Thursday, February 12, 2009

Differentiating

Yesterday, for some strange reason, I actually had more time than my usual 2 seconds to prepare for classes, and I was giving a test in precalculus, and I have a handful of very smart kids that are polite and bored in class because it's going too slow for them.

This all adds up to a differentiated test on vectors and polars. The bulk of the class just had the standard test that asked them to:
find the angle between 2 vectors,
convert a polar point to a rectangular point and visa versa,
plot r = 3 sin theta + 2, etc.

Without saying anything to them, I handed the super-smart kids a different version of the test and kept an eye on them throughout the period to see their reaction. They did fine. It took them the whole allotted time (whereas usually they're done in less than 1/2 the time of the other students). They're aware of this fact, so periodically, one of them would look up as another student handed in his test. I wonder what was going through their minds.

Their questions were more of the variety of (and maybe I could have made them harder, but ...) :

give me 2 vectors that are perpendicular to each other and neither lies on the axes or has equal components,

plot 4 points on the polar plane that when connected form a rectangle, none are on the axes. then give me their coordinates, each in 2 ways.

vector u is <6,> find me a vector in the same direction that is 1 unit long (and we did NOT cover this in our short time with vectors). I did give them a hint by making them answer a "similar triangle" type question right before this one.

Anyway, I'm glad I could "unbore" them briefly, and hopefully I can do this again.

3 comments:

  1. That's interesting! I'm curious, though, how you dealt with (or plan to deal with) grading.

    What happens if a super-smart kid makes a 70% on the hard test when they would probably have made a 99% on the regular test? How does that finally go down in your gradebook?

    (Or is it set up so that all the problems on the regular test are also on the hard test, and you can just exclude the "extra" questions for the grade?)

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  2. Anonymous11:12 AM

    In the past it's depended on how they do and how hard I think the test is. They usually earn or I usually give them about the same grade they would have earned on the "easier" version: 95-98%. I guess I grade it more leniently ... or I tell them that they can go home to do corrections, and I'll up their points. It hasn't been an issue (yet?).

    Ms. Cookie

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  3. I had the same question as James, but as long as you stayed within their abilities, I guess you are safe. I think I would have, as a student, accepted a 91 on the harder test rather than a 97 on the easier, as long as it didn't happen like that all the time.

    In my classes I offer two different homework assignments each night - a core for everyone, and a choice of a fistful of routine problems or one or two challenging problems. The kids themselves decide which way to go with each assignment.

    But the test? I want to think more about that. Let us know if any objections develop, ok?

    Jonathan

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