February 8, 2010

Here’s what happens when you didn’t get any all of your grading done this weekend (but the Saints won!!!!!!! Yay New Orleans!), and then instead of catching up before class your department gathers informally and starts to talk about Friday’s wacky trillion point grading scheme, and if there’s a class that lends itself to that, and someone mentions that Physics would really be the ideal course for this, because they have to deal with measures of scale so often.

Well, there’s only one place for this conversation to go:  the other extreme.  What if you had a class that, instead of having 500 points for the semester, or even 1,000,000,000,000, had only 1 point.  Total.  Exams could be worth 2/10 of a point, each homework assignment might only be worth 1/250 of a point, etc.  If someone had an unexcused absence, you’d knock 1/500 off a grade.   It might make it easier to defend points deducted, too, because you could say, “Look, I only took off 5 thousandths of a point for that mistake, so it’s hardly worth arguing about.”

Plus, this could be a learning experience because you could use Official Prefixes:  “This exam is worth 2 decipoints (not to be confused with decapoints)”.   The trouble is, most science students are pretty familiar with deci, centi, and milli so if you really want to make it…memorable….having 1 point for the whole semester is still too much.

The problem is, in looking online, we don’t really seem to have enough prefixes.  The prefixes start off simply enough (deci, centi, and milli being 1/10, 1/100, and 1/1000 respectively) but then decrease by factors of 1000:  the next smallest amount would be a micropoint, which is actually a thousandth of a millipoint, or 1/1,000,000 of an actual point.     Then there are nanopoints (1/1000 of a micropoint) and picopoints (1/1000 of a nanopoint) and while those words are fun to say, we’d need something closer in scale to a micropoint to be able to distinguish amounts, or else it becomes essentially a 1000 point grading scheme with a twist:  “This exam is worth 200 yoctopoints out of a total of 1 zeptopoint for the semester.”

I guess maybe this isn’t so practical after all.  And that’s truly a shame, because who wouldn’t want to write a grading scheme that used yoctopoints?

What has 8 legs and no room for anything else?  A yoctopus!

### Carnivals and Clowns. Clowns who shouldn’t be allowed to grade.

February 5, 2010

The Carnival of Mathematics #62 is up today at The Endeavor, and I can tell you right now that I’m totally jealous of the giant Dorito Sierpinski.    Now I’m looking forward to seeing Nerd High!

Speaking of Carnivals, though wonder of wonder we’re posting about #62 on the day it appears, there was also a Math  Teachers at Play #22 up at math hombre [hey, author John works with a friend of mine!  Yup, the math world is getting smaller by the second.]

So that’s the carnival news.  And clowns, you ask?  Well, I’m thinking that the clowns are the faculty of  my department, for  coming up with a grading scheme that’s so absurd I’m really tempted to use it in one of my classes next year.

Here’s the idea:  Suppose you teach a course and you want to have 3 exams each worth 20% of your grade, homework worth 10%, and a final worth 30%.  One way to do this is to set the midterms at 100 points each, the final at 150 points, and homework scaled to 50 points for a total of 500 points in the class.

So far so good, right?  The problem with this is that if you offer extra credit you have to be careful not to give too much — you wouldn’t award 10 points for being the first to speak in class, right?  (OK, you might, but that would be pretty generous.)  So if you want to be able to offer smaller amounts but not have them sound small, you need to have a larger total number of points.

How large?  How about 1 trillion points!  That ties in nicely to the scale of the national debt, which you can tie together with mathematical literacy and/or an interdisciplinary math/political science activity.   Tests are now worth 200 billion points.  The final is 300 billion.  And now, if a student gives a good answer in class you can off the cuff award them one million points of extra credit!  The student feels good — who doesn’t like to receive a cool million points in extra credit? — and you don’t even have to bother remembering to enter it in your gradebook.  On the other hand, if there are little errors on an exam that you want to point out but don’t necessarily want to penalize (forgetting to write parenthesis, for example, so that 2·(3x+5) is written as 2 · 3x+5 ) you could take off 50 million points.  That’s enough to get anyone’s attention.

I think in some of our classes this would be intimidating, so it’s probably not the best scheme in general.  But in other classes, especially the upper level ones, I think our majors would see this as amusing and, perhaps, a help in internalizing the scale of some of these numbers.

Like I said, tempting.

Put these numbers in order: $\frac{x+5}{N+5}$, $\frac{x}{N-5}$, and $\frac{x+5}{N}$, assuming that $0 \leq x \leq N$.