My TA recently approached me about students in our class (stats/methods).

**TA: **I think we need to reassess where our students are.

**SK:** Oh, really? Why?

**TA: **Um… well… one just came up to me and asked, “what is this thing – a ‘mean’ – that he keeps talking about?”

**SK: **Oh! [eyes widened, worried surprise]

**TA:** Yeah, well, that’s not the problem. I said, “Oh! It’s just another term for the average” and the student replied, “Oh. Okay. How do you calculate that?”

**SK:** … [speechless]

At this moment I realized that I had assumed much too much. And that a sizable chunk of the class could have no idea what I’m talking about. And that this has been going on for more than a month now. On Tuesday I think I’m going to give a non-graded, evaluative math quiz with basic concepts – just to see where they are. I won’t even ask them to put their names on it. But I worry a bit that this will freak them out and/or seem condescending. But I don’t know how else to see where they all stand. After this, I have a little less faith in the world.

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Eegads. My son is 8 – and is not a child prodigy – and can calculate a mean (or the median or mode, for that matter).

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There could be any number of things going on here, and some kind of assessment could help clarify matters. I once invited a very prominent mathematics educator to observe me teach statistics, and it was very humbling to learn that I really had no understanding of what my students knew and what they didn’t know. It also helped me clarify what I wanted my students to learn — and it wasn’t the various formulae for measures of central tendency and dispersion in a distribution, but rather the concepts of central tendency and dispersion. If you

reallywant to test your students’ understanding, don’t ask them to regurgitate the formula for a mean; instead, ask them to explain why the mean is measure of the middle of a distribution without using the formula.LikeLike

In my experience, most students (not all) actually do remember the mean if you call it, “you know, the average you learned about in the sixth grade, add them up and divide by how many there are.” It is helpful to make this reference when you are explaining the mathematical notation, as they really do know what it means and it aids in learning the notation. They just don’t remember that they know. Although the few truly clueless make your jaw drop. I was once asked if there was a way to do fractions on a calculator. When I said “it’s called the the divide key,” even the student who asked the question said, “Oh, right, I should have known that” and looked embarrassed. Now standard deviation, that’s another issue. Nobody remembers that from high school, or even last week’s lecture.

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kibitzer: I really like this idea. I’m going to design a “general ideas” math quiz. No formulas, just concepts. My example is clearly an extreme (ridiculous, even) case. But a lightbulb did go off about my assumptions. Thanks for the great advice!

It is funny how as a teacher occasionally I can’t see more than a foot in front of my own nose. I recently have been teaching another class where we’re reading a lot around the French Revolution. I kept talking about it, making casual reference to how it was important. After about two weeks it occurred to me that the class had no idea why it was important. Or at least why people thought it was. I spent the next half hour going over it. At the end, someone said, “Oh. I now get what we’ve been doing for the last couple weeks”. The rest of the class nodded.

I recall in a statistics class I once took I asked about the difference between the an odds and an odds ratio. I was told the formula. I replied, “I actually get the formula – I did it right on the test. I just don’t really know what the difference is, in the world.” My professor told me, “You’re looking for an intuition. I’m not good at giving intuitions… [pause]… have you ever been horse racing? [Reply: No]… Go to a track and look at how betting works. Then you’ll get the difference.” I never went to the track. But I get it now. And in fact telling me to go to the track actually produced the “intuition” the professor was looking for.

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If you’re worried about the “quiz” being condescending, make it for bonus points. Then they’ll try harder on it too.

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shakha, i just started using the clicker system in one of my classes — if columbia has them, it occurs to me that they would work really well for a stats course. you could check in with students periodically during the lecture with a “general idea” question as you describe above and get a sense of what percentage of the class is with you so far… on-the-spot feedback and less stigmatizing relative to an exam.

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