What do we measure, how do we measure it, and why?

I had an interesting conversation with a coworker earlier. She teaches an honors geometry class, and they are engaged in a really cool project right now, rather than traditional class time. She also wants them to learn about volume – which is what they would be doing in class – and so she is assigning them reading and homework on volume. It is pretty straightforward material in some ways, so she is actually going to give them a take-home assessment on the volume material without ever covering it in class.

She was concerned about fairness. Some students who would do well if she did straightforward “lecture->3 examples->homework” classes on this material will likely do worse. As she phrased it “I’m grading their innate abilities since I’m never teaching it. Is that fair?”

What does it mean, fair? If she gives this take-home assessment, it will measure something different from other tests. Most tests in a traditional environment measure ability to memorize, ability to process lecture and notes, ability to apply class-discussed examples to new (but usually similar) situations. Good ones test some ability to apply techniques in a larger context, or with a new wrinkle. These are fine and good things to measure. But ability to read and learn information from a text without explicit guidance is also a reasonable thing to measure. It isn’t the same, but that doesn’t make it less fair. I told her she should do it if she wants to.

And this made me think: what do we want to measure in a student? If grades are part of the process – and there’s certainly no way we will be removing them systemically any time soon – what would we ideally like those grades to reflect, and how are we doing at making that so?

There are many things I like about traditional tests, which I admit to using almost exclusively (along with homework completion and occasional classwork problems and exercises) at the moment. I think they are a good way to assess fluency in vocabulary and basic procedures, and a good traditional test will include problem-solving questions that call for “putting it all together.” But mathematical modeling is usually tested in a limited way or not at all. Same for explanations and derivations, which I emphasize heavily in class discussion then barely use at all on assessments. I think I often struggle putting in questions that can be viewed as “subjective,” as if my tests need to be unimpeachably numeric, a “numbers don’t lie” attitude that is specious but hard to shake. I also think I struggle with the idea of making a test too “hard,” both so as not to crush their spirits (because they don’t like feeling confused and it’s easier to cave to that than teach them to be fine with it) and because I feel weirdly tied to the arbitrary 70=D, 80=B, 90=A system we have created for ourselves. But by keeping things simple, I am overemphasizing the skills of the good memorizers and example-appliers and underemphasizing the skills of the problem-solvers and explorers, who would be able to demonstrate their brilliant attempts given more space to try. All with the goal of making it so that ones that freeze and give up under pressure can still squeeze out an arbitrarily-defined 70%.

It is also a hard truth that straightforward tests are easy to make, grade, and find time for, while problem solving and modeling can be hard and time consuming. And students expect tests. They expect a life of mostly-coasting with occasional nights of insane study. So it is simply the path of least resistance to take that path; no complaints, except in my own mind. And I definitely overemphasize a life of no conflict.

I don’t know the solution. I do not have the time or energy to do the sort of constant assessing of thinking that I think I would do in my ideal world. With two young children at home, there is not the window to look through exit slips every day and leave detailed feedback. It isn’t maintainable. And I haven’t yet found a way to keep my workload bearable and also do an honest assessment of the skills I actually find most important. And so, when I realize that I don’t have “enough grades” I write another test with a sigh and continue in the status quo.

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