## Friday, December 31, 2010

John

It makes more sense to me to grade as follows:

Create tests that measure a lot of easy stuff, a lot of grade level stuff, and a bunch of stuff above grade level.

Take the raw scores, which can range from 1 (you get a point just so the math works), to several hundred (for some genius type kids) with "grade level" calibrated at 100.  Then you take the natural log of the scores.

So Lenny from "Of Mice and Men" might score 40 on his tests, so his grade will be 3.689... Joe "trying hard" might get a 70 (4.25), On Grade level Sally would get a 100 (4.6) and perhaps, if this is a math test, Srinivasa Ramanujan might have scored a 536 as a kid (a mind boggling 6.28 grade).

If you want more granularity you can choose a different base for the log (2, or 1.5 or something)-- everything crams together if you use log10 though...  4.5-5 would be a reasonable thing to try to achieve on tests (there might be factors that make it difficult, but it is not superhuman).

I haven't thought it out completely, and I imagine things would need to be curved and given to a large number of students to figure out where the middle should lie, but its a system of nearly infinite granularity that is expressed with numbers less than 10...