I think I’ll pass

The other day I saw an article about some math test and thought “I bet I’d blow that away now.”

Anyone who has spent a career using some skill ought to blow away an exam intended for people who have been learning that skill for a semester.

However, after thinking about it more, I’m pretty sure I’d pass the test in question, but I’m not at all sure I’d ace it. Academic exams often test unimportant material that is in the short term memory of both the instructor and the students.

From Timbuktu to …

When I was in middle school, I remember a question that read

It is a long way from ________ to ________.

I made up two locations that were far apart but my answer was graded as wrong.

My teacher was looking for a direct quote from a photo caption in our textbook that said it was a long way from Timbuktu to some place I can’t remember.

That stuck in my mind as the canonical example of a question that doesn’t test subject matter knowledge but tests the incidental minutia of the course itself [1]. A geography professor would stand no better chance of giving the expected answer than I did.

The three reasons …

Almost any time you see a question asking for “the 3 reasons” for something or “the 5 consequences” of this or that, it’s likely a Timbuktu question. In open-world contexts [2], I’m suspicious whenever I see “the” followed by a specific number.

In some contexts you can make exhaustive lists—it makes sense to talk about the 3 branches of the US government or the 5 Platonic solids, but it doesn’t make sense to talk about the 4 causes of World War I. Surely historians could come up with more than 4 causes, and there’s probably no consensus regarding what the 4 most important causes are.

There’s a phrase teaching to the test for when the goal is not to teach the subject per se but to prepare the students to pass a standardized test related to the subject. The phenomena discussed here is sort of the opposite, testing to the teaching.

When you ask students for the 4 causes of WWI, you’re asking for the 4 causes given in lecture or the 4 causes in the text book. You’re not testing knowledge of WWI per se but knowledge of the course materials.

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[1] Now that I’m in middle age rather than middle school, I could say that the real question was not geography but psychology. The task was to reverse-engineer from an ambiguous question what someone was thinking. That is an extremely valuable skill, but not one I possessed in middle school.

[2] A closed world is one in which the rules are explicitly known, finite, and exhaustive. Chess is a closed world. Sales is not. Academia often puts a box around some part of an open world so it can think of it as a closed world.

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