second thing to do, I think, is to assign more homework. (They’ll be so thrilled.) Most of them need practice in basic math like converting mass and volume to concentration and back – I can write homework to target that, at the very least. I think they’ll benefit more also from a steadier stream of smaller problems, set explicitly “out of context” so that they can focus on the problem itself.

(I still want them to be able to recognize the problem in context, because that’s a far more useful thing to take out into the world. But they need to walk first before I make them run.)

When I teach this again next fall, I think I’m going to spend the first week, maybe 2, in a review of the first semester of analytical. It should be boring review for the undergrads who’ve already had the quant class here… but most of the grad students taking this class are badly underprepared on the basics. I assumed that they’d all had those basics already, and… well, the question on relative standard deviation should not have been missed by anyone, if that were true.