Wrong, Wronger, Wrongest (Adventures in Grading)

In science, a potential answer to a problem is either right or wrong. But when it comes to teaching and learning, and especially grading student exams, there is wrong and then there is WROOONG.

Here’s an example. Let’s say you need to compute a certain distance that has to do with the behavior of electrons in a nanostructure.

Correct answer: 160 nm

Incorrect answers:

Wrong: 300 nm (wrong, but within the order of magnitude)

More wrong: 1.6 μm  or 1.6 nm (wrong order of magnitude, but still meaningful, within the scales of nanostructures)

Nonsensically wrong: 1.6 m (height of an adult woman) or 1.6 fm (size of an atomic nucleus; fm=10^(-15) m). While it may seem that mistaking the 160-nm length for a macroscopic height of a woman is more silly and thus more wrong than the nuclear size, the latter is actually “wronger” because it is 8 orders of magnitude off (versus 7 orders of magnitude for the former).

Two things that we don’t teach our students enough, that we perhaps don’t insist enough on, are minding units and building intuition about orders of magnitude. They are amazing, priceless tools for sanity checking.

9 comments

  1. I agree! The ability to do a quick back of the envelope calculation and check what sort of number you are expecting (e.g. round everything to multiples of ten, work the calculation, that gives an estimate of the order of magnitude your answer should be) seems to be completely alien to even students with decent qualifications in the more mathematical areas of science. I don’t teach there… Students happily report that there are 6 trees per square metre in a forest or 30 pubs per hectare in a city, or claim that a fast runner can run 1000m in less than ten seconds, and actually ARGUE WITH ME about the result because it’s “just units”

  2. I actually do this often – have them check units and estimate orders of magnitude of various things that we study in class. I also ask them stuff like “what would make this smaller” or “how large could this possibly get” and tell them precisely that this builds intuition that they don’t currently have because they don’t live in a microscopic world. I occasionally get “The professor insists on memorizing numbers instead of focusing on understanding the material” in the reviews, but the majority of students like it and eventually appreciate it.

  3. In my stats class I have explicitly added a step to every procedure they’re expected to know, “Does this answer make sense?” It’s amazing how just thinking about a problem can catch enormous errors. I also give them more partial credit for wrong answers that won’t kill anybody than wrong answers that will.

  4. Unrelated, can you make a link to all your posts with doodles? They are brilliant and would love to see them aggregated.

  5. TheGrinch, I am glad you enjoy them!

    You can find the doodles under the category “Cartoons” or under the tag “Comics”. These are supposed to be identical in content, but I think I occasionally forget to tag or categorize. Will have to clean them up.

    Btw, are doodles-with-attemps-at-humor better classified as comics or cartoons? Or something else?

  6. I am always amazed at the weakness in basic math that afflicts many biology majors. I don’t ask difficult quantitative questions but am surprised at what i get with an easy one.

    e.g., calculating a ratio–students memorize two exact numbers, actually write them beside the question, and then cannot tell me how many fold one is of the other

    interpreting a graph with a log10 scale. Students who tell me the difference is five fold rather than five orders of magnitude

  7. This semester I have four sections of intro chem lab, which is nothing but units! I tell all my students the first-Mars-Rover story. And I do always ask them if their answer is reasonable, tell them that if they’ve got the wrong units/ the units don’t cancel/ their answer is 100 moles being generated from 4 grams then it is probably WRONG. I repeat “Units are important!” about ten times per lab session.

    Answers that are WROOOOOONG, I’m always torn between laughing and crying.

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